CHAPTER 4. THERMODYNAMICS: THE FIRST LAW

4-9
!3
= 30.8 kJ/mol - (8.314x10 kJ/mol-K)(353.2 K) = 27.9 kJ/mol.
E. Heat capacity
The amount of heat released or absorbed in a process may be determined by measuring the
change in temperature of a mass in thermal contact with the process. The heat capacity is defined
as the change in heat divided by the change in temperature, C = dq/dT. However, this definition is
not very useful unless a path is specified, since the value of dq depends on how the process is carried
out. In the laboratory, there are two convenient paths; the constant volume path, where a reaction
is carried out in a closed container so that the volume cannot change, and the constant pressure path,
where a reaction is carried out in an open container so that the pressure remains constant at the
pressure of the surrounding atmosphere. Consider a process carried out at constant volume. Then
dw = 0 and so dq = dU, therefore, the heat capacity (per mole) at constant volume is
and
,
.
For a process carried out at constant pressure, dq = dH, therefore, the heat capacity (per mole) at
constant pressure is
,
and
.
Physically, the difference between C V and C P is related to the fact that when the volume is