Physical Chemistry Third Edition

2.1 Work and the State of a System 47

Exercise 2.2

a.Calculatewif 0.500 mol of nitrogen expands irreversibly from a volume of 5.00 L to a volume

of 10.00 L with a constant external pressure equal to 1.000 atm.

b.Calculatewif 0.500 mol of nitrogen expands reversibly from a volume of 5.00 L to a volume

of 10.00 L at a constant temperature of 25.00◦C.

Compression Processes

IfPis smaller thanPext, a fluid system will be compressed to a smaller volume. If the

process is irreversible, the system’s pressure will be nonuniform. It will be compressed

to a greater extent near the piston than in the rest of the system, so thatP(transmitted)

will be greater than the equilibrium pressure of the gas, but smaller thanPext. We are

not prepared to discuss a nonuniform pressure and will not attempt calculations ofw

for an irreversible compression. We can obtain some limits for the work done.

EXAMPLE 2.6

Assume that 1.00 mol of an ideal gas is initially confined in a cylinder with a volume of 22.4 L

at a temperature of 273.15 K. The external pressure is increased to 1. 50 × 105 Pa and the gas

is compressed irreversibly and isothermally untilP 1. 50 × 105 Pa. Find the largest and

smallest values thatwmight have.

Solution

The final volume is

V(final)

(1.000 mol)(8.3145 J K−^1 mol−^1 )(273.15 K)

(1. 50 × 105 Pa)

 0 .0151 m^3

SinceP(transmitted) cannot exceedPext,

w(maximum)−Pext∆V−(1. 50 × 105 Pa)(0.0151 m^3 − 0 .0224 m^3 )2270 J

SinceP(transmitted) will exceed the equilibrium pressure that the gas would have at any

volume,

w(minimum)−(1.000 mol)(8.3145 J K−^1 mol−^1 )(273.15 K) ln

(

0 .0151 m^3

0 .0224 m^3

)

890 J

The actual value must lie between these values, but would depend on the rate of the process

and other things that we cannot evaluate using thermodynamics.

In Chapter 10 we will discuss the rates of certain irreversible processes from a

nonthermodynamic point of view. Thermodynamics has also been extended to include

such irreversible processes by the use of additional assumptions,^1 but we will not

discuss this subject.

(^1) See for example S. R. deGroot and P. Mazur,Nonequilibrium Thermodynamics, North Holland,
Amsterdam, 1962.