Page 266 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 21] THERMODYNAMICS 251

SOLVED PROBLEM 21.10
Three designs are proposed for an engine that is to operate between 500 and 300 K. Design A is claimed
to produce 750 J of work per kilojoule of heat input, B is claimed to produce 500 J, and C is claimed to
produce 250 J. Which design would you choose?

The efficiency of an ideal engine operating between T 1 = 500 K and T 2 = 300Kis
T 2 300 K
Eff = 1 − = 1 − = 0.40 = 40%
T 1 500 K
The claimed efficiencies of the proposed engines are
work output 750 J
Eff (A) = = = 0.75 = 75%
heat input 1000 J
500 J
Eff (B) = = 0.50 = 50%
1000 J
250 J
Eff (C) = = 0.25 = 25%
1000 J
Both A and B claim efficiencies greater than that of an ideal engine and hence could not possibly work as stated.
Design C is therefore the only possible choice.

SOLVED PROBLEM 21.11
A steam engine is being planned that is to use steam at 400 F and whose efficiency is to be 20 percent.
◦
Find the maximum temperature at which the spent steam can emerge.
◦
◦
The intake temperature is T 1 = 400 F + 460 = 860 R. We proceed as follows:
◦
T 2 T 2
Eff = 1 − = 1 − Eff
T 1 T 1
◦
◦
T 2 = T 1 (1 − Eff) = (860 R)(1 − 0.20) = 688 R
The maximum exhaust temperature is therefore T 2 = 688 R − 460 = 228 F.
◦
◦
◦
INTERNAL COMBUSTION ENGINES
An internal combustion engine is relatively efficient because it generates the input heat within the engine itself.
The operating cycle of a four-stroke gasoline engine is shown in Fig. 21-7. In the intake stroke, a mixture of
To
Intake From exhaust Exhaust
valve carburetor valve

Intake Compression Power Exhaust
stroke stroke stroke stroke
Fig. 21-7. (From Konrad B. Krauskopf and Arthur Beiser, The Physical Universe, 10th Ed., c 2003, The McGraw-
Hill Companies. Reproduced with permission of The McGraw-Hill Companies.)