Physical Chemistry Third Edition

46 2 Work, Heat, and Energy: The First Law of Thermodynamics

decreases in the volume of the system and is not restricted to reversible changes, so

long asPis constant and equal toP(transmitted).

EXAMPLE 2.4

The thermal decomposition of a sample of solid KClO 3 produces 0.345 mol of CO 2 gas at a

constant temperature of 245◦C and a constant barometric pressure of 755 torr. Find the work

done on the atmosphere, assuming that CO 2 is an ideal gas. Neglect the volume of the solid

KClO 3 and the solid KCl that is produced.

Solution

∆V

(∆n)RT

P



(0.345 mol)(8.3145 J K−^1 mol−^1 )(518 K)

(755 torr)

(

101325 Pa

760 torr

)  0 .0148 m^3

wsurrP∆V(755 torr)

(

101325 Pa

760 torr

)

(0.0148 m^3 )1490 J

Expansion Processes

IfPis larger thanPextthe system will expand against the surroundings. If the process

is not too rapid, we can assume to a good approximation thatP(transmitted) is equal

toPext, although we cannot assume that is equal toP. The details of the nonuniformity

of the system’s pressure are not important, becausePdoes not enter into the formula

forw. We can write

w−

∫

PextdV (irreversible expansion process) (2.1-18)

EXAMPLE 2.5

A sample of 0.500 mol of nitrogen expands irreversibly from a volume of 5.00 L to a vol-

ume of 10.00 L at a constant external pressure of 1.000 atm (101,325 Pa). Assume that

P(transmitted) is equal toPext. Calculatewfor the process. Explain why the result does

not depend on the temperature or the amount of gas. Does it matter if the gas is ideal or

nonideal?

Solution

w−

∫

PextdV−Pext∆V−(101325 Pa)(5.00 L)

(

1m^3

1000 L

)

−507 Pa m^3 −507 J

The result depends only on the external pressure and the volume change. The amount of gas

would affect the pressure of the system, but this pressure does not enter into the calculation.

For the same reason it does not matter if the gas is assumed to be ideal.

BecausePmust be greater thanPextfor the irreversible process to occur,wsurrwill

be smaller for the irreversible expansion than for an equivalent reversible expansion.