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/TD T .@^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 /.Vm b/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 cD 8:6 105 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