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 - Search and Learn - Page 442: 7

Answer

15 kg.

Work Step by Step

Use the given work input, and the Carnot efficiency, to find the energy that is removed from the low-temperature reservoir. $$e=1-\frac{T_L}{T_H}=\frac{W}{Q_H}=\frac{W}{W+Q_L}$$ $$Q_L=W\frac{T_L}{T_H-T_L}$$ Now, following the hint in the problem, use the latent heat of vaporization to determine the mass of water. $$Q_L=W\frac{T_L}{T_H-T_L}=mL_V$$ The heat of vaporization is given on page 399 in Chapter 14 for evaporation at $20^{\circ}C$. $$m=\frac{W}{L_V}\frac{T_L}{T_H-T_L}$$ $$m=\frac{(600W)(3600s)}{2.45\times10^6 J/kg}\frac{(273+8)K}{17K}=14.6kg\approx 15kg$$
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