Physical Chemistry , 1st ed.

that when the total energy of a system changes, the energy change goes into
either work or heat; nothing else. Mathematically, this is written as

Uq+ w (2.11)

Equation 2.11 is another way of stating the first law. Note both the simplicity
and the importance of this equation. The change in the internal energy for a
process is equal to the work plus the heat. Only work or heat (or both) will ac-
company a change in internal energy. Since we know how to measure work and
heat, we can keep track ofchangesin the total energy of a system. The follow-
ing example illustrates.

Example 2.6

A sample of gas changes in volume from 4.00 L to 6.00 L against an external

pressure of 1.50 atm, and simultaneously absorbs 1000 J of heat. What is the

change in the internal energy of the system?

Solution

Since the system is absorbing heat, the energy of the system is being increased

and so we can write that q

1000 J. Using equation 2.4 for work:

wpextV(1.50 atm)(6.00 L 4.00 L)

w(1.50 atm)(2.00 L) 3.00 Latm ^1

L

0



1

a

.3

tm

2J

w304 J

The change in internal energy is the sum ofwand q:

Uq+ w1000 J 304 J

U696 J

Note that qand whave opposite signs, and that the overall change in inter-

nal energy is positive. Therefore, the total energy of our gaseous system in-

creases.

If a system is insulated well enough, heat will not be able to get into the
system or leave the system. In this situation,q0. Such systems are called
adiabatic.For adiabatic processes,

Uw (2.12)

This restriction, that q0, is the first of many restrictions that simplify the
thermodynamic treatment of a process. It will be necessary to keep track of
these restrictions, because many expressions like equation 2.12 are useful only
when such restrictions are applied.

2.4 State Functions

Have you noticed that we use lowercase letters to represent things like work
and heat but a capital letter for internal energy? There is a reason for that.
Internal energy is an example of a state function, whereas work and heat are not.
A useful property of state functions will be introduced with the following
analogy. Consider the mountain in Figure 2.7. If you are a mountain climber

2.4 State Functions 33