Explanations and Definitions

Question 1

thermal equilibrium

Answer 1

If there is no net flow of thermal energy between two physical systems

Question 2

zeroth law

Answer 2

allows us to determine if two systems are in thermal equilibrium

Question 3

exact differential

Answer 3

path independent

i.e. dU

Question 4

inexact differential

Answer 4

path-dependent and relate to irreversible processes

i.e. δQ and δW

Question 5

isothermal process

Answer 5

Temperature does not change

Question 6

isobaric process

Answer 6

Pressure does not change

Question 7

Isochoric process

Answer 7

Volume does not change

Question 8

the link between the first law and Bernoulli’s equation

Answer 8

they are identical if there is no work, heat and no change in internal energy

Question 9

the significance of the 2nd law in modern physics

Answer 9

the second law breaks the symmetry in Newtonian mechanics, quantum mechanics, electrodynamics and relativity.

it gives the concept of an ‘arrow of time’

Question 10

carnot cycle PV diagram

Answer 10

see notes for PV diagram

1 -> 2 isothermal heat absorption Q(in)
2 -> 3 adiabatic expansion
3 -> 4 isothermal heat loss Q(out)
4 -> 1 adiabatic compression

Question 11

kelvin Planck form of the 2nd law

Answer 11

it is impossible to construct a device that operating in a cycle will produce no other effect other than the conversion of heat into work

Question 12

Clausis form of the 2nd law

Answer 12

it is impossible to construct a device that operating in a cycle produces no other effect than the transfer of heat from a colder body to a hotter body

Question 13

kelvin planck and clausis statement of the second law

Answer 13

are equivalent

Question 14

carnot’s theorem

Answer 14

no engine operating between two thermal reservoirs can be more efficient than a reversible engine operating between reserviors

Question 15

consequences of carnot’s theorem

Answer 15

The efficiency is independent of the working substance and internal workings of the engine and solely dependent on the reservoir temperatures.

Providing a means to define an absolute temperature scale

Question 16

the corollary to carnot’s theorem

Answer 16

all Carnot engines operating between the same two temperature reservoirs have the same efficiency

Question 17

the thermodynamic temperature scale

Answer 17

is the triple point of water

Question 18

the operation of a heat pump

Answer 18

3 loops connected by 2 heat exchangers to take heat from the ground to heat up a house.

Question 19

the significance of the clausius inequality

Answer 19

the purpose of the Clausius inequality is to introduce entropy

for a closed system, we always need to consider the entropy of the surroundings.

Question 20

discuss the significance of entropy

Answer 20

the entropy increases for an irreversible process

the total entropy of the universe cannot decrease

local decreases in S are allowed

it is necessary to consider the surroundings for systems that are not thermally isolated

Question 21

carnot cycle on a TS diagram

Answer 21

see notes

it is a square

adiabatic lines are vertical lines

and isothermals are horizontal lines

Question 22

functions of state

Answer 22

U,S and V

Question 23

conjugate variables

Answer 23

T and S

S is extensive and T is intensive

Question 24

four common thermodynamic potentials

Answer 24

U,H,F and G

Question 25

the use of the four common thermodynamic potentials

Answer 25

express a given derivative into a measurable quantity

Question 26

the need for a third law of thermodynamics in terms of absolute values of entropy

Answer 26

what is the standard point s(0) and whether is it the same for an ideal case can be provided by the third law

Question 27

van der waals forces give rise to

Answer 27

a potential which is repulsive at short distances, but attractive at longer distances

become pronounced at small volumes and negligible at large volumes.

Question 28

define a throttling process

Answer 28

a process to regulate or restrict the flow of a fluid by using a porous plug.

Question 29

inversion curve

Answer 29

connects the maxima of different isenthalps on a PT diagram where µ = 0

µ < 0 heating upon expansion

µ > 0 cooling upon expansion

Question 30

the physical process of producing liquid nitrogen and other liquid gases

Answer 30

gases can be directly liquified by throttling.

Question 31

the operation of a domestic refrigerator

Answer 31

four stages

1. throttling
2. evaporation
3. compression
4. condensation

Question 32

sketch of a typical refrigerator cycle on a TS plot

Answer 32

see notes

Question 33

sketch of a Rankine cycle on a TS plot

Answer 33

see notes

Question 34

the operation of a Rankine cycle

Answer 34

state a: pump
state b: boiler
state e: turbine
state f: condenser

Question 35

steam engines utilise

Answer 35

the Rankine cycle

Question 36

gas turbines utilise

Answer 36

the Brayton cycle

Question 37

Brayton cycle TS plot

Answer 37

see notes

Question 38

Brayton cycle PV plot

Answer 38

see notes

Question 39

brayton cycle can be maximised for

Answer 39

the output of work W - W(c)

Question 40

rocket engine sketch

Answer 40

see notes

Question 41

define a first-order phase change

Answer 41

will have a discontinuous first derivative of G.

Measurement of the specific heat capacity will show a discontinuity at the phase transition temperature

Question 42

higher order phase changes

Answer 42

third-order phase transitions occur in ferromagnetics or superfluids.

Question 43

S(T)

Answer 43

∂S/∂T)(P) = c(P)/T > 0 and c(P) is always positive so the gradient on either side of the transition is positive.

Nothing can be said of the curvature

Question 44

G(T)

Answer 44

∂G/∂T)P = -S < 0 so the gradient is negative on either side of the transition

Question 45

∂^2G/∂T^2)P =

Answer 45

-∂S/∂T)P = -c(P)/T < 0 so the plots are curved downwards on either side

Question 46

sketch of S(T) and G(T)

Answer 46

see notes

Question 47

significance of F = -k(B)TlnZ

Answer 47

the equation links macroscopic classical thermodynamic variables to statistical mechanics quantities

Question 48

PV diagram guide

Answer 48

See diagram

Question 49

TS diagram guide

Answer 49

See diagram

Question 50

why is Gibbs free energy used to describe phase changes

Answer 50

at a phase transition, two phases co-exist at the transition temperature and the Gibbs free energy for each phase is the same.

G is preferred over F because it is appropriate to the more commonly-used isobaric conditions

Question 51

why is C(P) greater than C(V) for fluids

Answer 51

most materials expand upon heating, so C(P) includes work done by the material against the surrounding atmosphere.

Question 52

why can we usually only consider either C(P) or C(V) for solids

Answer 52

for solids, the expansion is relatively small and the difference between them can often be ignored

Question 53

Einstein model of specific heat capacity

Answer 53

1. assumes a simple cubic lattice of N atoms with interatomic potentials modelled by springs, so that atoms can be modelled as simple harmonic in 3 dimensions
2. assumed that each oscillator has a single frequency of oscillaton
3. assumed that the solid can be treated as 3N independent oscillators

Question 54

extensive thermodynamic variable

Answer 54

Variables that scale proportionally system size such as total mass or volume

Question 55

throttling process

Answer 55

the rapid expansion of a fluid flowing through a restriction from a high-pressure region to a low pressure region, conducted under adiabatic conditions

Question 56

an experiment that uses the Joule-Kelvin coefficient to determine whether a gas is well-described by the ideal gas law

Answer 56

porous plug experiment

Question 57

porous plug experiment

Answer 57

throttling a high-pressure gas through a restriction in a pipe. The temperature drop across the restriction is measured. As the joule-kelvin coefficient is zero, there should be no temperature drop.

Question 58

adiabatic

Answer 58

ΔQ = 0, exchanges no heat with its surroundings

Question 59

blackbody

Answer 59

an object that perfectly absorbs all radiation that falls on it regardless of wavelength

Re radiates at energies characterised by a black body distribution

Question 60

modern-day use of the Brayton cycle

Answer 60

used in jet turbines, for propulsion

Question 61

why is the Debye model an improvement on the Einsten model

Answer 61

1. allows a spectrum of excitation frequencies rather than the single frequency assumed by Einstein
2. uses the concept of phonons, or coupled oscillations rather than the independent oscillations of the Einstein model.
3. correctly predicts the low temperature T^3 dependence of heat capacity that is seen experimentally for simple solids.

Question 62

Equipartition of energy

Answer 62

the thermal energy of an atomic or molecular system will be uniformly distributed between each ‘degree of freedom’ each of which accounts for energy 1/2 k(B)T

Question 63

how does the equipartition of energy lead to differences in thermodynamic calculations for monatomic and diatomic gases

Answer 63

in monatomic systems, thermal energy is distributed between three degrees of freedom.

for diatomic molecules, there are also vibrational and rotational degrees of freedom to consider.

Question 64

heat exchanger

Answer 64

enables the transfer from a hot material to cold material without the two materials physically mixing.

Question 65

Heat pumps

Answer 65

operate similarly to refrigerators, taking some work to transfer heat from a cold body to a warmer body.

Question 66

how to determine temperature from infrared intensity

Answer 66

Stefan-Boltzmann law on the formula sheet alongside the spectral density given by the Planck distribution, produces a unique curve that is only a function of T.

Question 67

isentropic

Answer 67

where ΔS = 0

adiabatic process, where there is no transfer of heat ΔQ = 0.

It is also a reversible adiabatic process.

Question 68

the kelvin temperature scale

Answer 68

is defined with respect to 273.16K

which is the triple point of pure water

which specifies a unique pressure and temperature which can be easily replicated in a lab

the scaling ensures that 1K is equivalent to 1 degree C.

Question 69

The Joule-Kelvin process

Answer 69

a throttling process that is isenthalpic ΔH = 0. The gas is forced through a restriction or throttling valve in a lower-pressure region.

Question 70

heat engine diagram

Answer 70

see notes

warm body

engine -> w

cold body

Question 71

refrigerator diagram

Answer 71

see notes

warm body at T(1)

engine <- W

cold body at T(2)

Question 72

How do we determine the one-particle partition function

Answer 72

by considering the Schrodinger equation for a particle in a box, which produces quantised energy levels that derive from standing wave solutions with nodes at the box walls.

Question 73

Gibbs paradox is solved

Answer 73

if the particles are assumed to be
indistinguishable

Question 74

The Gibbs Paradox

Answer 74

S is expected to be an extensive property but is not extensive in the above result.