Page 57 - Physical chemistry eng

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

As n increases, the pressure difference P external – P for each individual step decreases.
In the limit that n : q , the pressure difference P external - P : 0 , and the total area
of the rectangles in the indicator diagram approaches the area under the reversible
curve. In this limit, the irreversible process becomes reversible and the value of the
work equals that of the reversible process.
By contrast, the magnitude of the irreversible compression work exceeds that of the
reversible process for finite values of n and becomes equal to that of the reversible
process as n : q . The difference between the expansion and compression processes
results from the requirement that P external 6 P at the beginning of each expansion
step, whereas P external 7 P at the beginning of each compression step.
On the basis of these calculations for the reversible and irreversible cycles, we
introduce another criterion to distinguish between reversible and irreversible processes.
Suppose that a system undergoes a change through one or more individual steps, and
that the system is restored to its initial state by following the same steps in reverse
order. The system is restored to its initial state because the process is cyclical. If the
surroundings are also returned to their original state (all masses at the same height and
all reservoirs at their original temperatures), the process is reversible. If the surround-
ings are not restored to their original state, the process is irreversible.
We are often interested in extracting work from a system. For example, it is the expan-
sion of the fuel–air mixture in an automobile engine upon ignition that provides the torque
that eventually drives the wheels. Is the capacity to do work similar for reversible and irre-
versible processes? This question is answered using the indicator diagrams of Figures 2.14
and 2.15 for the specific case of isothermal expansion work, noting that the work can be
calculated from the area under the P–V curve. We compare the work for expansion from V 1
to V in a single stage at constant pressure to that for the reversible case. For the single-
2
stage expansion, the constant external pressure is given by P external = nRT>V 2 . However,
if the expansion is carried out reversibly, the system pressure is always greater than this
value. By comparing the areas in the indicator diagrams of Figure 2.16, it is seen that

w reversible Ú w irreversible (2.23)
By contrast, for the compression step,

w reversible … w irreversible (2.24)

The reversible work is the lower bound for the compression work and the upper bound
for the expansion work. This result for the expansion work can be generalized to an
important statement that holds for all forms of work: The maximum work that can be
extracted from a process between the same initial and final states is that obtained under
reversible conditions.
Although the preceding statement is true, it suggests that it would be optimal to
operate an automobile engine under conditions in which the pressure inside the cylin-
ders differs only infinitesimally from the external atmospheric pressure. This is clearly
not possible. A practical engine must generate torque on the drive shaft, and this can
only occur if the cylinder pressure is appreciably greater than the external pressure.
Similarly, a battery is only useful if one can extract a sizable rather than an infinitesimal
current. To operate such devices under useful irreversible conditions, the work output is
less than the theoretically possible limit set by the reversible process. 3

Determining ≤U and Introducing
2.9 Enthalpy, a New State Function

Measuring the energy taken up or released in a chemical reaction is of particular inter-
est to chemists. How can the ¢U for a thermodynamic process be measured? This will
be the topic of Chapter 4. However, this topic is briefly discussed here in order to
enable you to carry out calculations on ideal gas systems in the end-of-chapter

3 For a more detailed discussion of irreversible work, see D. Kivelson and I. Oppenheim, “Work in
Irreversible Expansions,” Journal of Chemical Education 43 (1966): 233.