Thermodynamics and Chemistry

CHAPTER 7 PURE SUBSTANCES IN SINGLE PHASES

PROBLEMS 188

Problems

An underlined problem number or problem-part letter indicates that the numerical answer appears
in AppendixI.

7.1 Derive the following relations from the definitions of ,T, and:

D

1





@

@T



p

TD

1





@

@p



T

7.2 Use equations in this chapter to derive the following expressions for an ideal gas:

D1=T TD1=p

7.3 For a gas with the simple equation of state

VmD

RT

p

CB

(Eq.2.2.8), whereBis the second virial coefficient (a function ofT), find expressions for ,

T, and.@Um=@V /Tin terms of dB=dTand other state functions.

7.4 Show that when the virial equationpVmDRT .1CBppCCpp^2 C


/(Eq.2.2.3) adequately

represents the equation of state of a real gas, the Joule–Thomson coefficient is given by

JTD

RT^2 ådBp=dTC.dCp=dT /pC


ç

Cp;m

Note that the limiting value at low pressure,RT^2 .dBp=dT /=Cp;m, is not necessarily equal to

zero even though the equation of state approaches that of an ideal gas in this limit.

7.5 The quantity.@T=@V /U is called theJoule coefficient. James Joule attempted to evaluate

this quantity by measuring the temperature change accompanying the expansion of air into a

vacuum—the “Joule experiment.” Write an expression for the total differential ofUwithT

andVas independent variables, and by a procedure similar to that used in Sec.7.5.2show that

the Joule coefficient is equal to

pT=T

CV

7.6 p–V–Tdata for several organic liquids were measured by Gibson and Loeffler.^11 The follow-

ing formulas describe the results for aniline.

Molar volume as a function of temperature atpD 1 bar ( 298 – 358 K):

VmDaCbTCcT^2 CdT^3

where the parameters have the values

aD69:287cm^3 mol^1 cD1:0443 10 ^4 cm^3 K^2 mol^1

bD0:08852cm^3 K^1 mol^1 dD1:940 10 ^7 cm^3 K^3 mol^1

Molar volume as a function of pressure atTD298:15K ( 1 – 1000 bar):

VmDefln.gCp=bar/

where the parameter values are

eD156:812cm^3 mol^1 fD8:5834cm^3 mol^1 gD2006:6

(^11) Ref. [ 65 ].