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18 CHAPTER 2 Heat, Work, Internal Energy, Enthalpy, and the First Law of Thermodynamics

The total of all these forms of energy for the system of interest is given the symbol
U and is called the internal energy. 1
The first law of thermodynamics is based on our experience that energy can be
neither created nor destroyed, if the energies of both the system and the surroundings
are taken into account. This law can be formulated in a number of equivalent forms.
Our initial formulation of this law is as follows:

The internal energy U of an isolated system is constant.

This form of the first law looks uninteresting because it suggests that nothing happens
in an isolated system when viewed from outside the system. How can the first law tell
us anything about thermodynamic processes such as chemical reactions? Consider sep-
arating an isolated system into two subsystems, the system and the surroundings. When
changes in U occur in a system in contact with its surroundings, ¢U total is given by

¢U total =¢U system +¢U surroundings = 0 (2.1)
Therefore, the first law becomes
=-¢U (2.2)
¢U system surroundings
For any decrease of U system , U surroundings must increase by exactly the same amount. For
example, if a gas (the system) is cooled, the temperature of the surroundings must increase.
How can the energy of a system be changed? There are many ways to alter U, several
of which are discussed in this chapter. Experience has shown that all changes in a closed
system in which no chemical reactions or phase changes occur can be classified only as
heat, work, or a combination of both. Therefore, the internal energy of such a system can
only be changed by the flow of heat or work across the boundary between the system and
surroundings. For example, U for a gas can be increased by putting it in an oven or by
Mass
compressing it. In both cases, the temperature of the system increases. This important
recognition leads to a second and more useful formulation of the first law:
Mechanical
stops Piston ¢U = q + w (2.3)
where q and w designate heat and work, respectively. We use ¢U without a subscript to
indicate the change in internal energy of the system. What do we mean by heat and
work? In the following two sections, we define these important concepts and discuss
P i ,V i
how they differ.
The symbol ¢ is used to indicate a change that occurs as a result of an arbitrary
process. The simplest processes are those in which one of P, V, or T remains constant.
A constant temperature process is referred to as isothermal, and the corresponding
terms for constants P and V are isobaric and isochoric, respectively.
Initial state

2.2 Work
Mass
In this and the next section, we discuss the two ways in which the internal energy of a
system can be changed. Work in thermodynamics is defined as any quantity of energy
Piston that “flows” across the boundary between the system and surroundings as a result of a
force acting through a distance. Examples are moving an ion in a solution from one
region of electrical potential to another, inflating a balloon, or climbing stairs. In each
P f ,V f
of these examples, there is a force along the direction of motion. Consider another
example, a gas in a piston and cylinder assembly as shown in Figure 2.1. In this exam-
ple, the system is defined as the gas alone. Everything else shown in the figure is in the
surroundings. As the gas is compressed, the height of the mass in the surroundings is
Final state
lowered and the initial and final volumes are defined by the mechanical stops indicated
FIGURE 2.1 in the figure.
A system is shown in which compression
work is being done on a gas. The walls 1 We could include other terms such as the binding energy of the atomic nuclei but choose to include only the
are adiabatic. forms of energy that are likely to change in simple chemical reactions.