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thermal physics > Formulas > Flashcards

Formulas Flashcards

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1
Q

differential form of the first law

A

dU = δQ + δW

all infinitesimal changes

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

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2
Q

second law

A

ΔS ≥ 0

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3
Q

reciprocal theorem

A

(∂x/∂y)(z) = [(∂y/∂x)(z)]^-1

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4
Q

reciprocity theorem

A

(∂x/∂y)(z) (∂y/∂z)(x) (∂z/∂x)(y) = -1

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5
Q

work during reversible processes

A

δW = -PdV

W = -(2 ∫ 1) PdV

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6
Q

heat capacity at constant volume

A

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

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7
Q

enthalpy

A

H = U + PV

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8
Q

enthalpy in differential form

A

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

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9
Q

heat capacity at constant pressure

A

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

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10
Q

efficiency of an engine

A

η = 1 - Q(2)/Q(1)

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11
Q

efficiency of a carnot engine

A

η(C) = 1 - T(2)/T(1)

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12
Q

triple point of water

A

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

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13
Q

efficiency of a carnot refrigirator

A

η(C)^(R) = T(2)/T(1)-T(2)

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14
Q

efficiency of a carnot heat pump

A

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

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15
Q

Clausius inequality

A

∮ δQ/T(0) ≤ 0

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16
Q

central equation of thermodynamics

A

dU = TdS - pdV

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17
Q

δQ

A

= TdS

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18
Q

δW

A

= -PdV

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19
Q

entropy change for heating a body

A

ΔS = cmln(Tf/Ti)

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20
Q

entropy change for adding heat to a reservoir at constant T

A

ΔS = Q/T

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21
Q

entropy change for phase changes

A

phase changes are isothermal processes

ΔS = mL/T

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22
Q

absolute entropy of an ideal gas

A

ΔS = n[c(V) ln(T2/T1) + Rln(V2/V1)]

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23
Q

molar specific entropy of an ideal gas

A

Δs = c(V) ln(T2/T1) + R ln(V2/V1)

24
Q

c(P) - C(V) =

A

R

25
Q

isobaric coefficient of thermal cubic expansion

A

β(P) on the formula sheet

26
Q

adiabatic coefficient of thermal cubic expansion

A

β(S) on the formula sheet

27
Q

isothermal bulk compressibility

A

κ(T) on the formula sheet

28
Q

adiabatic bulk compressibility

A

κ(S) on the formula sheet

29
Q

isothermal bulk modulus

A

K(T) on the formula sheet

30
Q

latent heat of expansion change

A

L(V) on the formula sheet

31
Q

latent heat of pressure change

A

L(P) on the formula sheet

32
Q

absolute entropy

A

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

33
Q

enthalpy in a chemical reaction under constant pressure

A

Q = ΔH for ΔP = 0

34
Q

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

A

ΔS + ΔS(0) ≥ 0

ΔG ≤ 0 for ΔP = ΔT = 0

35
Q

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

A

ΔS + ΔS(0) ≥ 0

ΔF ≤ 0

36
Q

molar specific enthalpy of an ideal gas

A

h = u + pV(m)

= u + RT

37
Q

monoatomic

A

3/2 RT

38
Q

diatomic

A

5/2 RT

39
Q

enthalpy for a phase change at constant pressure

A

ΔH = ΔQ + VΔP = mL(p)

40
Q

enthalpy for a incompressible fluid

A

ΔH = CΔT + VΔP

or

Δh = cΔT + ΔP/p

where p is density

41
Q

van der waals gas

A

see formula sheet

a, accounts for attractive forces between molecules

b, accounts for the finite particle volume

42
Q

dieterici equation

A

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

43
Q

joule-kelvin coefficient

A

µ on formula sheet

44
Q

inversion temperature

A

= joule-kelvin coefficient

where µ is the gradient of the curve

45
Q

overall enthalpy is conserved in the liquification and hence

A

h(i) = αh(f,l) + (1-α)h(f,v)

α = [h(i)-h(f,v)]/[h(f,l)-h(f,v)]

46
Q

phase change equilibria

A

g(1) = g(2)

47
Q

Clausius-Clapeyron equation for first-order phase changes

A

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

48
Q

partition function

A

Z = ( Σ i) exp[-ε(i)/k(b)T ]

ε(i) is the microstates of energy

49
Q

boltzmann’s hypothesis

A

S = k(b) ln Ω

Ω is the number of ways a system can be configured

50
Q

three dimensional density of states

A

g(k)dk on formula sheet

51
Q

maxwell-boltzmann distribution

A

f(k)dk on formula sheet

52
Q

rayleigh-jeans law

A

u(BB) (λ) on formula sheet

53
Q

the entropy for a single particle

A

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

54
Q

probability or fraction of particles in a state

A

P(i) = 1/Z exp[-ε(i)/k(B)T]

55
Q

Z = 1/N! [V (mk(B)T/2πℏ^2) ]^N

A

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

56
Q

entropy

A

dS = δQ/T

where entropy is measured in JK^(-1)kg^(-1)

thermal physics (10 decks)

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