Thermodynamics and Chemistry

CHAPTER 7 PURE SUBSTANCES IN SINGLE PHASES

PROBLEMS 190

at the second virial coefficient,B. In the temperature range 300 K– 800 K the dependence ofB

on temperature is given by

BDa^0 Cb^0 TCc^0 T^2 Cd^0 T^3

where the constants have the values

a^0 D 521 cm^3 mol^1

b^0 D2:08cm^3 K^1 mol^1

c^0 D2:89 10 ^3 cm^3 K^2 mol^1

d^0 D1:397 10 ^6 cm^3 K^3 mol^1

(a)From information in Prob. 7. 12 , calculate the standard molar heat capacity at constant

pressure,Cp;m, atTD400:0K.

(b)Estimate the value ofCp;munder the conditionsTD400:0K andpD100:0bar.

7.14 A chemist, needing to determine the specific heat capacity of a certain liquid but not having an
electrically heated calorimeter at her disposal, used the following simple procedure known as
drop calorimetry. She placed500:0g of the liquid in a thermally insulated container equipped
with a lid and a thermometer. After recording the initial temperature of the liquid,24:80C,
she removed a60:17-g block of aluminum metal from a boiling water bath at100:00C and
quickly immersed it in the liquid in the container. After the contents of the container had
become thermally equilibrated, she recorded a final temperature of27:92C. She calculated
the specific heat capacityCp=mof the liquid from these data, making use of the molar mass of
aluminum (M D26:9815g mol^1 ) and the formula for the molar heat capacity of aluminum
given in Prob. 7. 11.
(a)From these data, find the specific heat capacity of the liquid under the assumption that its
value does not vary with temperature. Hint: Treat the temperature equilibration process
as adiabatic and isobaric (ÅHD 0 ), and equateÅHto the sum of the enthalpy changes
in the two phases.
(b)Show that the value obtained in part (a) is actually an average value ofCp=mover the
temperature range between the initial and final temperatures of the liquid given by
ZT 2

T 1

.Cp=m/dT

T 2 T 1

7.15 Suppose a gas has the virial equation of statepVmDRT .1CBppCCpp^2 /, whereBpand
Cpdepend only onT, and higher powers ofpcan be ignored.
(a)Derive an expression for the fugacity coefficient,, of this gas as a function ofp.
(b)For CO 2 (g) at0:00C, the virial coefficients have the valuesBpD 6:67 10 ^3 bar^1
andCpD3:4 10 ^5 bar^2. Evaluate the fugacityfat0:00C andpD20:0bar.

7.16 Table7.6on the next page lists values of the molar volume of gaseous H 2 O at400:00C and
12 pressures.
(a)Evaluate the fugacity coefficient and fugacity of H 2 O(g) at400:00C and 200 bar.
(b)Show that the second virial coefficientBin the virial equation of state,pVmDRT .1C
B=VmCC=Vm^2 C


/, is given by

BDRTplim! 0



Vm

RT



1

p



where the limit is taken at constantT. Then evaluateBfor H 2 O(g) at400:00C.