Thermodynamics and Chemistry

CHAPTER 7 PURE SUBSTANCES IN SINGLE PHASES

PROBLEMS 189

(a)Use these formulas to evaluate ,T,.@p=@T /V, and.@U=@V /T(the internal pressure)

for aniline atTD298:15K andpD1:000bar.

(b)Estimate the pressure increase if the temperature of a fixed amount of aniline is increased

by0:10K at constant volume.

7.7 (a)From the total differential ofHwithTandpas independent variables, derive the relation

.@Cp;m=@p/TDT .@^2 Vm=@T^2 /p.

(b)Evaluate.@Cp;m=@p/Tfor liquid aniline at300:0K and 1 bar using data in Prob. 7. 6.

7.8 (a)From the total differential ofVwithTandpas independent variables, derive the relation

.@=@p/TD.@T=@T /p.

(b)Use this relation to estimate the value of for benzene at 25 C and 500 bar, given that

the value of is1:2 10 ^3 K^1 at 25 C and 1 bar. (Use information from Fig.7.2on

page 165 .)

7.9 Certain equations of state supposed to be applicable to nonpolar liquids and gases are of the

formpDTf .Vm/a=Vm^2 , wheref .Vm/is a function of the molar volume only andais a

constant.

(a)Show that the van der Waals equation of state.pCa=Vm^2 /.Vmb/DRT(whereaand

bare constants) is of this form.

(b)Show that any fluid with an equation of state of this form has an internal pressure equal

toa=Vm^2.

7.10 Suppose that the molar heat capacity at constant pressure of a substance has a temperature
dependence given byCp;mDaCbTCcT^2 , wherea,b, andcare constants. Consider the
heating of an amountnof the substance fromT 1 toT 2 at constant pressure. Find expressions
forÅHandÅSfor this process in terms ofa,b,c,n,T 1 , andT 2.

7.11 AtpD 1 atm, the molar heat capacity at constant pressure of aluminum is given by

Cp;mDaCbT

where the constants have the values

aD20:67J K^1 mol^1 bD0:01238J K^2 mol^1

Calculate the quantity of electrical work needed to heat2:000mol of aluminum from300:00K

to400:00K at 1 atm in an adiabatic enclosure.

7.12 The temperature dependence of the standard molar heat capacity of gaseous carbon dioxide in
the temperature range 298 K– 2000 K is given by

Cp;mDaCbTC

c

T^2

where the constants have the values

aD44:2J K^1 mol^1 bD8:8 10 ^3 J K^2 mol^1 cD8:6 105 J K mol^1

Calculate the enthalpy and entropy changes when one mole of CO 2 is heated at 1 bar from

300:00K to800:00K. You can assume that at this pressureCp;mis practically equal toCp;m.

7.13 This problem concerns gaseous carbon dioxide. At 400 K, the relation betweenpandVmat
pressures up to at least 100 bar is given to good accuracy by a virial equation of state truncated