Section 5: Real Gases & Throttling

Question 1

violating kelvin?

Answer 1

gas kept in contact with thermal reservoir at T
U≡U(T) only so dU=0
first law |W|=|Q|

there is no process whose only effect is to accept heat from a single source and convert it entirely into mechanical work

Question 2

van der waals a and b

Answer 2

a accounts for attractive forces between molecules

b accounts for the finite particle volume

Question 3

the van der waals forces give rise to

Answer 3

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

Question 4

the effects of the corrections to the ideal gas law become pronounced when

Answer 4

the volume is small and pressure is high

Question 5

van der waals equation for large volumes

Answer 5

term describing intramolecular forces will become negligible

ideal gas law recovered

Question 6

other equations of state

Answer 6

dieterici’s equation - a’,b’ similar to van der waals

virial expansions - coefficients

Question 7

entropy difference delta s= s2-s1 suggests

Answer 7

to use a standard point so(T0,P0) or s0(T0,V0) to define an absolute entropy of the form

s=s0+cvln T/T0 + R ln V/V0

for independent variables T and V (similar results can be derived for P and V or P and T)

Question 8

what is s0

Answer 8

discussed in next section - third law discussed in the context of statistical mechanics

Question 9

in general, chemical reactions are irreversible which means we cannot use

Answer 9

δQ=TdS

(but can use the first law of thermodynamics delta U=Q-P0deltaV)

Question 10

since deltaP=0, delta U=Q-P0deltaV can be rearranged to

Answer 10

Q=delta U +P0 delta V
= delta (U+P0V)

Question 11

Q= delta (U+P0V) shows that

Answer 11

change in enthalpy is the heat of the reaction under isobaric conditions

Q=deltaH for delta P=0

Question 12

if the whole system is enclosed in an adiabatic wall such that no heat is transferred, then the second law is

Answer 12

delta S + delta S0 > or =0

Question 13

delta S0

Answer 13

=-Q/T0

change in entropy in the reservoir providing heat for the reaction

Question 14

delta G < or =0 for

Answer 14

delta P= delta T=0

Question 15

for spontaneous processes, the Gibbs free energy will

Answer 15

be decreased

Question 16

the helmholtz function is most useful for

Answer 16

isothermal and isochoric conditions

Question 17

delta (U-T0S)=

Answer 17

delta F < or =0

for spontaneous processes under isochoric and isothermal conditions

Question 18

for monatomic gases

Answer 18

u=3/2RT
cv=3/2R
cp=5/2R
gamma=5/3

h=5/2RT

Question 19

for diatomic gases

Answer 19

u=5/2RT
cv=5/2R
cp=7/2R
gamma = 7/5

so h=7/2RT

Question 20

what is throttling

Answer 20

to regulate or restrict the flow of a fluid

Question 21

a pressure drop exists across

Answer 21

a porous plug pf<pi enacted by an irreversible process

the pressures are maintained by pistons on the end of the pipe

Question 22

throttling heat exchange

Answer 22

no input heat Q or other heat exchange with surroundings and the whole process is adiabatic

Question 23

throttling - work

Answer 23

no external work done but the gas itself does work PV

Question 24

enthalpy in throttling

Answer 24

it is an isenthalpic process with delta H=0

Question 25

although there is no external heat in throttling, there could be

Answer 25

a temp change during a throttling process

Question 26

throttling - joule kelvin coefficient

Answer 26

u=(dT/dP)H with dT=udP

Question 27

using cyclical and inverse rules u=(dT/dP)H=

Answer 27

-(dT/dH)p(dH/dP)T first term is inverse of cP

Question 28

the throttling process is commonly used for

Answer 28

refrigeration and liquefaction

Question 29

for an ideal gas, V/T prop to R/P so

Answer 29

d/dT)p V/T=0 and thus u_ideal=0

Question 30

u_ideal=0 implies that

Answer 30

an ideal gas does not change temperature during throttling

Question 31

as dH=TdS+VdP we can calculate the entropy change during throttling as

Answer 31

- ∫V/T dP between Pi and Pf

Question 32

how to prove throttling is an irreversible process

Answer 32

delta s = - ∫V/T dP for an ideal gas, Rln(Pi/Pf)>0

Question 33

the joule-kelvin coefficient u can be measured via

Answer 33

a porous plug experiment

Question 34

for an expansion process with delta P<0, a result of u>0 implies

Answer 34

delta T<0 a cooling process

Question 35

in most cases, u is

Answer 35

positive leading to cooling on expansion this is because most real gases have weak attractive forces and so it takes energy to separate the particles

Question 36

as throttling is an isenthalpic process, isenthalps on a PT diagram indicate

Answer 36

potential throttling processes with u=(dT/dP)H being the gradient along an isenthalp

Question 37

the inversion curve connects the

Answer 37

maxima of different isenthalps on a PT digram where u=0

Question 38

cooling during throttling is only possible in

Answer 38

a limited region of the PT diagram

Question 39

maximal cooling happens by

Answer 39

starting on the inversion curve and moving into the u>0 (blue) region

Question 40

cooling becomes impossible

Answer 40

above a maximal temp for a given isenthalp

Question 41

gases can be liquified by

Answer 41

throttling gas at high pressure often with a heat exchanger to cool the gas before the throttling

Question 42

steady-state of throttling is

Answer 42

a simple flow problem there is no heat exchange with the surroundings and no work is done kinetic and potential energy terms are negligible

Question 43

in the heat exchanger, incoming gas loses

Answer 43

δq per mole, returning gas which has not been liquified yet, gains δq per mole

Question 44

enthalpy with liquification

Answer 44

overall enthalpy is conserved

Question 45

nitrogen gas can be liquified directly by

Answer 45

throttling

Question 46

condensed liquid evaporates at

Answer 46

constant pressure, extracting heat from the fridge without any work done

Question 47

steps for domestic refrigerators

Answer 47

1. throttling ΔH=0 2. evaporation w=0, ΔP=0 3. compression ΔS=0 4. heat rejection, ΔP=0