Thermal Physics

Question 1

Thermal expansion coefficient

Answer 1

B = 1/V*dV/dT = d(lnV)/dT

Question 2

Fourier’s heat conduction law

Answer 2

Rate of heat flow = q(dot) = -kA*dt/dx

k is thermal conductivity.

Question 3

Virial Equations of State

Answer 3

PV = nRT(1+B/(V/n) + C/(V/n)^2)

Question 4

Approximation of e^-x for small x

Answer 4

e^-x = 1-x for small x

Question 5

Van der Waals equation

Answer 5

P=nRT/(V-nb)-a(n/v)^2

Question 6

Equipartition theorem

Answer 6

At temperature T, the average energy of any quadratic degree of freedom is kT/2.

Question 7

Total thermal energy

Answer 7

U = NfkT/2

Question 8

First law

Answer 8

deltaU = q+w

Question 9

Adiabatic process

Answer 9

No heat transfer between system and surroundings. q=0.

Question 10

Isothermal

Answer 10

deltaU = 0

Question 11

Max work

Answer 11

Available when change takes place reversibly

Question 12

Isothermal + reversible

Answer 12

deltaU = 0, q = -w = nRT*ln(Vf/Vi)

Question 13

heat capacities

Answer 13

c(v) = q(v)/deltaT = deltaU/deltaT, c(p)=q(p)/deltaT

Question 14

Work in terms of heat capacity

Answer 14

w=nc(v)deltaT
work + means work done on the gas, compression, T of gas increases
work - means work done by the gas, expansion, T of gas decreases

Question 15

Latent Heat

Answer 15

q = mL

Question 16

Enthalpy

Answer 16

H = U+PV

Question 17

Virial Theorem

Answer 17

In any system where particles are held together by mutual gravitational attraction: U(potential) = -2U(kinetic)

Question 18

Adiabatic expansion/compression of ideal gas

Answer 18

PV^gamma = constant
gamma = (f+2)/f = c(p)/c(v)
c(p) = c(v)+R

Question 19

Mechanical equilibrium

Answer 19

Net force = 0

Question 20

Temperature

Answer 20

A measure of how easily the multiplicity of the system changes with energy

Question 21

Stirling’s approximation

Answer 21

ln(N!) = NlnN - N

Question 22

Approximation of ln(1+x) for small x

Answer 22

ln(1+x) = x for small x

Question 23

Second law

Answer 23

Any large system in equilibrium will be found in the macrostate with greatest entropy

Question 24

Boltzmann’s equation

Answer 24

S = kln(multiplicity) in J/K

Question 25

Spontaneous

Answer 25

deltaS > 0

Question 26

High temp, large N, entropy estimate

Answer 26

S = Nk(ln(q/N)+1)

Question 27

In Einstein solid or ideal gas, entropy estimate

Answer 27

S = Nk

Question 28

Sackur-Tetrode equation

Answer 28

S = Nk(ln(V/N*((4*pi*m*U)/(3*N*h^2))^(3/2))+5/2)

Question 29

Entropy of mixing

Answer 29

``` deltaS(A) = N(A)kln(((V(A)+V(B))/V(A)) deltaS(B) = N(B)kln(((V(A)+V(B))/V(B)) deltaS(mix) = deltaS(A)+deltaS(B) = 2Nkln2 ```

Question 30

Isentropic

Answer 30

``` deltaS = 0 Isentropic = adiabatic + mechanically reversible ```

Question 31

Thermodynamic identity

Answer 31

dU = TdS-PdV+(mu)dN

Question 32

Thermal interaction

Answer 32

1/T = PartialS/PartialU at constant V,N

Question 33

Mechanical interaction

Answer 33

P/T = PartialS/PartialV at constant U,N

Question 34

Diffusive interaction

Answer 34

(mu)/T = - PartialS/PartialN at constant U,V

Question 35

Third law

Answer 35

Systems cannot absorb energy at T=0. Systems cannot exceed their temperature at maximum entropy. Occurs in systems with finite numbers of energy levels, or a maximum energy U.

Question 36

Curie's Law

Answer 36

``` M = (mu)(N(up)-N(down)) M = N(mu)tanh((mu*B)/kT) M = -U/B tanh(x) = (e^x-e^(-x))/(e^x+e^(-x)) ```

Question 37

Change in entropy of surroundings

Answer 37

``` deltaS(surroundings) = -q/T(surroundings) q = U/hfN ? hf is energy difference between ground and excited state ```