Formulas

Question 1

differential form of the first law

Answer 1

dU = δQ + δW

all infinitesimal changes

U - internal energy (J)
Q - heat or thermal energy (J)
W - work (J)

Question 2

second law

Answer 2

ΔS ≥ 0

Question 3

reciprocal theorem

Answer 3

(∂x/∂y)(z) = [(∂y/∂x)(z)]^-1

Question 4

reciprocity theorem

Answer 4

(∂x/∂y)(z) (∂y/∂z)(x) (∂z/∂x)(y) = -1

Question 5

work during reversible processes

Answer 5

δW = -PdV

W = -(2 ∫ 1) PdV

Question 6

heat capacity at constant volume

Answer 6

C(V) =lim(ΔT->0) (∂Q/∂T)(V) = (∂U/∂T)(V)

Question 7

enthalpy

Answer 7

H = U + PV

Question 8

enthalpy in differential form

Answer 8

dH = d(U+PV) = dU +PdV + VdP = ∂Q + VdP

Question 9

heat capacity at constant pressure

Answer 9

C(P) =lim(ΔT->0) (∂Q/∂T)(P) = (∂H/∂T)(P)

Question 10

efficiency of an engine

Answer 10

η = 1 - Q(2)/Q(1)

Question 11

efficiency of a carnot engine

Answer 11

η(C) = 1 - T(2)/T(1)

Question 12

triple point of water

Answer 12

T(K) = 273.16K Q/[Q(TP) H(2)O]

Question 13

efficiency of a carnot refrigirator

Answer 13

η(C)^(R) = T(2)/T(1)-T(2)

Question 14

efficiency of a carnot heat pump

Answer 14

η(C)^(HP) = Q(1)/Q(1)-Q(2) = T(1)/T(1)-T(2)

Question 15

Clausius inequality

Answer 15

∮ δQ/T(0) ≤ 0

Question 16

central equation of thermodynamics

Answer 16

dU = TdS - pdV

Question 17

δQ

Answer 17

= TdS

Question 18

δW

Answer 18

= -PdV

Question 19

entropy change for heating a body

Answer 19

ΔS = cmln(Tf/Ti)

Question 20

entropy change for adding heat to a reservoir at constant T

Answer 20

ΔS = Q/T

Question 21

entropy change for phase changes

Answer 21

phase changes are isothermal processes

ΔS = mL/T

Question 22

absolute entropy of an ideal gas

Answer 22

ΔS = n[c(V) ln(T2/T1) + Rln(V2/V1)]

Question 23

molar specific entropy of an ideal gas

Answer 23

Δs = c(V) ln(T2/T1) + R ln(V2/V1)

Question 24

c(P) - C(V) =

Answer 24

R

Question 25

isobaric coefficient of thermal cubic expansion

Answer 25

β(P) on the formula sheet

Question 26

adiabatic coefficient of thermal cubic expansion

Answer 26

β(S) on the formula sheet

Question 27

isothermal bulk compressibility

Answer 27

κ(T) on the formula sheet

Question 28

adiabatic bulk compressibility

Answer 28

κ(S) on the formula sheet

Question 29

isothermal bulk modulus

Answer 29

K(T) on the formula sheet

Question 30

latent heat of expansion change

Answer 30

L(V) on the formula sheet

Question 31

latent heat of pressure change

Answer 31

L(P) on the formula sheet

Question 32

absolute entropy

Answer 32

s = s(0) + c(v) ln[T/T(0)] + R ln[V/v(0)]

Question 33

enthalpy in a chemical reaction under constant pressure

Answer 33

Q = ΔH for ΔP = 0

Question 34

entropy in a chemical reaction under constant pressure and enclosed in an adiabatic wall

Answer 34

ΔS + ΔS(0) ≥ 0 ΔG ≤ 0 for ΔP = ΔT = 0

Question 35

entropy in a chemical reaction under constant volume and enclosed in an adiabatic wall

Answer 35

ΔS + ΔS(0) ≥ 0 ΔF ≤ 0

Question 36

molar specific enthalpy of an ideal gas

Answer 36

h = u + pV(m) = u + RT

Question 37

monoatomic

Answer 37

3/2 RT

Question 38

diatomic

Answer 38

5/2 RT

Question 39

enthalpy for a phase change at constant pressure

Answer 39

ΔH = ΔQ + VΔP = mL(p)

Question 40

enthalpy for a incompressible fluid

Answer 40

ΔH = CΔT + VΔP or Δh = cΔT + ΔP/p where p is density

Question 41

van der waals gas

Answer 41

see formula sheet a, accounts for attractive forces between molecules b, accounts for the finite particle volume

Question 42

dieterici equation

Answer 42

Pexp(an/RTV)(V-nb) = nRT

Question 43

joule-kelvin coefficient

Answer 43

µ on formula sheet

Question 44

inversion temperature

Answer 44

= joule-kelvin coefficient where µ is the gradient of the curve

Question 45

overall enthalpy is conserved in the liquification and hence

Answer 45

h(i) = αh(f,l) + (1-α)h(f,v) α = [h(i)-h(f,v)]/[h(f,l)-h(f,v)]

Question 46

phase change equilibria

Answer 46

g(1) = g(2)

Question 47

Clausius-Clapeyron equation for first-order phase changes

Answer 47

dP/dT = mL/[T(V(2) - V(1))] where P is the saturation vapour pressure L is the specific latent heat of vaporisation in J/kg V(1) and V(2) are the specific volumes of the vapour and liquid phases

Question 48

partition function

Answer 48

Z = ( Σ i) exp[-ε(i)/k(b)T ] ε(i) is the microstates of energy

Question 49

boltzmann's hypothesis

Answer 49

S = k(b) ln Ω Ω is the number of ways a system can be configured

Question 50

three dimensional density of states

Answer 50

g(k)dk on formula sheet

Question 51

maxwell-boltzmann distribution

Answer 51

f(k)dk on formula sheet

Question 52

rayleigh-jeans law

Answer 52

u(BB) (λ) on formula sheet

Question 53

the entropy for a single particle

Answer 53

S = k(b) [lnV + 3/2ln[mk(B)T/2πℏ^2 + 3/2]

Question 54

probability or fraction of particles in a state

Answer 54

P(i) = 1/Z exp[-ε(i)/k(B)T]

Question 55

Z = 1/N! [V (mk(B)T/2πℏ^2) ]^N

Answer 55

the partition function given derives from Z(gas) = 1/N! Z^N(particle) for Z^N(particle) the one-particle partition function N! derives from the indistinguishability of particles

Question 56

entropy

Answer 56

dS = δQ/T where entropy is measured in JK^(-1)kg^(-1)