Page 263 - Schaum's Outline of Theory and Problems of Applied Physics

248 THERMODYNAMICS [CHAP. 21

Fig. 21-5

SOLVED PROBLEM 21.4
◦
At 100 C and atmospheric pressure the heat of vaporization of steam is L v = 2260 kJ/kg, the density of
3
3
3
water is 10 kg/m , and the density of steam is 0.6 kg/m . What proportion of L v represents work done
to expand water into steam against the pressure of the atmosphere?
The volumes of 1 kg of water and 1 kg of steam at 100 C and atmospheric pressure are, respectively,
◦
m 1kg 3
V water = = = 0.001 m
3
d water 10 kg/m 3
m 1kg
V steam = = 3 = 1.667 m 3
d steam 0.6 kg/m
5
Atmospheric pressure is p = 1.013 × 10 Pa. Hence the work done in the expansion is
5
3
5
W = p(V steam − V water ) = (1.013 × 10 Pa)(1.667 − 0.001) m = 1.69 × 10 J = 169 kJ
This is
W 169 kJ
= = 0.075 = 7.5%
L v 2260 kJ

of the heat of vaporization of water. The remainder of the heat of vaporization goes into pulling the water molecules
apart to create a gas from a liquid and so becomes internal energy of the steam.

SOLVED PROBLEM 21.5
Show that the power output of each cylinder of a reciprocating engine of any kind (steam, gasoline, diesel)
is given by the formula P c = pL An, where

p = average pressure on piston during each power stroke
L = length of piston travel
A = cross-sectional area of piston
n = number of power strokes per second

In general, P = Fs/t. Here F is the force exerted on the piston during each power stroke by the pressure p,so
since p = F/A, F = pA. The distance traveled by the piston per power stroke is L, and the distance it covers per
second is therefore s/t = Ln. Hence

Fs
P c = = pL An
t