2.1 Work and the State of a System
47
Exercise 2.2
a. Calculate w if 0.500 mol of nitrogen expands irreversibly from a volume of 5.00 L to a volume
of 10.00 L with a constant external pressure equal to 1.000 atm.
b. Calculate w if 0.500 mol of nitrogen expands reversibly from a volume of 5.00 L to a volume
of 10.00 L at a constant temperature of 25.00 ◦ C.
Compression Processes
If P is smaller than P ext , a fluid system will be compressed to a smaller volume. If the
process is irreversible, the system’s pressure will be nonuniform. It will be compressed
to a greater extent near the piston than in the rest of the system, so that P(transmitted)
will be greater than the equilibrium pressure of the gas, but smaller than P ext . We are
not prepared to discuss a nonuniform pressure and will not attempt calculations of w
for an irreversible compression. We can obtain some limits for the work done.
E X A M P L E 2.6
Assume that 1.00 mol of an ideal gas is initially confined in a cylinder with a volume of 22.4 L
at a temperature of 273.15 K. The external pressure is increased to 1.50 × 10 5 Pa and the gas
is compressed irreversibly and isothermally until P 1.50 × 10 5 Pa. Find the largest and
smallest values that w might have.
Solution
The final volume is
V (final)
(1.000 mol)(8.3145 J K −1 mol −1 )(273.15 K)
(1.50 × 10 5 Pa)
0.0151 m 3
Since P(transmitted) cannot exceed P ext ,
w(maximum) −P ext ∆V −(1.50 × 10 5 Pa)(0.0151 m 3 − 0.0224 m 3 ) 2270 J
Since P(transmitted) will exceed the equilibrium pressure that the gas would have at any
volume,
w(minimum) −(1.000 mol)(8.3145 J K −1 mol −1 )(273.15 K) ln
0.0151 m 3
0.0224 m 3
890 J
The actual value must lie between these values, but would depend on the rate of the process
and other things that we cannot evaluate using thermodynamics.
In Chapter 10 we will discuss the rates of certain irreversible processes from a
nonthermodynamic point of view. Thermodynamics has also been extended to include
such irreversible processes by the use of additional assumptions, 1 but we will not
discuss this subject.
1 See for example S. R. deGroot and P. Mazur, Nonequilibrium Thermodynamics, North Holland,
Amsterdam, 1962.
47
Exercise 2.2
a. Calculate w if 0.500 mol of nitrogen expands irreversibly from a volume of 5.00 L to a volume
of 10.00 L with a constant external pressure equal to 1.000 atm.
b. Calculate w if 0.500 mol of nitrogen expands reversibly from a volume of 5.00 L to a volume
of 10.00 L at a constant temperature of 25.00 ◦ C.
Compression Processes
If P is smaller than P ext , a fluid system will be compressed to a smaller volume. If the
process is irreversible, the system’s pressure will be nonuniform. It will be compressed
to a greater extent near the piston than in the rest of the system, so that P(transmitted)
will be greater than the equilibrium pressure of the gas, but smaller than P ext . We are
not prepared to discuss a nonuniform pressure and will not attempt calculations of w
for an irreversible compression. We can obtain some limits for the work done.
E X A M P L E 2.6
Assume that 1.00 mol of an ideal gas is initially confined in a cylinder with a volume of 22.4 L
at a temperature of 273.15 K. The external pressure is increased to 1.50 × 10 5 Pa and the gas
is compressed irreversibly and isothermally until P 1.50 × 10 5 Pa. Find the largest and
smallest values that w might have.
Solution
The final volume is
V (final)
(1.000 mol)(8.3145 J K −1 mol −1 )(273.15 K)
(1.50 × 10 5 Pa)
0.0151 m 3
Since P(transmitted) cannot exceed P ext ,
w(maximum) −P ext ∆V −(1.50 × 10 5 Pa)(0.0151 m 3 − 0.0224 m 3 ) 2270 J
Since P(transmitted) will exceed the equilibrium pressure that the gas would have at any
volume,
w(minimum) −(1.000 mol)(8.3145 J K −1 mol −1 )(273.15 K) ln
0.0151 m 3
0.0224 m 3
890 J
The actual value must lie between these values, but would depend on the rate of the process
and other things that we cannot evaluate using thermodynamics.
In Chapter 10 we will discuss the rates of certain irreversible processes from a
nonthermodynamic point of view. Thermodynamics has also been extended to include
such irreversible processes by the use of additional assumptions, 1 but we will not
discuss this subject.
1 See for example S. R. deGroot and P. Mazur, Nonequilibrium Thermodynamics, North Holland,
Amsterdam, 1962.