Lecture 11_190627 Flashcards
Hydrostatics – Pressure
W(weight) = F = m * g = ρ * V * g = ρ * A * h * g
P = W / A = ρ * A * h * g / A = ρ * h * g
P = ρ * h * g > h = P / (ρ * g) ….. ρ = 1 g/cm3 = 1000 kg/m3
Pressures are additive
P2 = P1 + ρ * h * g
Pascal’s Principle
P1 = P2, so
F1/A1 = F2/A2 at balance
F1 = F2 * ( A1/A2)
Hydrodynamics
Flow = volume (m3) / time (s) = m3 / sec Flow = area (m2) * velocity (m/s) Flow = A1 * v1 = A2 * v2
velocity = Flow / Area v2 = v1 * (A1 / A2)
The Bernoulli Equation
Work = ΔKE = KEfinal – KEinitial
= ½ m * vfinal^2 – ½ m * vinitial^2
Work = F1 * d1 – F2 * d2 = P1A1d1 – P2A2d2
For an incompressible fluid, A1d1 = A2d2 = V
Dividing by V yields:
P1 – P2 = ½ ρ * (v2^2 – v1^2)
Venturi Tube Flowmeter
From the Bernouli equation:
P1 – P2 = ½ ρ * (v2^2 – v1^2) and v2 = v1 * (A1 / A2)
P1 – P2 = ½ ρ * v12 * ((A1/A2)2 – 1)
NOTE: the velocity determined from the pressure depends on ρ of measurement device.
Viscosity
P1 – P2 = 8 * π * η * v * L / A
where (P1 – P2) is the pressure drop in length L of the tube, η is the viscosity of the fluid, v is the velocity of the fluid, L is length, and A is the area
v = (P1 – P2) * A / (8 * π * η * L)
Flow = A * v = (P1 – P2) * A2 / (8 * π * η * L)
Poiseuille’s equation
assume a round tube, A = π * r2, so
Flow = (P1 – P2) * π2 * r4 / (8 * π * η * L)
canceling π gives Poiseuille’s equation:
Flow = (P1 – P2) * π * r4 / (8 * η * L)
Electrical Circuits
Charge
charge on an electron, e:
e = 1.602e-19 C (Coulomb)
1 C = 6.24e+18 e
Coulomb’s Law
F = k * q1 * q2 / r2
k = 8.99e+9 N*m2/C2 (Coulomb’s constant)
F can be positive (repulsive) or negative (attractive) – opposites attract otherwise this looks just like gravitational attraction between all matter
Electric potential energy
Force between 2 charges, one of them is free to move = work will be done (F * d). So there is “potential” energy that can be converted to kinetic energy – much like we saw for gravity.
U = kqq0/r
Electric potential energy has units of Joule
Electric Potential
The electric potential is normalized for charge:
V = U/q0 = K*q/r
Electric potential has units of Joule/Coulomb
1 Volt = 1 Joule / Coulomb
Electric Current
Electric field → An electron placed in the field would move to the + end. Electric current is this movement of electrons.
Current is measured in charge / time
1 Amp = 1 Coulomb / second
Conductors
carry electrical current efficiently – metals are generally good conductors.
Insulators
resist carrying electrical current – most non-metals are insulators.
Ohm’s law
Ohm’s law:
I = V / R
Where I is current (Coulombs / sec), V is voltage, and R is resistance.
Resistance is measured in Ohms (Ω) :
1 Ω = 1 Volt / Amp
Conductance
Conductance (G), measured in mho or (S) siemens is the opposite of resistance:
G or S = 1 / R
mho = S = 1 / Ω = 1 Amp / Volt
Resistors in Series
Rtotal = R1 + R2 + …. Rn
Resistors in Parallel
Gtotal = G1 + G2 + … Gn
1/Rtotal = 1/R1 + 1/R2 + … 1/ Rn
Electrical Power
Power is current times voltage.
P (W) = I (A) * V (V) 1 watt (W) = 1 amp (A) * 1 volt (V) or J/sec = C/sec * J/C = J/sec
by Ohm’s law (I = V / R), the power dissipated by a resistor is:
P = I * V = V2 / R = I2 * R
In the US, most appliances use 120 V AC (alternating current) for instance, a 60 W light draws 0.5 amps at 120 volts
60W = 0.5 A * 120 V
Electrical Energy
Energy (J) = power (J/s) * time (s)
electrical energy is often expressed as kilowatt-hour:
1 kWh = 1000 W * hr
Example, a 60 W light is left on for 24 hours, how many kilowatt-hours does it consume? 60 W * 24 hr = 1440 W * hr = 1.44 kWh
In DC, 1 kWh costs ~$0.09 (9 cents/kWh), how much does it cost to leave a 60W light on for 24 hours?
1.44 kWh * $0.09/kWh = $0.13 (13 cents)
Semiconductors
Semiconductors have properties of both conductors and non-conductors. They are made from Group IV semi-metals, usually silicon, as well as germanium.
(Interestingly, carbon is often used to make resistors.)
Silicon has a valence of 4 and forms a cubic crystal where each silicon atom has 4 neighbors. Pure crystalline silicon is a very poor conductor of electricity. However if a small amount of Group III (e.g. boron) or Group V (e.g. arsenic or phosphorus) is added to the silicon, then it is much more conductive.
p-type semiconductors
A p-type semiconductor is a Group IV semi-metal (e.g. silicon) doped with a Group III material (e.g. boron).
Boron has a valence of 3, and so wherever a B sits in the crystal, some Si is missing an electron. This leaves a positive hole in the structure.
n-type semiconductors
An n-type semiconductor is a Group IV semi-metal (e.g. silicon) doped with a Group V material (e.g. arsenic).
Arsenic has a valence of 5, and so wherever a As sits in the crystal, there is an extra electron. This leaves a negative hole in the structure.
Diodes
A diode is a p-type semiconductor bound to an n-type semiconductor.
A diode will conduct electricity in one direction, but not the other direction.
Transistors
SLIDES 19 & 20!!!
Spectroscopy
Spectroscopy involves shining light through, or reflecting light off, a material. Wavelengths of light that are absorbed by the material will not be transmitted or reflected.
*PULSE OX!
Beer’s Law
Absorbance (A) for a wavelength of light depends on the absorbtivity (a) of the material, the concentration (c) and the thickness (b).
A = a * b * c
Alpha decay
usually very large nuclei
Alpha particles (He ions) are big and don’t go far, so radiation is not a problem. Unless the radioactive material is in your body already – then it’s a big problem.
SEE SLIDE 24 for rxn!!!
Beta decay
β- decay
n → p+ + e- + ν̅ + energy
Neutron goes to proton + kicks out an electron
Β+ decay (positron decay)
p+ → n + e+ + ν
proton goes to neutron + kicks out a positron & neutrino
Used with PET (Positron Emission Tomography) scans C-11, N-13, O-15, F-18 are used
SEE SLIDE 25 for ex!!!
Gamma decay
Gamma decay does not change the configuration of the nucleus.
SEE SLIDE 26 for rxn!!!
Decay rate & half-life
Half-life (t½ ) is the time it takes for half a radioactive material to decay.
Decay constant (λ) is the inverse of the half-life. λ = ln(2) / t½
The decay of radioactive material follows
N(t) = N(0) * e–λ*t
The shorter the half-life the quicker it decays, and the greater the activity.
Most medically relevant isotopes have short half-lives (20 min – 20 days)
*t½ increase = more difficult to manage if given to pt!
Electromagnetic spectrum
E = hc/λ = h * f
**Energy increases with frequency.
h = Planck’s constant (6.626E-34 J/s)
***Energy = 1/wave length
SLIDE 28!!!
