Page 231 - Schaum's Outline of Theory and Problems of Applied Physics

216 HEAT [CHAP. 18

of T pot = T − 20 C. We proceed as follows:
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Heat gained by pot = heat lost by water

m pot c pot T pot = m water c water T water
(0.2kg)[0.84 kJ/(kg· C)](T − 20 C) = (0.6kg)[4.185 kJ/(kg· C)](90 C − T )
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(0.168T − 3.36) kJ = (225.99 − 2.511T ) kJ
2.679T = 222.63
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T = 83 C
SOLVED PROBLEM 18.10
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Three pounds of water at 100 F is added to 5 lb of water at 40 F. What is the final temperature of the
mixture?
If T is the final temperature, then the 5 lb of water initially at 40 F undergoes a temperature change of
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T 1 = T − 40 F and the 3 lb of water initially at 100 F undergoes a temperature change of T 2 = 100 F − T .We
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proceed as in Prob. 18.9:
Heat gained = heat lost
m 1 c 1 T 1 = m 2 c 2 T 2
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(5lb)[1 Btu/(lb· F)](T − 40 F) = (3lb)[1 Btu/(lb· F)](100 F − T )
(5T − 200) Btu = (300 − 3T ) Btu
8T = 500
T = 62.5 F
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SOLVED PROBLEM 18.11
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To raise the temperature of 5 kg of water from 20 to 30 C, a 2-kg iron bar is heated and then dropped
into the water. What should the temperature of the bar be [c iron = 0.46 kJ/(kg· C)]?
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Let the temperature of the iron bar be T . Then the change in the water’s temperature is T w = 30 C − 20 C =
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10 C, and the change in the bar’s temperature is T iron = T − 30 C. We proceed in the usual way:
(5kg)[(4.185 kJ/(kg· C)](10 C) = (2kg)[(0.46 kJ/(kg· C)](T − 30 C)
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209.3kJ = (0.92T − 27.6) kJ
0.92T = 236.9
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T = 258 C

CHANGE OF STATE
When heat is continuously added to a solid, the solid grows hotter and hotter and finally begins to melt (Fig. 18-1).
While it is melting, the material remains at the same temperature and the absorbed heat goes into changing its
state from solid to liquid. After all the solid is melted, the temperature of the resulting liquid then increases as
more heat is supplied until it begins to boil. Now the material again stays at a constant temperature until all of it
has become a gas, after which the gas temperature rises.
The amount of heat that must be added to a unit quantity (1 kg or 1 lb) of a substance at its melting point to
change it from a solid to a liquid is called its heat offusion L f . The same amount of heat must be removed from
a unit quantity of the substance when it is a liquid at its melting point to change it to a solid.