Thermal & Mechanical Properties of Matter

Question 1

Avogadro’s number

Answer 1

No of molecules in one mole

One mole contains 6.022x10^23 molecules

Question 2

V^2

Answer 2

Vx^2+Vy^2+Vz^2

<Vx^2>=<Vy^2>=<Vz^2>
<V^2>= 3<Vx^2>

Question 3

N

Answer 3

Number of molecules

Question 4

n

Answer 4

Number of moles

Question 5

Na

Answer 5

Avogadro’s number

Question 6

Relating n, N and Na

Answer 6

N=n*Na

Question 7

u

Answer 7

Mass of a mole of molecules =Nam

Question 8

Number density

Answer 8

=u/V

Question 9

Gas temperature

Answer 9

Measure of the random motion of molecules

Question 10

Mean free time between collisions

Answer 10

Found by using inverse of Dan/dt

Question 11

Mean free path

Answer 11

Multiply mean free time by velocity

Question 12

Temperature of ideal gas

Answer 12

Measure of thermal kinetic energy of translation of molecules

Question 13

Constant volume

Answer 13

All heat goes into Ek

Question 14

Cv

Answer 14

3/2R

*perfect for monatomic, fails for diatomic/polyatomic

Question 15

Heat flows into monatomic gas, constant volume

Answer 15

All goes to increase translational Ek

Question 16

Diatomic

Answer 16

Additional Ek
Rotational and vibrational

Question 17

Principle of equipartition of energy

Answer 17

Each component of energy has associated energy per molecule 1/2kbT

Question 18

Degrees of freedom

Answer 18

Number of energy components to describe molecule completely

Question 19

Dof monatomic

Answer 19

3 dof so 3/2kbT

Question 20

Dof diatomic

Answer 20

5 dof so 5/2kbT

Question 21

Dof vibrational

Answer 21

7 dof so 7/2kbT

Question 22

For constant volume, dW

Answer 22

=0 so dQv=dKtr

Question 23

For constant pressure dQp=

Answer 23

dKtr+dW

So dQp=dQv+dW

Question 24

Cp=

Answer 24

Cv+R

Question 25

Heat capacities of solids

Answer 25

Each atom: 3 Ek dof and 3 Ep dof so 6 dof
Average energy=6(1/2kbT) = 3kbT

Question 26

f(v) allows what to be calculated

Answer 26

Most probable speed
Average speed
RMS speed

Question 27

Most probable speed

Answer 27

df(v)/dv =0

Question 28

Average speed

Answer 28

No of molecules having speeds in each interval
X by v, add up and divide by N

Integral between 0 and infinity of vf(v) dv

=root 8kbT/pi n

Question 29

Mean square velocity

Answer 29

Integral between 0 and infinity of v^2f(v) dv
=3kbT/m
Root it for RMS

Question 30

Pressure in fluids, if surface pressure increases

Answer 30

Pressure at all points increases by same amount

Question 31

Archimedes principle

Answer 31

When a body is partially or completely immersed in a fluid, the fluid exerts an upward force on the body equal to the weight of the fluid displaced

Question 32

Laminar flow

Answer 32

Steady

Question 33

If cross sectional area reduced (laminar flow)

Answer 33

Becomes much faster
Eg if deep, wide river running slowly, faster when narrow and shallow

Question 34

Bernoulli’s equation

Answer 34

p+pay+1/2pv^2= constant at all points

Question 35

Applications of bernaoulli’s equation

Answer 35

Aeroplane wing

Question 36

Stress

Answer 36

Measure of applied force causing deformation “force per unit area”

Question 37

Strain

Answer 37

Measure of deformity

Question 38

Elastic deformation

Answer 38

Returning to original shape once stress removed

Question 39

Young’s modulus

Answer 39

Stress/strain
F/A / delta l/l
Units Nm^-2

Question 40

Stiffness

Answer 40

Stress required to produce 100% strain

Question 41

Bending

Answer 41

Both extension and compression

Question 42

Bulk modulus

Answer 42

B= delta p / -delta v/ v0 still Nm^-2

Question 43

Compressibility k

Answer 43

1/B

Question 44

Graph of stress against strain for ductile material

Answer 44

y=x up to limit of proportionality
Gradient decreases until elastic limit
Then curves up and back down to fracture point

stress on y axis, strain on x

Question 45

Stress strain graph for brittle material

Answer 45

y=x until limit of proportionality
Then gradient decreases for short length before fracture point