General Flashcards

Question

Solving linear equations with 3 unknowns

Answer 1

If we have three equations we can create three matrices; C=A\*b where A=3x3 coefficient matrix, b = 3x1 matrix of xyz (or any three unknowns) and C= 3x1 matrix of constants Then b= A^-1\*C

Answer 2

a dot b= a_x\*b_x+a_y\*b_y+a_z\*b_z=|a|\*|b|\*cos(alpha) Where: a dot b represents the magnitude of the shared a and b vector space

Answer 3

axb is the cross product of a and b and represents the magnitude of the distance between the tips of a nd b in the direction that is normal to the plane created by a and b. axb is given by the determinate of a and b axb= | i j k | |a_xa_ya_z| |b_x b_y b_z|

Answer 4

When one root is given you can divide the third order equation by the root to make it a quadratic which is then solved via the quadratic formula.

Answer 5

To do long division of an equation you always eliminate the higher order term.

Answer 6

The answer to a log is the exponent log_bn=a -\> b^a=n and n=b^{logb^n}

Answer 7

=0 because b⁰=1

Answer 8

=1 because b¹=b

Answer 9

log_bm\*n= log_bm+log_bn

Answer 10

log_b(m/n)=log_bm-log_bn

Answer 11

log_b(1/n)=-log_bn because log_bn^-1=-1\*log_bn

Answer 12

log_bm^(1/n)=(1/n)\*log_bm

Answer 13

radians= degrees \* (pi/180) AKA there are 180^o in pi radians

Answer 14

30^o=pi/6 radians

Answer 15

5pi/4 radians

Answer 16

-pi/6 or 11pi/6

Answer 17

2pi/3 radians

Answer 18

rpm\*(360/rev)\*(pi rad/180)\*(min/60 sec)=rad/sec

Answer 19

17pi/6= 12pi/6+5pi/6 sin(5pi/6)=1/2 cos(5pi/6)= -3^.5/2 tan(5pi/6)= -1/3^.5

Answer 20

sin (5pi/3)= -3^.5/2 cos(5pi/3)= 1/2 tan(5pi/3) = -3^.5

Answer 21

(x, y) = (r, θ) where: r=(x² + y²) and θ=tan^-1(y/x) x=rcosθ and y = rsinθ

Answer 22

for a triangle with angles A,B,C opposite to sides a,b,c c² = a² + b² - 2abcos(C)

Answer 23

a/sin(A)=b/sin(B)=c/sin(C)

Answer 24

Law of cosines can be used to find: Distances between objects starting at one point and travelling in different directions. diagonals of a parallelagram

Answer 25

Ax+By+C=0 m=-A/B and b=-C/B

Answer 26

y=mx+b where: m=(y2-y1)/(x2-x1)

Answer 27

y-y1/x-x1=(y2-y1)/(x2-x1)

Answer 28

m₁=-1/m₂

Answer 29

tan(α)=(m₁-m₂)/(1+m₁\*m₂)

Answer 30

ANY second order equation Ax² + Bxy + Cy² + Dx + Ey + F

Answer 31

ellipses occur when (B²-4AC)\<0 parabolas occur when (B²-4AC)=0 Hyperbolas occur when (B²-4AC)\>0

Answer 32

(x-h)²/a² + (y-k)²/b²= 1 where C=(h,k) and a,b are the radius in the x and y directions

Answer 33

Limits are the value a function approaches at some independent variable value. **If,** the function exists at the limit **then** it is continuous.

Answer 34

Suppose we have two functions, f(x) and F(x) where both go to zero as x approaches A. The limit for f(x)/F(x) is given by f'(x)/F ' (x)

Answer 35

The derivative of a function, y=f(x) is the instantaneous rate of change or dy/dx=lim (Δx-\>0) (Δy)/(Δx) and can be proven by subbing y+Δy for y and x+Δx for x within a function given by y=f(x) and then solving for Δy/Δx and taking the limit as Δx approaches 0

Answer 36

d/dx u\*v= u dv/dx + v du/dx

Answer 37

y=n x^m y' = (m\*n)x^m-1

Answer 38

d/dx uⁿ = nu^n-1 du/dx via the chain rule

Answer 39

d/dx(v^u) = u\*v^u-1 dv/dx + v^u lnv du/dx

Answer 40

d/dx (u/v) = [v(du/dx) - u(dv/dx)] / v²

Answer 41

d/dx (log_cu) = 1/u log_ce \* du/dx

Answer 42

Derivatives act as differentials so they can be inversed or have parts cancel (eg (dy/dt)/(dx/dt)=dy/dx

Answer 43

**if** f(x,y)=c **then** to find dy/dx 1. ) differentiate f(x,y) where d/dx(xy)= y + x(dy/dx) 2. ) isolate dy/dx

Answer 44

These are written with the funky d symbol (∂) or f '_x and are formally defined by if z=f(x,y) then ∂f/∂x = lim Δx-\>0 [f(x+Δx,y) - f(x,y)]/ (Δx) where: if the variable is not in the denominator it is treated like a constant

Answer 45

**if** z=f(x,y) and x=f(t) ; y =f(t) **then** ∂z/∂t = [(∂z/∂x \* ∂x/∂t) + (∂z/∂y \* ∂y/∂t)]

Answer 46

**if** f ' \>0 **then** the slope of f at whatever x is positive so f(x+dx)\>f(x) **if** f '' \>0 **then** the slope of f at x is increasing therefore f ' (x+ dx)\> f ' (x)

Answer 47

1. ) find the first derivative 2. ) Find the values of x so that the first derivative (f ' )=0 . These are the function's **critcal values** 3. ) find the second derivative f '' 4. ) Substitute the critical values from 2 into f '' **if** f '' (x)\>0 **then** at x there is a **local minima** **if** f '' (x) \<0 **then** at x there is a **local maxima**

Answer 48

To evaluate if f(x) is a local maxima or minima when f '' is 0 you must find f ' (x+1) and f ' (x-1) and use those values to evaluate what f(x) is

Answer 49

This is the process of finding the function where the function's derivative is given d( ∫ f(x) dx) = f(x) dx ∫=the function whose differential is

Answer 50

∫ ax^b dx = [ax^b+1/(b+1)] + c

Answer 51

∫_a^b f(x) dx = F(b)-F(a)

Answer 52

When the integrand can be split into two functions; one that represents a u where u=f(x) and another that represents dv where dv=g(x)dx and g(x) is easily integrated. Under these conditions: ∫ udv = uv - ∫ vdu

Answer 53

Generally allow ln to be u (du=dx/x) and x, e^x, or other easily integrated functions be dv

Answer 54

When using dy the slice is taken perpendicular to the y axis. 1. ) with f(x) solve for x so that way x=f(y) 2. ) determine the bounds and integrate ∫ f(y) dy

Answer 55

V= ∫_a^b pi y² dx where y= f(x)

Answer 56

These involve the transformation of derivatives where ∫₀^inf e ^-st F(t) dt = f(s) and can be written f(s) = L {F(t)} = L{F} = F(s)

Answer 57

∫ e^{x n} dn = (1/x) e^{x n} + c

Answer 58

F_r= ΣF d_r = ΣF_i\*d_i / ΣF_i where d is the perpendicular distance to some point O

Answer 59

F_r = Σ F_i where each F is a vector so vector addition is used. This is a system where all the forces intersect at one point.

Answer 60

In a nonconcurrent system the forces do not intersect at a common point and the body is not static. A moment around the center of gravity is given by Σ F_i \* d_i= F_r \* d_r where the direction of F_r is determined by vector addition

Answer 61

A couple is a torque that is produced by two parallel but opposite forces. The resulting moment is given by M= F\*d where d is the total distance between the parallel forces and F is the force of one of the forces The **magnitude** of the couple is not a function of location. AKA the couple has the same magnitude regardless the center of the moment.

Answer 62

The idea of this method is that each joint must be in equilibrium therefore if we isolate each and every joint and solve for the internal forces then each will be in equilibrium. Procedure: 1. ) Draw FBD with everything internal in **tension** 2. ) Solve for the reaction forces (use logic not tension) 3. ) choose a joint where 2 unknowns exist and solve. 4. ) rinse and repeat

Answer 63

This says that for a static body: ΣF_x = ΣF_y = ΣF_z = ΣM₀ = 0 When solving a structure we can assume that the internal reactions cancel each other out and only treat the system by analyzing the external forces with these equations.

Answer 64

This "cuts" the structure and analyzes the internal forces at the cut. Procedure: 1. ) Draw FBD 2. ) solve for Rxns 3. ) "cut" the structure and draw internal forces in **tension**. Do NOT cut more than three members at once. 4. ) ΣMo = 0 where o is the intersection of two of the forces which leaves the third unknown and the external forces which makes solving easy. 5. ) ΣFx = ΣFy =0 solve for the other two unknowns

Answer 65

Tension in a cable or a rope is **constant** throughout the cable/rope. The direction does NOT matter.

Answer 66

1. ) break forces into their three components 2. ) ΣMx = F_z\*d_z + F_y \* d_y It is the same as 2-space but everything that is not in the direction of the axis is considered to be causing a moment about the said axis.

Answer 67

Friction is the contact resistance between bodies in contact with one another and is proportional to the normal force. It acts parallel to the interface across the surface and is summated at the point where the normal force acts. F_max= N \* μ_s F_motion=N \* μ_k where μ_s \>μ_k

Answer 68

R = N + F_f where F_f = μ \* N and the angle of R is given by tan ϕ = F_f /N= μ and ϕ is the angle between F_f and N not to the horizontal

Answer 69

This is the idea that a belt going over a solid has unequal tensions where the greater tension is in the direction of impending motion. T₂_max = T₁ \*e^(μ_s\*β) where β is the angle of contact in **radians**

Answer 70

x̄ = [Σ W\*x]/W and similar with the y bar Where: x represents the distance of a homogenous chunk of the object from any defined x axis and W is the weight of that chunk.

Answer 71

x̄ = ∫ x dA/∫dA

Answer 72

This is fundamentally similar to the centroid of an area but uses a line integral given by x̄ = ∫ x dL/∫dL where L refers to the line coordinates This is most common for arcs where dL=rdθ and x=rcosθ and y=rsinθ

Answer 73

This says that when you rotate a line about an axis 360^o that the resulting surface area is given by A=L 2 pi X where X is equal to the cg or centroid

Answer 74

This states that the volume of an area revolved around an axis is given by V = 2\*pi\*x\*D where x is the centroid or cg of the area

Answer 75

When a material is put into a stress state it experiences deformation by a total amount given by δ . and the strain is given by δ/L = ε Twisting or angular deformation is given by γ = δ/L = tan ϕ where ϕ is the angle from vertical to the deformation

Answer 76

E= σ/ε = (P/A)/(δ/L) and represents the per unit stress over per unit strain within the elastic region of deformation

Answer 77

This the ratio of lateral to longitudinal strain

Answer 78

δ_T = L α (ΔT)

Answer 79

These are structures where the number of unknowns exceeds the number of equations of equilibrium so we need to use the material properties of the material to solve. 1. ) Draw FBD for a selected member 2. ) ID known and unknowns. Write all equations to constrain via equilibrium then for material properties 3. ) Use material properties to solve for an unknown. Plug into Equations of Equlibrium.

Answer 80

When a shaft is placed under some torque T it experiences a shear stress *τ* where dF= *τ* dA and the internal resisting moment is given by *τ* r dA = dM_T

Answer 81

J= ∫ r² dA = the polar moment of inertia across the cross sectional area J_max= pi\*d⁴/32 and *τ* = Tr/J

Answer 82

This is the angle of rotation caused by a torque. It is related to the shear force by the shear modulus G. *τ* / γ =G where γ is the shear strain G= TL/θJ where J is from 0 to R

Answer 83

γ = C θ /L where θ is in radians

Answer 84

This is the summation of individual twists. J does not depend on the material but G is material dependent

Answer 85

"walk the beam" These are usually subject to several loads and moments. 1. ) solve reactions 2. ) "walk the beam" to find moment and stress diagrams

Answer 86

Shear is positive when walking the beam left to right and the shear points upwards. Moments are positive when the forces on either side of the point make the beam bend like a smiley face.

Answer 87

The shear is ALWAYS 0 at x=0 and x=L because otherwise the beam would be mobile and not static

Answer 88

∫_A^B dM = ∫_A^B V dl where V=V(l) and is determined by the shear diagram This means that the change in the bending moment from A to B = the area under the shear curve from A to B

Answer 89

This is the formula for understanding the tension/compression within a bent beam. It says that in a uniform beam that σ_y/y = constant and that the total moment M_t = σ_max/y_max ∫ y² DA = I_y σ_max/y_max

Answer 90

This influence the moment about the x axis and represents the line of the beam where σ=0 It is given by the centroid of the cross section.

Answer 91

I_x = ∫_-l/2^l/2 y² dA where the bounds are measured from the centroid

Answer 92

This says that the moment of inertia about any axis parallel to the neutral axis is equal to I_b = I_NA + A\*D² where D is the distance from the NA to the reference axis

Answer 93

1. ) Divide each cross-section into several chunks with known Icg 2. ) located the neutral axis via finding the centroid (C = ∫ y dA/∫dA) 3. ) Calculate I_NA about each centroid. 4. ) Use the parallel axis theorem to relate each component to the overall cross-sectional I where holes are treated as negative values and the others summate.

Answer 94

L⁴ when solving for anything with moment of inertia try to use inches and centimeters

Answer 95

This is simply put in terms of pounds. It represents the total shear throughout the cross section

Answer 96

This is in F/L² because strain is unitless (L/L)

Answer 97

Fixed connection to walls create opposite moments. These also will have shear at their open end.

Answer 98

This is the study of motion of particles and bodies. Particles are point objects where it is assumed to be concentrated at one point. Bodies are systems of particles that form an object where the relative motion of different parts of the object must be considered.

Answer 99

1. ) A particle acted upon by a balanced force system has no acceleration. AKA an object in motion stays in motion unless acted upon by an external force 2. ) F=ma 3. ) Action and reaction forces are always equal and opposite

Answer 100

Assuming that a is a constant S= V_ot + at²/2 V_f = V_o + at V_f² = V_o² + 2a\*s

Answer 101

When a body is under constant acceleration and the problem is trying to describe the motion of a particle or body in terms of time and position identify the known variables (t_o, t_f, V_o, V_f, a) and the unknown variables. Use the kinematic equations to solve.

Answer 102

**given** s = f(t) then s ' = V(t) and s '' = a(t) Also s = ∫ V(t) = ∫∫ a(t)

Answer 103

ds = (VdV)/f(V)

Answer 104

x = (1/m) ∫∫f(t) dt dt + C1\*t + C2

Answer 105

ω = θ/t where θ is in radians and the change in position is given by rθ

Answer 106

V = r \* ω

Answer 107

This is the change of angular velocity given by d² θ/dt² = α Also α\*dθ = ω\*dω

Answer 108

Yes. Replace V with ω; a with alpha; S with theta

Answer 109

Centripital acceleration is a_n = V ω = rω² = V²/r and is directed towards the center of rotation Centrifugal acceleration is a_t = dV/dt = rα + 2ω dr/dt and is directed in the direction tangent to the path of the object at that moment

Answer 110

the centripetal F; F_n = WV²/gr = W\*a_n/g The centrifugal F; F_t= (W/g)\*dV/dt = (W/g) \* a_t

Answer 111

tanθ = V²/gR + tanθ_f for sliding down the curve and -μ for sliding up where: θ_f = friction angle = tan^-1 μ θ = ideal bank angle where an object travelling at V through a curve with R will neither slide up or down.

Answer 112

ΣF_n= (W/g)\*r_o\* ω² ΣF_t= (W/g)\*r_o \* α ΣM_z= α I_z where: r_o=the distance from the center of rotation to the center of mass of the object in rotation I_z = I_o + m\*r_o² alpha= rotational acceleration r_o ω² = a_n and r_o \* α=a_t

Answer 113

k is a distance and it can regarded as the distance from the axis of inertia to the center of gravity for an object that is rotating around a center that is not outside of the object. k = (I/m)^.5

Answer 114

This is a state where V is constant and an object is rotating. The first step is to draw FBD and find the resultant force on the said object. In this state (W/g)r_o α d -I_zα = 0 where d is the distance from the CG to the point of rotation

Answer 115

The work done on a translating object where the force is in the direction of motion is equal to the change in kinetic energy of that object. This is given by F\*S=(W/2g)(V_f²-V_i²)

Answer 116

Work = kS²/2 where k is the spring constant and S is the spring's displacement.

Answer 117

**if** springs are in parallel **then** k_f= Σ k_i

Answer 118

For springs in a series (1/k_f) = Σ(1/k_i)

Answer 119

ω = +-[2k/m]^.5 and f (1/s) = +-(1/2pi)[2k/m]^.5

Answer 120

T = 1/f = 2pi[m/2k]^.5

Answer 121

These are systems that lack friction or other dissipative forces. Therefore KE + PE = K + U = c and (d/dt)(KE+PE) = 0

Answer 122

1. ) FBD 2. ) ID known forces, unknown forces, and what you are attempting to solve for 3. ) ΣF = ma = external forces

Answer 123

1. ) FBD 2. ) if the system is **conservative** then PE = W\*h + kx²/2 = Wg(L-Lcosθ) + (k/2)(bsinθ)² KE = (1/2)mV²= (1/2) m (ωL)² where ω= dθ/dt 3. ) d/dt(PE+KE)=0 and for small θ sinθ=θ and cos=1 4. ) Simply and (1/2pi)\*(coefficient of θ) = f

Answer 124

Momentum is p=m\*V and because dV/dt=a then F=dp/dt where p is a **vector**

Answer 125

This is a force that acts on an object for a short duration of time such that F(t)dt = impulse force. ∫_t0^t F(t) = (V-V₀)m = ∫_v^v mdV

Answer 126

If force = F = f(t) then (Σ ∫F(t))/m = dV over the period

Answer 127

IF there are no external forces acting on a system then the internal components of a system have the property where m₁ \* V₁ = m₂ \* V₂ It generally works when dt~0 but there is a dV

Answer 128

conservation of momentum should be used when there is an impulse and a change in mass/velocity that occurs over dt~0 Ex: a bullet hitting a pendulum

Answer 129

1. ) apply the conservation of momentum to find v 2. ) assuming it is a conservative system then KE₁ + PE₁ = KE₂ + PE₂

Answer 130

These are when two objects collide and it is assumed that the time over which the collision takes place ~0. Therefore conservation of momentum and impulse physics applies.

Answer 131

This assumes that there is ~0 loss of energy due to deformation and impact is over a time interval =0

Answer 132

this is a constant that is used to adjust for deformation upon impact of otherwise elastic objects such that e = (relative V before)/(relative V after) = separation V/approach V where the relative nature of the velocity is described as the absolute value of their convergence/divergence

Answer 133

When collisions are non parallel but both are spheres you can break the problem down into the x and y componenets where the y component does not change unless an external force acts upon it. Therefore the coefficient of restitution only applies to the x velocities.

Answer 134

1. ) Use conservation of momentum in the x and y directions. V_y does not change. 2. ) e = abs(V₂/V₁) (summate for each object) 3. ) separate e so that one of the two terms is the unknown in the conservation of momentum. 4. ) You should now have two equations and two unknowns. Solve 5. ) Use the resulting vs initial velocities to find changes in momentum, KE, or other

Answer 135

Use pressure prisms and remember that the F_r (fluid) does NOT go through the CG of the plane.

Answer 136

1. ) Choose an A and B point 2. ) move from point A to B where when moving down you add P= γh 3. ) Remeber that equal heights are of equal pressures

Answer 137

When an object is submerged the center of pressure measured from the **fluid surface** is given by X_c = ∫ (X² dA) / ∫(X dA) or through using the parallel axis theorem: X_c-X_o=I_o/AX_o where X_o is the CG measured from the free surface

Answer 138

There are generally two stresses acting on the walls. There is the hoop stress σ₁ and the longitudinal stress, σ₃. Note: at the boundary of the pressure and the wall there is a pressure that acts opposite to the internal pressure. On the outer edge there is no pressure.

Answer 139

If the cylinder's wall is \>(1/10)\*diameter then σ = pr/t where t is the thickness, p is the pressure, and r is the radius

Answer 140

These are cylinders where the wall is thicker than (1/10)\*diameter so that the hoop stress within the material varies with radial position. f= [(r_i² + r_o²)/(r_o²-r_i²)] = inner σ/internal p = σ/p

Answer 141

This is the force of the displaced fluid. It acts through the center of gravity of the displaced fluid in the up direction

Answer 142

1. ) FBD 2. ) find all relevant weights, hydrostatic forces, and buoyant forces and the places that they are acting on the other object. 3. ) summate forces to find reactions 4. ) summate moments to find positions

Answer 143

**if** a fluid is both **inviscid** (frictionless) and **incompressible** then E= (P/γ) + z + V²/2g

Answer 144

The energy equation is the equivalent to bernoullis when there is head loss or energy is added to the system. To use identify to place where the system has less energy to add loss. Head loss and power is in terms of feet of energy. (P₁-P₂)/γ + (z₁-z₂) + (V₁² - V₂²)/2g = H_L - H_p

Answer 145

Frictional head loss is proportional to the length of the pipe. Inversely proportional to the diameter to some power because SA = f(d²). Varies as a function of the roughness of the pipe and flow turbulence. Varies with velocity like solids but is **independent** of pressure. h_f = f (L/d) (V²/2g) where L is the pipe length, f is the friction factor, V is the average velocity ( ∫ V dA/ ∫dA)

Answer 146

This is a result of the vena contracta effect where the change in momentum causes the discharge of flow to have a smaller diameter than the outlet. The smallest diameter in comparison to the orifice diameter is related by the coefficient of contraction.

Answer 147

C_c = smallest area of jet/ area of orifice

Answer 148

Q is the volumetric flowrate given in ft³/s

Answer 149

V = C_v [2gh]^.5 where C_v is the velocity coefficient (usually .98) and h is the distance from the free surface to the discharge. This only works if there is not a turbine or other thing being moved by the flow.

Answer 150

These are losses due to changes in the geometry of the flow (conservation of momentum requires external forces) H_L = Σ k_sys(V²/2g)

Answer 151

The viscosity of a fluid is defined by its internal resistance to flow.

Answer 152

This is the ratio of applied shear to the change in velocity throughout a fluid. μ = *τ* /(dV/dy) where y is the vertical distance from the stationary surface to the point of interest within the fluid.

Answer 153

This is ν = μ/ρ and has units of L²/s. It represents the viscosity of a fluid without relating it to the density of the fluid.

Answer 154

These are common fluids where viscosity is independent of shear.

Answer 155

for a non-Newtonian fluid the viscosity depends on the rate of applied shear such that it becomes more viscous as the shear increases

Answer 156

Pipes: Re = ρVd/μ = Vd/ν Open channels: VL/ν where L is the characteristic length The reynolds number is related to whether a flow is considered turbulent or laminar which dictates whether the flow lines of the fluid move in parallel or at random.

Answer 157

Work/ γ \* Q = (z2-z1)+(P2-P1)/γ + (V₂²-V₁²)/2g +h_l Where: h_l = f(l/D)(V²/2g) where V is the V exiting the pump and throughout the pipe of length l and diameter d hl can also be minor losses with are equal to the summation of the loss coefficients times V²/2g

Answer 158

Q is the volumetric flow rate it is given in cubic feet/sec

Answer 159

1. ) draw diagram and ID end states for P, V, Z, l, and D + unknowns 2. ) write energy equation from 1-\>2 , 1-\> 3... where h_L = f₁(l₁/d₁)(V₁²/2g) + f₂(l₂/d₂)(V₂²/2g) + minor losses. This is added to the second state of the fluid. 3. ) Conservation of matter says that Q_in = Q_out 4. ) Solve

Answer 160

This is a L-shaped tube that measures the **stagnation pressure** of a moving flow. If we consider h to be the difference in heights of a fluid in a pitot tube and a static pressure tube (vertical tube) then V_flow= [2gh]^.5

Answer 161

This is a tube for measuring the velocity of a flow that uses a differential pressure across a contraction. For the formula A₁\>A₂ and P is measured through h of the fluid where h=P/γ

Answer 162

**weirs** are notched openings in vertical gates. H=height from the crest to the level upstream surface= energy head of weir. To solve weirs be aware that the velocity is proportional to the height of the flow and that the vena contracta effect influences the flow.

Answer 163

These are gates where the flow is moving out of the bottom of the tank, under the gate.

Answer 164

1. ) Draw FBD 2. ) label end states where 1 is on the top of the resivoir and 2 is on the top of the outer flow and datum is given at the ground. 3. ) apply Bernoulli's equation or the energy equation

Answer 165

F_x = ρ (ΔV_x ) with an equal for F_y V₂ is found through conservation of mass

Answer 166

Current, I, is a measure of the flow of electric charges in a conductor. It is given in amperes which is related to the number of mols of electrons that are flowing through the cross-sectional area of a wire

Answer 167

Charge, Q, is the total current over a one second time interval Amps= Coloumbs/second Q=coloumbs which are proportional to the mols of electrons

Answer 168

This is given in units of Volts, V, and is related to the difference in potential energy. It causes for current to flow.

Answer 169

Restitance, R, is the discrete resistance to current and arises from the physical characteristics of the material that current is flowing through. It is measured in ohms, Ω

Answer 170

Capacitance is a measure of how well two conductive materials separated by an insulator hold charge. It is measured is Farads, F

Answer 171

Inductance is a measure of property of a coil to create an EMF that opposes the net flow of current through the coil. It is given by the symbol L and is measured in henrys H

Answer 172

Energy is considered to be the amount of work a system is capable of doing on another object. This is measured is Joules where 1 joule = 1 N\*m because Work = F X d

Answer 173

Power is the rate of doing work. It is measured in Watts where 1 W = 1 J/s

Answer 174

This is a type of power where 1 hp = 746 W = 2546 btu/hr

Answer 175

For electrical systems efficiency is given by μ = (Power delivered to load)/(Power Generated) = P_o / P_i it is measured as a percent For mechanical pumps and things μ = (Power produced - loss)/(power produced)

Answer 176

This is efficiency for voltage defined as: (No load V - Full load V)/(Full V) and given as a percentage

Answer 177

This is the energy required to raise the temperature of 1 gram of water 1 degree centigrade measured in joules and dependent of the specific heat of the material in question.

Answer 178

μ = 10^-6

Answer 179

p = 10^-12

Answer 180

This says the mutual force acting between two particles is given by the electrostatic force: F = kq₁q₂/d² where k ~ 9\*10⁹ Nm²/C² q is the charge of each particles in coulombs where oppositely charged particles attract

Answer 181

This is the idea that is we were to have some charged particle and then we place a **positive** charge in its vicinity that it would experience a force/coloumb of positive charge given by E = F/q₁ =N/C

Answer 182

This will depend on the charge of the particle/s but if only one particle is present the direction is radial to the charge. If more than one is present you can break it into two+ systems and add vectors.

Answer 183

These are concepts for different materials that behave differently when current flows through them. Metals are conductors because their large shells and abundant valence electrons allows them to transfer charges easily. Insulators are generally materials that have small orbitals and less discrete ways to transfer charge.

Answer 184

Ionic substances when in solution or as a molten solid are great conductors because the charge can "bounce" between atoms but as solids they are very poor conductors because charges are within the tight inner bonds.

Answer 185

These are materials that act as insulators when the voltage across the material is less than the threshold value which prevents charge from flowing through the system. Above the threshold value this shifts.

Answer 186

These include things like heat, humidity, and other

Answer 187

This is a law relating the amount of dissolved or precipitated material in an electrolytic cell as a function of the charge flowing through the system. If you find: (atomic mass/valency) that is the total mass of a substance that would change if 96500 coulombs passed through the system. then: (mass/valency/96500) = (mass change / # coloumbs) and: Q (coloumbs) = I \* t

Answer 188

This is a convenient way to group coloumbs (charge). it says that one faraday = 96500 coulombs

Answer 189

R= ρ L/A where: ρ = CM\*Ω / ft ; CM = circular mils (1 mill = .001 in) ; A= d² where d is the wire diameter in cm ; L = wire length in feet

Answer 190

R₂ = R₁ (1+ α dT) where α = temperature coefficient

Answer 191

^oR = ^oF + 459.67

Answer 192

electrons do not flow at absolute zero (in theory)

Answer 193

^oK = ^oC + 273.15

Answer 194

^oF = ^oC\*(9/5) + 32 ^oF is always greater than Celsius

Answer 195

R_EQ = Σ R_i Use this to combine resistors in parallel and simplify circuits

Answer 196

1/R_eq = Σ 1/R_i or R_eq = 1/Σ(1/R_i)

Answer 197

This is simply the inverse of resistance given in siemens, G G=1/R

Answer 198

Conductance acts opposite to resistance so G_series = 1/(Σ 1/G_i) and G_parallel = ΣG_i

Answer 199

For parallel plates separated by a diaelectric C (farads) = K\*∈\*A\*(n-1)/d where: K = diaelectric constant ∈ = 8.85 \* 10^-12 C²/N\*m² d = plate seperation A = area of ONE plate n = # of plates

Answer 200

Capacitence in a series: C_eq = 1/ (Σ(1/C_i)) because charge is being distributed linearily among the capacitors like how charge is distrubuted among resistors Capacitence in parallel: C_EQ = Σ C_i This is because the charge can be transfered between lines

Answer 201

In a series: L_eq= ΣL_i because charge flows through each inductor like resistors In parallel: L_eq = q/(Σ(1/L_i))

Answer 202

L (henrys) = N²μ A/l where μ = constant of magnetic permeability l = avg length of form A= cross sectional area of hypothetical cylinder within the coil

Answer 203

Within a closed DC circuit current flows in one direction from the positive to negative battery terminal

Answer 204

V = I\*R where voltage is the potential energy difference across the resistance. I is the charge flowing through the resistance and R is the amount of resistance

Answer 205

Σ I_in= ΣI_out where I is the current flowing in and out of a **node** which is just an intersection of wires. This represents the conservation of charge/matter. AND Σ V_rise = Σ V_drop where V is the voltage found through "walking the circuit" This represents the conservation of energy

Answer 206

This represents the distribution of current throughout parallel resistors and is given by I₁ = R₂\*I/(R₁+R₂) and I₂ = R₁\*I/(R₁+R₂) Where I₁ and I₂ represent the current flowing through the resistor of the same subscript. I = ΣI₁ + I₂ and represents the total current distributed through the parallel resistors

Answer 207

This is for resistors in series where V₁ = R₁ \* V/(R₁ + R₂) and vice versa for V₂ where V is the total voltage drop Voltage across parallel resistance is equal among each of the resistors.

Answer 208

This is alternating current where V=f(t) and V(t) = V_psin ωt where ω = radians/sec and represents the angular frequency of the AC V_p= peak voltage at which V(t) is oscilating between

Answer 209

ω (rad/sec) = f\*2pi = (1/s)\*rad

Answer 210

This is the weighted average voltage given by V_RMS = [(1/T) ∫₀^t V(t)² dt]^.5 = V_p/2^.5 = .707 V_p because the integration is based on a 2pi cycle where T is the period (s) V_p = peak voltage

Answer 211

V_dc = (1/T) \* (∫₀^t V(t) dt) = 2V_p/pi = .637 V_p where t is chosen to equal 1/2 a full cycle (ωt = pi)

Answer 212

Just plug V(t) in for V in all of the other formulas

Answer 213

This represents the effective current moving through a resistor. This represents the current that would effectively flow through a resistor at time=t for a DC current

Answer 214

The current and voltage over time in sin/cos space are related by the **phase angle** which represents which is "ahead" of the other in time. **if** for voltage the phase angle \> 0 **then** it is a **phase lead**

Answer 215

If given V= V_p \*sin(ωt+θ) then V_rms = .707 V_p and can be represented in polar as V_rms (θ) which translates to a rectangular vector given by a+bi = (V_rms \*cosθ)+ (V_rms \*sinθ)\*i

Answer 216

Now that we have a bunch of imaginary numbers plain logic doesn't work so we have Z=impedance = V/I where V=Vrms and I=Irms as complex numbers (remember in DC that R=V/I)

Answer 217

Capacitance causes the voltage to lag the current by 90^o where I = ωCV_p cos(ωt) = V_p/(1/ωC) \* sin(ωt+90)

Answer 218

V_p sin(ωt) = ∫₀^t i(t)/c d(t) where C is measured in farads

Answer 219

V(t) = -L d(i(t))/dt

Answer 220

Seperate d(i(t)) from dt and solve for i(t) by integrating ∫ d(i) = ∫ V(t)/L dt

Answer 221

P_avg = V²/R (watts) where V = V_dc

Answer 222

P_avg = Vr_msI_rms

Answer 223

Power =VI which has real and non-real (imaginary) components which can be written in vector space. Apparent power = S = magnitude Real power = VIcosθ in watts reactive power = VIsinθ in VARS

Answer 224

When there are many meshes you can assign each a loop current (I₁, I₂...) and find the total voltage drop through the loop. When using this method **always** move counter clockwise and when wires are shared use V=R(ΣI)

Answer 225

The resonant frequency, f_o, represents the frequency at which Z=Z_o=Z_max f_o = 1/2pi[LC]^.5 where Z_o = L/CR =Q²R and I_t = V/Z_o

Answer 226

f_o(hz) = 1/2pi[LC]^.5

Answer 227

This is the frequencies for AC where P and I are \>.707 max

Answer 228

These are networks designed to discriminate frequencies of signals. A pass band creates constant amplitudes whereas a reject band has a low amplitude response.

Answer 229

This is a network that is designed to isolate one network from another preserve a match between networks.

Answer 230

This is fundamentally based on the concept that if you have three voltages each 120^o from one another the time weighted average is equal to V_RMS and can be used to power systems like motors without as much vibration.

Answer 231

This is where there is a three phase delta load connected to a delta power source where Z is between nodes. In these systems the V_line = V_AB=V_BC=V_CA **but** the phase currents (I_CA, I_CB, I_AB) are equal to 1/([3]^.5) \* I_L and in a balanced system P = [3]^.5 V_L\*I_L

Answer 232

Line currents are the currents delivered to the loads (A,B,C) and are denoted by either I_L or I_A,B,C... where I_B = I_BC- I_AB and so on where the rule is that the inner subscripts of the numbers cancel each other out

Answer 233

P_T = summation of all lines (V_AB²/Z_AB)

Answer 234

This is a circuit with a Y configuration that is similar to a delta configuration but it is not balanced so it has a N wire (neutral) at the core.

Answer 235

In a wye system line currents are equal to one another and the neutral.

Answer 236

V_coil = V_L/[3]^.5 where V_L is measured from the node to nuetral.

Answer 237

This is the same as a delta system P = [3]^.5 V_L I_L cosθ

Answer 238

This similar to an electric circuit where Resistance = Reluctance Magnetic force = voltage flux flow = current

Answer 239

This is like resistance for a magnetic circuit and is given by R = L/μA where μ is the magnetic permeability constant of the core of the material, L is the mean length, and A is the cross-sectional area

Answer 240

This is a measure of the density of magnetic field lines given by B (teslas) = ϕ/A = μH

Answer 241

H = t/L = t/2pi r

Answer 242

These are electromagnetic devices that consist of one or more coils that is used to "step up" or "step down" voltages for various uses. They are generally rated in KVA or VA where a 100 KVA transformer can deliver 100KW of power if pf = 1

Answer 243

This says that V₁/V₂ = I₂/I₁ = N₁/N₂ = a

Answer 244

If we have a transformer with I₁ and Z_i represents the impedence from the coils with a Z₂ = load related to the other side of the transformer with I₂ then it is said that Zi = a² Z₂ where a = N₁/N₂ This is also referred to how much of the load is reflected into the primary.

Answer 245

A transformer is loaded with the various electrical character for which it is rated and then on the primary an ammeter, wattmeter, and voltmeter are attached. An ammeter is attached to the secondary. copper losses = wattmeter rating = losses from within the primary coil Equivalent impedence = Z_eq = V/I₁ where I₁ and V are measured by the ammeter and voltmeter respectively Equivalent Resistence = R_eq = W/I₁² equivalent reactance = X = [Z² - R²]^.5

Answer 246

These are similar to any coil where there are 1. ) **copper losses** which refers to the heat that is created in the copper 2. ) **core loss** related to eddy currents and hysteresis

Answer 247

This is definition oftentimes applied to electrical equipment to normalize quantities to a common base. This basically says that there are relative values of electrical properties within the equipment Base current (amps) = base KVA/ base KV Base Impedence = base voltage/ base current = (base voltage KV)²\*10/ base KVA

Answer 248

1. ) short circuit test 2. ) open circuit test

Answer 249

When stated to find current this means the line current.

Answer 250

This means finding the volts to nuetral and KVA per phase

Answer 251

This is when there are more than one coils serially connected usually in a way that there is a winding abc with a load parallel to bc.

Answer 252

N₁ = winding abc (the full winding) and N₂ = the winding parallel to the load usually winding bc

Answer 253

a = V₁/V₂ - I₂/I₁ + N₂/N₁ and I through the second winding is given by I_t-I₂

Answer 254

All rotating electrical machines operate on the principle of electromagnetic induction such that whenever there is a change in the magnetic flux there is an induced electrical force.

Answer 255

This says that whenever there is a change in magnetic flux an emf is produced and is given by e= - d(Nϕ)/dt where Nϕ is the magentic flux through a closed loop that has current flowing through it.

Answer 256

This is measured by ϕ and is given by B X A where B is the magnetic field and A is the loop such that if the loop is perpindicular to the main field that ϕ_max is achieved

Answer 257

For a loop with current, I, within a magnetic field, B the force on the loop is given by your thumb, your pointer is in the direction of the magnetic field, and I is the direction of your middle finger such that F = B X I

Answer 258

This is given by T = ϕ_maxI sin ωt where ωt is a term relating the rotation of the coil to radians because F = B X I where B is given by ϕ

Answer 259

This is relatively similar to an AC motor but there is a commuttor attached to the loop so that way the direction of current switches ever pi radians. This has the effect of keeping the net current unidirectional and is in the function of a abs(sin ωt) where ω is proportional to the angular frequency of the coil

Answer 260

With one loop the DC current oscilates between 0 and max every pi radians. With multiple loops you can have lead/lag @ 120^o or other to stabilize the avg voltage across the loop

Answer 261

This generally has many distributed N-S poles throughout a cylinder that maximizes the flux throughout the entire rotating and prevents the coil from being stagnate because it will never reach a stable equilibrium where it can be perturbed with changing phase.

Answer 262

This is very similar to a DC generator but has slip rings not a commutor so that way voltage/current oscilates in both positive and negative space

Answer 263

f = pN/2 where p is the number of poles, N is the rev/sec of the mechanically driven loop (gas powered)

Answer 264

This is the ratio of usable power to total power. Synchronous motors have a leading power factor

Answer 265

This is the idea of using diff eq to solve for various parameters of RLC circuits where the beginning and end states are known and we are solving for the middle period. Generally: t₀ = the time when a switch or something is turned on t₁= steady state when either there is not a fluctuation in the electrical parameters or there is nothing occurring. This is usually at infinity

Answer 266

These are usually RLC circuits which include a resistor, inductor, and capacitor. Only the resistor does not instantly change with t. Inductors and capacitors store charge so that when there is a change in the state of the system they do not instantaneouslt shift to the final state.

Answer 267

These are coils that having current flowing through them. The moving charges induce a magnetic field with the positive end in the direction of the **entering** current

Answer 268

The energy stored within an inductor is given by W = (1/2)LI² where W=joules, L=inductance (Henrys), and I = current (amps)

Answer 269

This is related to time and inductance by V_L = L di/dt where the positive voltage is in the direction of the current entering the coil. **If** there is not a change in the current across an inductor than the induced voltage is 0.

Answer 270

Because V_L = di/dt L if we have i drop to 0 in dt~0 then V_L= infinity. In the situation where the source is removed then the inductor become a source where current is generated as given by lenz's law to oppose the **change** of current within the inductor

Answer 271

These are effectively a series of parallel plates that accumulate charge proportional to the surface area of the interfacing plates.

Answer 272

This is given by W = (1/2) CV² where W = joules, C = capacitence (Farads), V = V_c across the capacitor

Answer 273

This is given by the relationship i_c = C (dV_c/dt) therefore in a DC circuit where dV/dt = 0 the capacitor acts like an open circuit and there will not be any current flowing across the capacitor

Answer 274

This is the description of an RL or RC circuit within a changing state. It is said that there are two sources of energy, **the natural response** refers to the internal response of either a capacitor or a inductor. The **forced response** is the induced response given by an external forcing like a battery or generator. This is also called the steady state response because it is the function that describes the system if closed at t=infiinity.

Answer 275

Because there are generally two forces that are influencing the system; the natural and forced responses we can independently analyze each response then add them together to find the **complete response.**

Answer 276

via Kichoff's voltage law L (di/dt) + Ri = V where i = i(t) i_n= K e^{-R /L} where K is determined from the conditions at t=0 and i_n(t) is the natural response. K = V/R i_ss = V/R = steady state i(t) = (V/R) (e^{-R/L * t} + 1)

Answer 277

These are circuits that have resistance and a capacitor connected to a source. Because electrons are matter they do not instantly accumulate onto the capacitor therefore when connected to a source there is a natural and forced response

Answer 278

by KVL: V_r + V_c = V_s i_t = (V/R) e^-1/RC^{* t} V_c= (1/C) Ve^{-1/RC * t} V_r= - V e^-1/RC ^*t

Answer 279

This can be described as a combination of diverse interacting elements that are integrated to achieve one objective.

Answer 280

This is the idea of looking at all of the interacting elements and evaluating if the system reaches its objective. Systems engineers do not care about design only outcomes.

Answer 281

This is a system where the output has no effect upon the input. This is basically y=f(x) where y, the output, only depends on the input, x

Answer 282

This is where the outcome of an input is fed back into the component to alter future outputs. It is similar to saying y = f(x,t) where the output, y, is not only a function of the input, x but also is influenced by time. In this specific instance with time the prior y values are used to change future y values. This means that y(x₁, t₁) =/ y(x₁, t₂) even though the input is the same

Answer 283

This is a closed system where the system is turned on/off if the error signal is a certain value. This is like a thermostat.

Answer 284

This is a type of on-off controller where the error signal varies the magnitude of the output. For example in a furnace, if the error signal returns that it is very cold then it may overshoot the desired temperature.

Answer 285

These are closed loop systems where the output is measured in comparison to a reference and the power to the system not only varies in magnitude but information to change the output. For example the autopilot on a plane tracks the course of the plane in reference to the ideal and uses that to create an output that varies velocity.

Answer 286

See chart given but a few notable symbols include v = the independent input b = feedback variable r = reference input = f(b, v) and is the signal the component uses e= r-b = actuating signal = the error c = controlled variable; the measured variable; the output G_v = reference input elements G = dynamic unit; both control systems and components H = feedback elements; the components

Answer 287

This is the method of describing the feedback system through implicit differentiation and series expansion. These are best for quantized systems where products or discrete values that can be returned into the function.

Answer 288

This basically uses a laplace transformation of a differential equation to interpret the magnitude, phase, and phase of a system.

Answer 289

Semiconductors in a pure sense include silicon and germanium. Both have 4 valence electrons and are covalent

Answer 290

This includes germanium and silicon and represent a group of materials when, at a certain temperature, the covalent bonds break down and the valence electrons are excited into the conductance band and leave a hole. The combination of these is called an **electron hole pair**

Answer 291

This is the idea of creating impurities in the crystal lattice that either enhances the ability for electrons to shift position or stifles it. These are the extrinsic semiconductors.

Answer 292

These are extrinsic semiconductors that are doped with elements that have 5 valence electrons so that the fifth electron is in the conductance band. Because these semiconductors carry more electrons they are considered to be negative thus the name N-type.

Answer 293

These are semiconductors that are doped with a trivalent atom so that there are electron vacancies that can then be filled. An example of this is placing Al within silica or germanium

Answer 294

This is the idea that at certain temperatures and under certain conditions the materials meant to insulate (silica and germanium) may break down and begin to conduct these are known as minority carriers

Answer 295

This is the junction between the positive and negative material. These are unidirectional interfaces of flow.

Answer 296

This is the idea that at the interface of the positive and negative charges that there is diffusion of electrons from the negative to the positive.

Answer 297

This says that because of diffusion across the P-N boundary that the negative material will gain many positive charges and the P material will fill its vacancies. They become saturated and there is a depletion region where flow is not occuring. The potential across this is significant.

Answer 298

These are simple devices with a P-N junction

Answer 299

This is defined as the positive charge of the battery pushing current into the positive end of the terminal. It requires a significant voltage for current to flow.

Answer 300

This is when the negative end of the battery is connected to the negative side of the semiconductor so that the depletion area becomes larger and only the minority carrier carry material. This current is called the reverse saturation current, I_s.

Answer 301

These are the horizontal rows on the periodic table. The row indicates the number of energy orbitals for the row.

Answer 302

These are vertical rows on the periodic table. Groups indicate the number of valence electrons for all elements in that row.

Answer 303

These are the total number of protons within an atom.

Answer 304

This is the weighted average of the proportions of isotopes of that atom commonly found in nature.

Answer 305

These are molecules with the same number of protons but different numbers of nuetrons which changes their mass.

Answer 306

0 ^oC ; 273 ^oK ; 32 ^oF @ 760 mm Hg; 1 atm; 2116.2 psfa

Answer 307

This is the molecular volume of a gas at STP. For any gas @ STP this is 22.4 liters/mole of gas. In imperial this is 359 ft³/pound of gas. This also says that if we have a 22.4 liter container of 1 mole of gas @ STP it will exert 1 atm of pressure

Answer 308

P₁/T₁ = P₂/T₂ This says that the pressure of a given mass of gas within a fixed volume is linearily related to the temperature of the gaseous volume

Answer 309

This says there are 6.024 \* 10²³ molecules/mol

Answer 310

PV = nRT where P = abs pressure; V = gaseous volume; T=^oK n= moles; R=.082 l \* atm/mole\*K

Answer 311

This says that the rate of diffusion (r) between two gasses is inversely proportional to the square root of the gas density/molecular weight r₁/r₂ = [ρ₂/ρ₁]^.5 = [m₂/m₁]^.5

Answer 312

This says the sum of the partial pressures of each gas is equal to the total pressure of the mixture P_T = Σ P_i

Answer 313

These are reactions that produce one product from 2+ reactents

Answer 314

These have one reactant that decomposes into several products

Answer 315

These are reactions where one more reactive atom replaces a less reactive atom to create a lower PE state Ex: Zn + 2HCl -\> ZnCl₂ + H₂

Answer 316

These are reactions where there is a double displacement of atoms. It commonly represents the neutralization process between acids and bases. AB + CD -\> AD + CB Ex: NaOH + HCl -\> NaCl + HOH which works because NaCl is in a low PE state as an ionic compound and HOH is a strong hydrogen bond

Answer 317

These are reactions that go either direction and do NOT go to completion because there is a constant system perturbation as long as all products and reactents remain in close proximity.

Answer 318

This is when the rate of forward reaction = rate of reverse reaction. Also known as dynamic equilibrium

Answer 319

This says that when a system in dynamic equilibrium is subjected to a stress that the system shifts so the stress is relieved and dynamic equilibrium is restored.

Answer 320

An increase in pressure will favor the smaller volume product/s or the side of the reaction with less separate molecules.

Answer 321

With a shift in the concentration of materials the other side of the reaction is favored

Answer 322

With an increase in temperature the endothermic product is favored, with a decrease in temperature the exothermic reaction is favored.

Answer 323

Catalysts lower the PE barrier to reacting therefore a catalyst equally increases the rate of both the forward and backwards reaction.

Answer 324

For some reaction given by WA+ZB \<=\> XC + YD at a position where R₁ = R₂and [] = molarity of the substance (moles/L) K_eq = [C]^x [D]^y/ [A]^w [B]^Z

Answer 325

K represents the proportion of products and reactants at equilibrium **If** K\>1 **then** the forward reaction (exothermic) is favored **If** K=1 **then** neither product or reactants are favored If K\<1 there are more reactants than products and the reverse reaction is favored

Answer 326

Q = K but when the reaction is **not** at dynamic equilibrium

Answer 327

These are K_eq for the ionization of different acids. The larger the ionization constant the more stronger the acid or base is. HA_a + H₂O \<=\> H₃O⁺ + A_a^-

Answer 328

This shows the solubility of slightly soluble salts where the large the solubility constant, the more soluble the salt AB_s \<=\> A⁺_aq + B^-_aq

Answer 329

The molarity of a solid is 1

Answer 330

This is K_w aka the water ionization constant which is equal to 10^-14 This means that within 10⁷ liters of water there is one mole of OH and H because K_w = 10^-7 \* 10^-7

Answer 331

pH = -log[H⁺] thus a smaller pH is a more acidic solution

Answer 332

This means that at equilibrium, the substance has a molarity of 10^-2 for OH or 10^-2 moles OH/L meaning that it is a very basic liquid

Answer 333

This is the number of units of weight of material is in 100 units of weight of the solution. It is a form of PPM.

Answer 334

M = moles of solute/litre of solution 1M means that in a solution with a total final volume of 1 litre that 1 mole of solute has been added.

Answer 335

N = # of equivalents/litres of solution = #of equivalents \* molarity where: # of equivalents is given by the number of moles of a reactent in the equation and the molarity is the other reactent or product in the equation. It is most common for titrations

Answer 336

This is the moles of solute/litres of solution

Answer 337

This is the spontaneous emission of an alpha particle (⁴He) which decreases the reactent by two protons and 2 nuetrons

Answer 338

This is the spontaneous emission of a beta particle (a nuetron that shifts to an electron) This causes the particle to add a proton increasing its mass number and atomic number by 1

Answer 339

If we have a mass at t=0 of m_o then m after some t is given by m = m_o e^-δt where δ = decay constant

Answer 340

t_1/2 = ln2/δ = .693/δ and represents the amount of time that it takes for half of a radioactive species to decay

Answer 341

This is the amount of energy needed to raise the temperature of 1 gram of water by 1 ^oC

Answer 342

This is the energy required to break the bonds of a solid as it is transitioning to a liquid even though the temperature does not shift.

Answer 343

it takes 79.7 calories to melt 1 gram of ice

Answer 344

This is the amount of energy needed to change the phase of a liquid to a gas. For water this is equal to 539.6 calories/gram. That also means that in the transition from a gas to a liquid that 539.6 calories are released.

Answer 345

This is the amount of energy needed to break the bond of two or more atoms. Using Hess's Law the bond energies of each reactent can be used to find the total heat released in a reaction

Answer 346

These are compounds solely composed of carbon and hydrogen. They are non-polar, covalent, and insoluble with low melting and boiling points. The general formula for hydrocarbons is R-H where R= the hydrocarbon with an added hydrogen, H

Answer 347

These are carbon compounds where carbon atoms are arranged in straight or branched chains

Answer 348

These are carbon compounds where the carbon atoms are arranged into rings

Answer 349

These are a family of hydrocarbons with the same general structure. They also share the same general formula and similar properties.

Answer 350

C_n H_2n+2 Methane is CH₄

Answer 351

These are hydrocarbons that are bonded singly to themselves and the H atoms.

Answer 352

These are hydrocarbons where the carbon atoms do not have all four bonds with other things aka they have double bonds.

Answer 353

Formula: C_nH_2n Ethelyne: C₂H₄ These are unsaturated hydrocarbons and the two carbon atoms have a double bond

Answer 354

General formula: C_nH_2n+2 Acetylene: C₂H₂ These are considered unsaturated because they have a triple bond between the carbons making them non-polar

Answer 355

Formula: C_nH_2n-6 Benzene: C₆H₆ These are also unsaturated because each carbon is bonded to one other thing

Answer 356

These are hydrocarbons where the hydrogen is replaced by a functional group which determines its properties.

Answer 357

General Formula: R-OH methyl alcohol: CH₃-OH

Answer 358

These are broadly a metallic salt of a fatty acid. They are made by boiling hydrocarbons with a strong base like NaOH or KOH to form soap

Answer 359

These are C, H, O compounds where the H:O ration is 2:1

Answer 360

Glucose, sucrose, starch, and cellulose

Answer 361

This refers to the number of electrons an atom may gain or lose to create orbital stability

Answer 362

This is the loss of electrons. It occurs at the anode (+ side) of an electrolytic cell. AN OX is Positive

Answer 363

This is the gain of electrons during electrolysis that occurs at the cathode (negative end) of the battery. RED CAT is Negative

Answer 364

1. ) Write half reactions (with electrons) for each of the elements in the reaction 2. ) multiply by coefficients to that electrons balance

Answer 365

These are the elements that oxidize or reduce the other element. The oxidizing agent is reduced during the reaction

Answer 366

This is a chart with a large number of half reactions of oxidation. A large electromotive potential represents that upon being oxidized the element is in a lower PE state thus it is more favored.

Answer 367

To use the E₀ values you summate the associated value with the half reactions created when balancing the reactions.

Answer 368

This is the process of decomposing or recomosing metals through electroplating

Answer 369

This is the amount of electrical charge to liberate one gram equivalent weight of an element from solution. One faraday is equal to one mole of electrons.

Answer 370

This is 6.24 \* 10¹⁸ electrons or other elementary charges. One faraday is equal to 96490 coulombs

Answer 371

This says that pressure and volume of a gas at a constant temperature are inversely related by a linear relationship given by: P₁ \* V₁= P₂ \* V₂ furthermore if dT/dt = 0 dP/dt = 0 and dV/dt = 0

Answer 372

If the pressure of a gas is held constant then dT/dV = c meaning that any change in temperature has a direct linear change in volume.

Answer 373

For an ideal, frictionless, steady flow system with dt~0 PE₁+ KE₁ + U₁ + FW₁ + Q_a = PE₂ + KE₂ + U₂ + FW₂ KE = Kinetic Energy = .5 gV² PE = Potential Engery = z U = internal heat FW = work done on/by the system = PV Q_a = work added to the system

Answer 374

This is the change in work Q_a = ΔU + W

Answer 375

Yes. Work = W = F x d meaning that if d changes as a vector the work done by/on the system changes.

Answer 376

W = ∫ P dV where P = f(V) for the volume of the piston being closed

Answer 377

This is the amount of energy needed to only increase the temperature of a substance **without phase change** If dQ heat is tranfered to a substance with a mass of m the temperature will change by some dT related to the internal character of the material. In other words C = dQ/mdT

Answer 378

Q = m\*c \* ∫ dT

Answer 379

k = C_P/C_v where C_P = specific heat when dP/dt = 0 C_v=specific heat when dV/dt = 0

Answer 380

Enthalpy = H H = U + PV and ΔH (for gases) = m\* ∫ C_p dT

Answer 381

For a reversible tansfer of heat dS = dQ/T and ΔS = ∫ dQ/T = m C ln (T₂/T₁)

Answer 382

For a mixture of gases at some temperature and pressure B_x + B_y + B_z = 100% where B = V(component)/V_T

Answer 383

G_x + G_y + G_z = 100% G = m(component)/m_T = V(component)\*rho / V_T \* rho_T

Answer 384

This is the amount of heat given up by the products of combustion when cooled to the original temperature that the reactants started.

Answer 385

Assume that air is .77 N₂ and .23 O₂

Answer 386

This assumes that the gaseous atoms have negligible or no volume and has no attractive forces between individual atoms.

Answer 387

These are gases that are in a state where they can reverse into a liquid state. When vapors are heated to temperatures that far exceed boiling point they are "superheated" and may form a perfect gas.

Answer 388

This is a thermodynamic term for describing the boiling point for a substance at some pressure.

Answer 389

This is defined as the % of mass that is in a saturated gas state.

Answer 390

This is a device used to measure the quality of a wet steam mixture. Steam's enthalpy is measured at two points of a tube. x = h₁ - h₂ / h_fgl

Answer 391

This is a chart that has various enthalpy values for wet steams

Answer 392

ϕ = P_w/P_g The relative humidity represents the ratio of the partial pressure of water vapor being the vapor in a superheated state to the partial pressure of saturated vapor at that same temperature.

Answer 393

This the ratio of mass of water to the mass of dry air and given by γ This is related to relative humidity by = γP_a /.622 P_g

Answer 394

A boiler converts chemical energy into heat which provides high temperature to a prime mover like a turbine or steam engine.

Answer 395

This describes the process of heat being absorbed from a low temperature region which is commonly done through evaporation and decompressing vapors to convert the latent heat into phase changes.

Answer 396

This is the most common form of heat transfer and is described by Q = kA(T₁ - T₂) /X where Q = heat transferred (btu/hr) A = area through which the heat flows X = the distance of the heat flow k = constant that is material dependent

Answer 397

This is a function of the exit pressure for the nozzle. If P₂ \< P_c then the flow out of the nozzle will be less than the maximum attainable value. P_c = critical pressure and represents the optimal exit pressure for the nozzle If the flow through the nozzle has exit pressures equal to or less than the stagnation pressure then flow is maximized

Answer 398

This takes the opinion that metals are crystalline structures that are composed of small composites of metals.

Answer 399

Generally metals with smaller grains are stronger

Answer 400

These are alloys that share basic physical characteristics to iron steel

Answer 401

These are non-ferrous metals like magnesium, zinc, nickel, and aluminum which are metals that recently came into the engineering toolbox

Answer 402

These are materials that are often capture in small quantities for use in specialized areas.

Answer 403

These are metals that have commoditized value in the international market.

Answer 404

They are generally face centered cubic, body centered cubic, or hexagonal

Answer 405

These will generally be body-centered cubic at room temperature and include materials like chromium, iron, moly, tantalum, tungsten, and vanadium

Answer 406

These are most commonly found as face centered cubic like aluminum, copper, gold, iridium, lead, nickel, palladium, platinum, rhodium, and silver

Answer 407

Beryllium, cadmium, magnesium, titanium, and zinc

Answer 408

This is the crystalline cleavage of metals along discrete planes. It is proportional to shear. After slip has occurred it is a self-stopping mechanism that results in definite work hardening.

Answer 409

These are generally eliptic curves where the upper limit is the liquidus the middle has liquids and solids and the base is the solidus line.

Answer 410

This says that when in a mixed state of liquid and solid that the %liquid = (S-X)/(S-L) where T = C and X is the specific composition being analyzed

Answer 411

Alloys are characteristically similar to geologic phase diagrams where there is immiscibility, phase changes, eutectics, and perieutectics.

Answer 412

This is the process of heating a metal to its critical point to heal any slip or internal deformation. It increases the malleability of the metal

Answer 413

This is a type of ferrous alloy with ~2% carbonaceous material

Answer 414

These have a layer of chromium oxide rich alloy (~10%) on the outer edge which prevents rust.

Answer 415

These are reversible shifts in material properties like structure, eletrical properties, and magnetic properties which occur in iron-carbon alloys at critical points/temperatures.

Answer 416

This is the result of chemical reactions between metals and the enviroment

Answer 417

Corrosion can be caused by acidity, oxidizing, electrolysis, film formation, agitatition, or temperature

Answer 418

Generally acidity and oxidation creates the corrosive enviroment but the rate of corrosion is determined by electrolysis, film formation, agitation, and temperature

Answer 419

This is the development of an oxidized film that separates the base metal from the corrosive environment. Agitation physically removes this layer and increases the rate at which corrosion occurs.

Answer 420

Generally in chemical corrosion increased temperature increases the extent of the reaction and increases the corrosion

Answer 421

This is when there are two metals with different electronegativities that are connected by a conductive medium. The higher electro-chemical potential element will act as the anode and these atoms will go into solution.

Answer 422

This is a form of material failure due to corrosive and dynamic stresses

Answer 423

This is basically corrosion related to the shear of two interfacing metals which is eliminated with proper lubrication

Answer 424

Radiography of an alloy can reveal where there are variations in density

Answer 425

These tests act very similar to seismeic scans where changes of material properties across boundaries are reflected and velocity is a function of density

Answer 426

This uses changes in the ferromagnetic reluctance because of internal heterogeneity to understand the material's internal structural flaws.

Answer 427

These are generally destructive tests that use a pendulum to collide with metal to understand the energy transfer.

Answer 428

This is the ability for heat to flow through materials expressed in Cal/cm² /cm /sec/ ^oC

Answer 429

These are relative measures of how well heat flows through a material using copper as the base

Answer 430

This is related to the atomic structure and atomic number of materials in a metal. Conductivity = R = rho L/A ohms R = resistance, rho = resistivity NOT density (ohm-cm), L = cm, A = cm²

Answer 431

In general less valence electrons in covalent or metallic states create lower thermal and electrical conductivity. Impurities, strain, and increased temperature increases the disorder of the lattice and increases the resistance to heat or electric conductivity and this defines some alloys

Answer 432

There are two forms of thermal expansion: Linear expansion is the expansion along a central axis and Volumetric expansion is the change in total volume

Answer 433

L_f = L₀ (1+α(ΔT)) V_f = V₀(1+ α_v (ΔT)) α_v ~3\*α

Answer 434

This is independent of weight and refers to the lack of porosity in a material

Answer 435

This is the quality of a material having voids which enable fluids to be transferred through the material

Answer 436

This is the relative ease for a metal to be melted. In general softer metals are more easy to fuse

Answer 437

This is the ease at which a substance is vaporized

Answer 438

They are not meaning that fusibility and volatility are dpendent on the specific material.