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Chapter 2 Summary
The First Law of Thermodynamics A perfect gas obeys PV nRT, has ( U/ V) 0 ( H/ P) , has U, H, C , and C
T T V P
depending on T only, has C C nR, and has dU C dT and dH C dT. These
P V V P
equations are valid only for a perfect gas. A common error students make is to use one
of these equations where it does not apply.

2.9 CALCULATION OF FIRST-LAW QUANTITIES
This section reviews thermodynamic processes and then summarizes the available
methods for the calculation of q, w, U, and H in a process.

Thermodynamic Processes
When a thermodynamic system undergoes a change of state, we say it has undergone
a process. The path of a process consists of the series of thermodynamic states through
which the system passes on its way from the initial state to the final state. Two processes
that start at the same initial state and end at the same final state but go through different
paths (for example, a and b in Fig. 2.3) are different processes. (The term “change of
state” should not be confused with the term “phase change.” In thermodynamics, a sys-
tem undergoes a change of state whenever one or more of the thermodynamic proper-
ties defining the system’s state change their values.)
In a cyclic process, the system’s final state is the same as the initial state. In a cyclic
process, the change in each state function is zero: 0 T P V U H, etc.
However, q and w need not be zero for a cyclic process (recall Example 2.4 in Sec. 2.8).
In a reversible process, the system is always infinitesimally close to equilibrium,
and an infinitesimal change in conditions can restore both system and surroundings to
their initial states. To perform a process reversibly, one must have only infinitesimal
differences in pressures and temperatures, so that work and heat will flow slowly. Any
changes in chemical composition must occur slowly and reversibly; moreover, there
must be no friction. We found that the work in a mechanically reversible process is
given by dw rev PdV. In Chapter 3, we shall relate the heat dq rev in a reversible
process to state functions [see Eq. (3.20)].
In an isothermal process, T is constant throughout the process. To achieve this, one
encloses the system in thermally conducting walls and places it in a large constant-
temperature bath. For a perfect gas, U is a function of T only, so U is constant in an
isothermal process; this is not necessarily true for systems other than perfect gases.
In an adiabatic process, dq 0 and q 0. This can be achieved by surrounding
the system with adiabatic walls.
In a constant-volume (isochoric) process, V is held constant throughout the
process. Here, the system is enclosed in rigid walls. Provided the system is capable of
only P-V work, the work w is zero in an isochoric process.
In a constant-pressure (isobaric) process, P is held constant throughout the
process. Experiments with solids and liquids are often performed with the system
open to the atmosphere; here P is constant at the atmospheric pressure. To perform a
constant-P process in a gas, one encloses the gas in a cylinder with a movable piston,
holds the external pressure on the piston fixed at the initial pressure of the gas, and
slowly warms or cools the gas, thereby changing its volume and temperature at con-
stant P. For a constant-pressure process, we found that H q .
P
Students are often confused in thermodynamics because they do not understand
whether a quantity refers to a property of a system in some particular thermodynamic
state or whether it refers to a process a system undergoes. For example, H is a prop-
erty of a system and has a definite value once the system’s state is defined; in contrast,
H H H is the change in enthalpy for a process in which the system goes from
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