Concise Physical Chemistry

c03 JWBS043-Rogers September 13, 2010 11:24 Printer Name: Yet to Come

REVERSIBLE PROCESSES AND PATH INDEPENDENCE 43

p

V

V 1 V 2

FIGURE 3.4 The energy change for reversible expansion of an ideal gas. The area under the

p–Vcurve is thep–Vwork done by an expansion fromV 1 toV 2.

where the unit of energy is the joule (J). One does not know how much work it will

take to bring this process about because the amount of work lost to friction is not

known. Work is not a thermodynamic function.

The ideal expansion of a gas driving a piston in the absence of frictional or other

heat loss produces work equal to the energy change. The energy change can be found

by integrating over the work which now follows a defined path and which in this

respect behaves like a state function (Fig. 3.4). In the absence of heat loss, work is

defined as the integral of forceFover displacementdsfrom positions 1 tos 2 :

w=

∫s 2

s 1

Fds

For an idealized piston, this is the same as the integral ofpover the changedV.The

amount of work done by expansion against a piston is represented by the area under

ap–Vcurve in Fig. 3.4. It can be written analytically as

w=

∫V 2

V 1

pdV

The amount of work done by the system on the surroundings during an expansion at

constant pressure is

w=p

∫V 2

V 1

dV=pV

At constant temperature (isothermal conditions) we have

w=

∫V 2

V 1

nRT

V

dV=nRT

∫V 2

V 1

dV

V

=nRTln

V 2

V 1