Physical Chemistry , 1st ed.

d, e.When a can of spray paint is discharged, the can itself usually does not

change in volume. Therefore, if the can itself is defined as the system, the

amount of work it does is zero. However, work is done by the spray itself as

it expands against the atmosphere. This last example shows how important it

is to define the system as specifically as possible.

If it were possible, we could change the volume of the gas inside the piston

chamber in infinitesimally small steps, allowing the system to react to each in-

finitesimal change before making the next change. At each step, the system

comes to equilibrium with its surroundings so that the entire process is one of

a continuous equilibrium state. (In reality, that would require an infinite num-

ber of steps for any finite change in volume. Sufficiently slow changes are a

good approximation.) Such a process is called reversible.Processes that are not

performed this way (or are not approximated this way) are called irreversible.

Many thermodynamic ideas are based on systems that undergo reversible

processes. Volume changes aren’t the only processes that can be reversible.

Thermal changes, mechanical changes (that is, moving a piece of matter), and

other changes can be modeled as reversible or irreversible.

Gaseous systems are useful examples for thermodynamics because we can

use various gas laws to help us calculate the amount of pressure-volume work

when a system changes volume. This is especially so for reversible changes, be-

cause most reversible changes occur by letting the external pressure equal the

internal pressure:

pextpintfor reversible change

The following substitution can then be made for reversible changes:

wrevpintdV (2.6)

So now we can determine the work for a process in terms of the internal

pressure.

The ideal gas law can be used to substitute for the internal pressure, be-

cause if the system is composed of an ideal gas, the ideal gas law must hold.

We can get

wrev

n

V

RT

dV

when we substitute for pressure. Although nand Rare constants, the temper-

ature Tis a variable and may change. However, if the temperature does remain

constant for the process, the term isothermalis used to describe the process,

and the temperature “variable” can be taken outside of the integral sign.

Volume remains inside the integral because it is the variable being integrated.

We g e t

wrevnRT

V

(^1) dV
This integral has a standard form; we can evaluate it. The equation becomes
wrevnRT(ln VVVif)
The “ln” refers to the natural logarithm, not the base 10 logarithm (which is
represented by “log”). Evaluating the integral at its limits,
wrevnRT (ln Vfln Vi)
28 CHAPTER 2 The First Law of Thermodynamics