Page 262 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 21] THERMODYNAMICS 247

Figure 21-4 shows a gas-filled cylinder with a movable piston. The cross-sectional area of the cylinder is A,
and the gas pressure is p. Since p = F/A, the force the gas exerts on the piston is

F = pA
The work done by the gas in moving the piston through the distance s is
W = (force)(distance) = F s = pA s

But A s is the change V = V 2 − V 1 in the volume of the gas, so
W = p(V 2 − V 1 )

Fig. 21-4

SOLVED PROBLEM 21.2
A gas expands by 1.2 L at a constant pressure of 2.5 bar. During the expansion 500 J of heat is added.
Find the change in the internal energy of the gas.
From Q = U + W we have

U = Q − W
5 5
Here W = p(V 2 −V 1 ) since the expansion is isobaric. Since p = (2.5 bar) (10 Pa/bar) = 2.5×10 Pa and V 2 −V 1 =
3
3
3
(1.2 L)/(10 L/m ) = 1.2 × 10 −3 m ,wehave
3
5
U = Q − p(V 2 − V 1 ) = 500 J − (2.5 × 10 Pa)(1.2 × 10 −3 m ) = 500 J − 300 J = 200 J
SOLVED PROBLEM 21.3
A sample of gas expands from V 1 to V 2 . Is the work done by the gas greatest when the expansion is
(a) isobaric, (b) isothermal, or (c) adiabatic? How does the temperature vary during each expansion?
(a) At the constant pressure p the work done is p(V 2 − V 1 ) and is the greatest of the three expansions. The
temperature must increase during the expansion in order to maintain the pressure constant despite the increase
in volume.
(b) Since pV/T = constant, during an expansion at constant temperature the pressure must drop as V increases,
and the work done is accordingly less than in (a).
(c) In an adiabatic expansion the temperature must drop since all the work done is at the expense of the internal
energy of the gas. The final pressure is therefore lower than in (a)or(b), and the least amount of work is done.
See Fig. 21-5.