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Thermal and Statistical Physics > Autumn Term Thermal > Flashcards

Autumn Term Thermal Flashcards

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1
Q

What’s the difference between System and Surroundings

A

System is what we are studying, Surroundings is what we’re not

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2
Q

Define a closed system.

A

No particle exchange between system and surroundings

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3
Q

Define Adiathermal.

A

No heat exchange allowed (thermally isolated)

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4
Q

Define adiabatic

A

Adiathermal and reversible (mostly used synonymously with adiathermal)

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5
Q

Define isothermal.

A

At constant temperature

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6
Q

Define isobaric.

A

At constant pressure.

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7
Q

Define isovolumic.

A

At constant volume.

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8
Q

Define phase (in reference to system).

A

A region within a system which is homogenous within well defined boundaries

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9
Q

Define Equilibrium.

A

Refers to a state without apparent change, allows functions of state to be defined.

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10
Q

Define an Extensive FoS.

A

A FoS that us proportional to system size.

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11
Q

Define an Intensive FoS.

A

A FoS that is independent of size.

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12
Q

Give an example of an extensive FoS.

A

Energy, volume

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13
Q

Give an example of an intensive FoS.

A

Pressure, Temperature

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14
Q

What are Functions of State (FoS) also known as?

A

Thermodynamic functions, thermodynamic variables.

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15
Q

What is the Zero-th law of thermodynamics?

A

If A and C are each in thermal equilibrium with B, then A and C are also in thermal equilibrium with eachother.

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16
Q

What are the 3 types of temperature scales?

A

Empirical, Thermodynamic, Statistical

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17
Q

What is an Empirical temperature scale?

A

One based on a physical material, e.g. volume of a dilute gas/ liquid

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18
Q

How is Celsius converted to Kelvin?

A

T(k) = T(c) + 273.15

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19
Q

What is the ideal gas equation?

A

pV=nRT

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20
Q

How many degrees of freedom does the ideal gas equation have?

A

2, since it contains 3 functions of state

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21
Q

What is the equation for mechanical work (dW)?

A

dW = F dx (force x change in distance)

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22
Q

What is the First Law of Thermodynamics?

A

Energy is conserved if heat is taken into account

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23
Q

What is the typical equation form of the First Law of Thermodynamics?
Define terms.

A

ΔE = ΔW + ΔQ

ΔW = Work done to system
ΔQ = Heat supplied to system

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24
Q

What is the differential form of the First Law?

A

dE = dW + dQ

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25
Q

How is the differential First law altered to include pressure and volume?

A

dE = -pdV + dQ

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26
Q

If x=x(y,z) is finite and single valued, how is the exact differential dx found?

A

dx = (∂x/∂y)z dy + (∂x/∂z)y dz

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27
Q

What rule for second order differentials holds for all FoS?

A

Both orders of partial differential are equal
e.g ∂2x/∂y∂z = ∂2x/∂z∂y

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28
Q

Do Functions of State always have exact differentials?

A

Yes because they are all finite and single valued

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29
Q

What is the reciprocal theorem?

A

(∂x/∂z)y = 1/ (∂z/∂x)y

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30
Q

What is the reciprocity theorem?

A

(∂x/∂y)z(∂y/∂z)x(∂z/∂x)y = -1

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31
Q

What is the ideal gas expansion equation for an Isothermal system?

A

pV = const

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32
Q

What is the ideal gas expansion equation for an Adiabatic system?

A

pVƔ = const

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33
Q

What does CV mean?

A

Heat capacity at constant volume

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34
Q

What does Cp mean?

A

Heat capacity at constant pressure

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35
Q

What equation relates the isovolumic and isobaric heat capacities? (for 1 mole of ideal gas)

A

Ɣ = Cp/CV = 1 + R/CV

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36
Q

For 1 mole of ideal gas, Cp-CV=?

A

R

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37
Q

What is the value of Ɣ for a mono-atomic gas?

A

5/3

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38
Q

What is the value of Ɣ for a di-atomic gas?

A

7/5

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39
Q

Is the typical ideal gas mono-atomic or di-atomic?

A

Mono-atomic

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40
Q

What is CV in terms of a differential?

A

CV = (∂E/∂T)V

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41
Q

For an ideal gas, (∂E/∂v)T = ?

A

0

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42
Q

What does C represent?

A

Heat capacity

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43
Q

What is C in terms of Q?

A

C=dQ/dT

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44
Q

What is R?

A

Molar gas constant, R=8.314 J⋅K−1⋅mol−1

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45
Q

What is the Joule Expansion?

A

Expansion of a gas into a vacuum upon the sudden lifting of a partition.

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46
Q

Is the Joule expansion reversible?
Why?

A

No, Too many gas particles

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47
Q

What is the Kelvin definition of the 2nd law of thermodynamics?

A

No process is possible whose sole result is the complete conversion of heat into work

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48
Q

What is the Clausius definition of the 2nd law of thermodynamics?

A

No process is possible whose sole result is the transfer of heat from a colder to a hotter body.

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49
Q

How do the two 2nd law definitions finish this sentence:

'’No process is possible whose sole result is the …..’’ ?

A

Kelvin: No process is possible whose sole result is the complete conversion of heat into work.

Clausius: No process is possible whose sole result is the transfer of heat from a colder to a hotter body.

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50
Q

What is the name for a cyclic process that (partially) converts heat into work?

A

heat engine

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51
Q

What’s different about Joule Kelvin expansion compares to Joule expansion?

A

It’s constrained, e.g partition lifted is over a very small connector between chambers

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52
Q

Loosely, how does a heat engine work?

A

A working substance (assuming here ideal gas) interacts with two heat reservoirs at temps Th and Tl where Th > Tl.
Heat Qh is obtained from Th and Ql is passed onto Tl.
The work output is then W = Qh - Ql

53
Q

What does the Carnot Cycle look like?

A
54
Q

What are the four stages of the Carnot cycle?

A

A -> B isothermal expansion (top left line)
B -> C adiabatic expansion (top right)
C -> D isothermal compression (lower right)
D -> A adiabatic compression (lower left)

55
Q

In the instance of the Carnot cycle, W represents what?

A

Work done by the system
(NOT on the system)

56
Q

What does Qh represent in relation to the Carnot cycle?

A

Heat absorbed by the system

57
Q

What does Ql represent in relation to the Carnot cycle?

A

Heat released by the system

58
Q

If the Carnot cycle is done in reverse, A -> D -> C -> B -> A, what is it?

A

Heat pump / refrigerator.
Collects heat from the lower temp and delivers it to the higher temp

59
Q

How is efficiency defined for a heat engine?

A

efficiency = η = W/Qh

60
Q

The ratio Qh/Ql is equal to?

A

Th/Tl

61
Q

Efficiency of a heat engine is defined as, η = W/Qh, how can this be written specifically for a Carnot engine in terms of T?

A

ηcarnot= (Th-Tl)/Th

62
Q

What is Carnot’s Theorem?

A

Of all heat engines working between two given temps, none is more efficient than a Carnot engine

63
Q

What is the general efficiency of a refrigerator defined as?

A

ηref=Ql/W
which is heat extracted over work input

64
Q

Refrigerator efficiency is defined as ηref=Ql/W, how can Carnot refrigerator efficiency be written?

A

ηcarnot-ref=Tl/(Th-Tl)

65
Q

How is Carnot’s theorem extended to reversible engines?

A

’ All reversible engines have the same efficiency as that of a Carnot engine’ which is then more efficient than any other heat engine.

66
Q

How does thermodynamic temperature work as a measurement?

A

From a reference temp Θ1, run a reversible heat engine between this and temp to measure. Amount of heat exchanged defines Θ2.

Θ2=Θ1(Q2/Q1)

67
Q

Why is the thermodynamic temperature scale important?

A

Conceptually it’s important to have a definition of temp which isn’t dependent on any material property, just on the
thermodynamic notion of reversibility.

68
Q

What differential defines thermodynamic entropy?

A

dS = đQrev/T

69
Q

What does the symbol đ
mean for a differential?

A

Not an exact differential

70
Q

What is the integral definition of entropy?

A

S(B)-S(A) = integral from A to B of dS
(a is lower bound)

71
Q

S represents what in thermodynamics?

A

entropy

72
Q

S is defined via it’s differential so can vary by……

A

A constant

73
Q

S is a/an _________ differential

A

Exact

74
Q

What is the 3rd statement of the 2nd Law? (Clausius Inequality)

A

Entropy of an isolated system always increases

75
Q

Can entropy decrease?

A

No, never

76
Q

By the first law, dE = dQ -pdV, how can this be altered to include entropy?

A

dE = TdS - p dV since dS = dQ/T

77
Q

By subbing S into the 1st law of thermodynamics, what do we gain?

A

The inexact differential for Q is removed and we can better manipulate the equation

78
Q

If a system undergoes phase change from phase 1 to phase 2 at temperature T, what is the entropy change between phases?

A

(S2-S1) = L/T where L is latent heat supplied to change phase

79
Q

How can Cp and CV be rewritten using S?

A

Cp=T(∂S/∂T)p
CV=T(∂S/∂T)V

80
Q

When written in terms of entropy, how do the constant volume and constant pressure heat capacities vary?

A

Both are the same T(∂S/∂T) differential just with either p or v held constant accordingly

81
Q

What energy, heat and temperature is involved in boiling a kettle?

A

Electric energy W is turned into heat Q that raises temperature T

82
Q

When T isn’t constant, how can dQrev be written?

A

dQrev = Cdt where C is heat capacity

83
Q

Define enthalpy (equation)

A

enthalpy, H = E + pV

84
Q

What letter represents enthalpy?

A

H

85
Q

What letter represents Helmholtz Free Energy?

A

F

86
Q

Define Helmholtz Free Energy (equation)

A

Helmholtz Free Energy, F=E-TS

87
Q

How are Helmholtz Free Energy and Gibbs Free Energy related?

A

F=E-TS
G=E-TS+pV
Therefore G=F+pV

88
Q

What letter represents Gibbs Free Energy?

A

G

89
Q

Define Gibbs Free Energy (equation)

A

Gibbs Free Energy, G=E-TS+pV

90
Q

For the properties; Enthalpy, Helmholtz Free Energy, and Gibbs Free Energy, a differential form can be found - how is this simplified?

A

Each contains E, so by substituting for dE=TdS - pdV some terms will cancel

91
Q

For a fixed temperature and volume, what is dF?

A

0, since dF relies on dT and dV

92
Q

What is the Gibbs-Helmholtz equation for energy?

A

E = F-T(∂F/∂T)V

93
Q

What ‘chart’ can be used to find the Maxwell relations?

A
94
Q

How is the ‘chart’ used to find Maxwell’s relations?

A

From a gap between letters, circle one way where last value is held equal then circle the other. If the line is crossed, that derivative is negative e.g.

95
Q

What is

A

R

96
Q

What does βp represent?

A

isobaric expansivity, the fractional volume increase with temperature at a fixed pressure

97
Q

What does KT represent?

A

Isothermal compressibility, the fractional volume decrease with pressure at fixed T

98
Q

What is isothermal compressibility? What symbol does it have?

A

The fractional volume decrease with pressure at fixed T, KT

99
Q

What is isobaric expansivity? What symbol does it have?

A

Fractional volume increase with temperature at fixed pressure, βp

100
Q

What states does this equation hold for?

A

All, solid, liquid and gas

101
Q

If entropy is constant, what does that mean for T and Q?

A

đQ = TdS = 0

102
Q

What is KS?

A

Adiabatic compressibility, fractional volume decrease with T when S is constant (e.g. no heat flow but reversible)

103
Q

How does this equation lead to a ratio of Cp and CV ?

A
104
Q

What is the equation for KT? What’s the reasoning behind this?

A

Fractional volume decrease, so -1/v
And its the decrease wrt to pressure so partial differential of V to p, and T is fixed!

105
Q

What’s the equation for βp?

A

Isobaric expansivity

106
Q

For an ideal gas, does temperature change during Joule expansion?

A

NO

107
Q

For real gas, does temperature change during Joule Expansion? Which way?

A

Yes, and for most gases it cools down

108
Q

What differential defines the Joule expansion coefficient αJ?

A
109
Q

Why is energy held constant for the Joule Expansion coefficient, αJ?

A

Because energy can’t change in a closed system, which the Joule expansion is.

110
Q

If, for Joule expansion, Heat and work supplied by the process = 0 , enthalpy is ______?

A

Conserved

111
Q

What is the Joule-Kelvin expansion coefficient,αJK?

A

Rate of change of T wrt pressure, holding enthalpy constant

112
Q

What sign does the Joule kelvin expansion coefficient, αJK, typically take?

A

negative at high pressures (heating for p2<p1) and positive for low pressures

113
Q

How to you get from

A

1) reciprocity theorem to turn differential into 2 that contain H
2) divide dH = Tds +Vdp by dp to substitute for (∂h/ ∂p)T
3) Use Cp=( ∂H/ ∂T)p to sub in
4) use maxwell relation to get final differential in terms of t and v

114
Q

The Clausius inequality says dS≥ ?

A
115
Q

How is availability defined?

A

A = E - T0S + p0V

where t0 and p0 are temp and pressure of surroundings that system is in contact with rather than the system itself

116
Q

For a reversible process, dA ≤ ?

A

0

117
Q

In Thermal isolation, with fixed volume dA = ?

A

dE

118
Q

In thermal isolation, with fixed pressure, dA = ?

A

dH

119
Q

For fixed T=T0 and fixed V, dA = ?

A

dF

120
Q

For fixed T=T0 and fixed p=p0, dA = ?

A

dG

121
Q

At equilibrium, dA = ?

A

0

122
Q

Is availability a function of state?

A

no, nor a thermodynamic potential

123
Q

In phase equilibrium, the specific Gibbs free energy is….?

A

The same for all co-existing phases

124
Q

What is specific Gibbs free energy?

A

Gibbs free energy, G , per unit mass, M , = g

125
Q

What is the Clausius Clapeyron relation for transitions between two phases?

A

where L = latent heat, l= specific latent heat

126
Q

What is the 3rd law of thermodynamics?

A

As a system approaches absolute 0, all processes cease and the entropy of the system approaches a minimum value (zero)

127
Q

As T approaches zero, what happens to the constant volume heat capacity CV?

A

It tends to 0

128
Q

Demagnetisation leads to…..

A

Cooling

129
Q

Adiabatic demagnetization is approximately what thermal process?

A

Joule-Kelvin Expansion

Thermal and Statistical Physics (3 decks)

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