Physical Chemistry Third Edition

2.1 Work and the State of a System 45

Solution

We first convert the equation of state to an expression in terms ofT,V, andninstead ofT

andVm:

P

nRT

V

+

n^2 RTB 2

V^2

wrev

∫

c

PdV−nRT

∫V 2

V 1

1

V

dV+n^2 RTB 2

∫V 2

V 1

1

V^2

dV

−nRTln

(

V 2

V 1

)

+n^2 RTB 2

(

1

V 2

−

1

V 1

)

−nRTln

(

Vm,2

Vm,1

)

+nRTB 2

(

1

Vm,2

−

1

Vm,1

)

(2.1-15)

Exercise 2.1

a.Calculate the work done in the reversible expansion of 100.00 g of CO 2 from a volume of

10.000 L to a volume of 50.00 L at a constant temperature of 25.00◦C. Use the truncated

virial equation of state of Example 2.3. The second virial coefficient of CO 2 is equal to

−128 cm^3 mol−^1 at this temperature.

b.Recalculate the work done in the process of part a, assuming CO 2 to be an ideal gas.

Work and Irreversible Processes

All real processes with nonzero rates are irreversible. If we knowP(transmitted) we

can write

dwirrev−P(transmitted)dV (2.1-16)

for a simple system. We cannot discuss irreversible processes in a general way, since

P(transmitted) can differ from the equilibrium pressure in complicated ways. However,

there are some processes for which we can obtain an adequate approximation for

P(transmitted).

Constant-Pressure Processes

In some chemical reactions and some phase changes the system is open to the

atmosphere andPextis equal to the barometric pressure, which is nearly constant.

In this case we can assume thatP(transmitted) is equal toPextand toP. We can

write

w−

∫

PextdV−Pext∆V−P∆V (constant-pressure process) (2.1-17)

where “constant-pressure” means not only that the pressure is constant, but also that

it is equal toP(transmitted) and toPext. This equation is valid for both increases and