Page 234 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 18] HEAT 219

If T is the final temperature, then T ice = T − 0 C and T water = 30 C − T . Therefore
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Heat gained by ice = heat lost by water
m ice L f + m ice c water T ice = m water c water T water

kJ kJ kJ
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(0.03 kg) 335 + (0.03 kg) 4.185 (T − 0 C) = (0.2kg) 4.185 (30 C − T )
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kg kg· C kg· C
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(10.05 + 0.126T ) kJ = (25.11 − 0.837T ) kJ
0.963T = 15.06
T = 15.6 C
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SOLVED PROBLEM 18.19
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How much steam at 150 C is needed to melt 1 kg of ice at 0 C?
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Here T 1 = 150 C − 100 C = 50 C and T 2 = 100 C − 0 C = 100 C. If m s is the mass of steam,
Heat gained by ice = heat lost by steam
m ice L f = m s c s T 1 + m s L v + m s c water T 2
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(1kg)(335 kJ/kg) = (m s )[2.01 kJ/(kg· C)](50 C) + (m s )[2260 kJ/(kg· C)]
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+ (m s )[4.185 kJ/(kg· C)](100 C)
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335 kJ = (100.5 + 2260 + 418.5)m s kJ = 2779m s kJ
335
m s = kg = 0.12 kg
2779
Multiple-Choice Questions

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18.1. Two thermometers, one calibrated in F and the other in C, are used to measure the same temperature. The reading
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in C
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(a) is proportional to that in F
(b) is less than that in F
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(c) is greater than that in F
(d) may be less or greater than that in F
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18.2. Nitrogen boils at −196 C. The Fahrenheit equivalent of this temperature is
(a) −228 F (c) −321 F
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(b) −295 F (d) −385 F
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18.3. Lead melts at 626 F. The Celsius equivalent of this temperature is
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(a) 316 C (c) 366 C
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(b) 330 C (d) 1069 C
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18.4. Steam at 100 C is more dangerous than the same mass of water at 100 C because the steam
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(a) moves faster
(b) is less dense
(c) contains more internal energy
(d) has a higher specific heat capacity