Thermodynamics and Chemistry

CHAPTER 7 PURE SUBSTANCES IN SINGLE PHASES

7.1 VOLUMEPROPERTIES 164

n-hexane(l)

1-propanol(l)

H 2 O(s)

H^2 O(l)

ideal gas H 2 O(g)

 25 0 25 50 75 100 125 150

0:5

0:0

0:5

1:0

1:5

2:0

2:5

3:0

t=ıC

.

̨=10

^3

K

1

Figure 7.1 The cubic expansion coefficient of several substances and an ideal gas as

functions of temperature atpD 1 bar.aNote that because liquid water has a density

maximum at 4 C, is zero at that temperature.

aBased on data in Ref. [ 49 ], p. 104; Ref. [ 70 ]; and Ref. [ 167 ], p. 28.

D

1

Vm



@Vm

@T



p

(7.1.3)

(pure substance,PD 1 )

TD

1

Vm



@Vm

@p



T

(7.1.4)

(pure substance,PD 1 )

whereVmis the molar volume.Pin the conditions of validity is the number of phases. Note
that only intensive properties appear in Eqs.7.1.3and7.1.4; the amount of the substance
is irrelevant. Figures7.1and7.2show the temperature variation of andT for several
substances.
If we chooseTandpas the independent variables of the closed system, the total dif-
ferential ofVis given by

dV D



@V

@T



p

dTC



@V

@p



T

dp (7.1.5)