Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 15 - The Laws of Thermodynamics - General Problems - Page 441: 59

Answer

$359K=86^{\circ}C$.

Work Step by Step

Find the rate at which the gasoline supplies heat. $$Q_H/t=(3.2\times 10^7 J/L)(1L/17000m)(21.8m/s)=41035W$$ We are told that the rate of work output is 7000 W. The minimum temperature for the hot reservoir is if the engine were a perfect Carnot engine. Calculate the efficiency of the engine from the given data and then find $T_H$. $$e=1-\frac{T_L}{T_H}=\frac{W}{Q_H}=\frac{W/t}{Q_H/t}=\frac{7000W}{41035W}$$ $$T_H=\frac{T_L}{1-e}=\frac{(273+25)K}{1-(7000W)/(41035W)}=359K=86^{\circ}C$$
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