Physical Chemistry , 1st ed.

which, using the properties of logarithms, is

wrevnRTln 

V

V

f

i

 (2.7)

for an isothermal, reversible change in the conditions of an ideal gas. Using
Boyle’s law for gas, we can substitute the expression pi/pffor the volumes in the
logarithm and also see that

wrevnRTln 

p

p

f

i (2.8)

for an ideal gas undergoing an isothermal process.

Example 2.3

Gas in a piston chamber kept in a constant-temperature bath at 25.0°C ex-

pands from 25.0 mL to 75.0 mL very, very slowly, as illustrated in Figure 2.4.

If there is 0.00100 mole of ideal gas in the chamber, calculate the work done

by the system.

Solution

Since the system is kept in a constant-temperature bath, the change is an

isothermal one. Also, since the change is very, very slow, we can presume that

the change is reversible. Therefore we can use equation 2.7. We find

wrev(0.00100 mol)8.314 

mo

J

lK

(298.15 K)ln 

7

2

5

5

.

.

0

0

m

m

L

L



wrev2.72 J

That is, 2.72 J is lost by the system.

Heat, symbolized by the letter q, is more difficult to define than work. Heat
is a measure of thermal energy transfer that can be determined by the change
in the temperature of an object. That is, heat is a way of following a changein
energy of a system. Because heat is a change in energy, we use the same units
for heat as we do for energy: joules.
Even historically, heat was a difficult concept. It used to be thought that heat
was a property of a system that could be isolated and bottled as a substance in

2.2 Work and Heat 29

n  0.001 mol

Constant

temperature

bath

Slowly 75.0 mL

25.0°C

25.0 mL

Figure 2.4 A piston chamber in a constant-temperature bath, undergoing a reversible change
in volume. See Example 2.3.