Page 229 - Schaum's Outline of Theory and Problems of Applied Physics

214 HEAT [CHAP. 18

SOLVED PROBLEM 18.2
What is the Fahrenheit equivalent of 80 C?
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T F = T C + 32 = (80 ) + 32 = 176 F
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SOLVED PROBLEM 18.3
Oxygen freezes at −362 F. What is the Celsius equivalent of this temperature?
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T C = (T F − 32 ) = (−362 − 32 ) =−219 C
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SOLVED PROBLEM 18.4
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Nitrogen freezes at −210 C. What is the Fahrenheit equivalent of this temperature?
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T F = (T C + 32 ) = (−210 ) + 32 =−346 F
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HEAT
Heat is a form of energy that, when added to a body of matter, increases the internal energy content of the body
and thereby causes its temperature to rise. The customary symbol for heat is Q.
Because heat is a form of energy, the proper SI unit of heat is the joule. However, the kilocalorie is sometimes
used with SI units: 1 kilocalorie (kcal) is the amount of heat needed to raise the temperature of 1 kg of water by
1 C. The calorie itself is the amount of heat needed to raise the temperature of 1 g of water by 1 C; hence 1 kcal
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= 1000 cal. (The calorie used by dieticians to measure the energy content of foods is the same as the kilocalorie.)
The British unit of heat is the Britishthermal unit (Btu): 1 Btu is the amount of heat needed to raise the
temperature of 1 lb of water 1 F. To convert heat figures from one system to the other, we note that
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1J = 2.39 × 10 −4 kcal = 9.48 × 10 −4 Btu
1 kcal = 3.97 Btu = 4185 J = 3077 ft·lb
1 Btu = 0.252 kcal = 778 ft·lb = 1054 J
Although weight rather than mass is specified in the British system when we are dealing with heat, in practice
this makes no difference in the various calculations. Whenever m appears in the equations of heat, it refers to
mass in kilograms when metric units are used and to weight in pounds when British units are used.

SPECIFIC HEAT CAPACITY
Different substances respond differently to the addition or removal of heat. For instance, 1 kg of water increases
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in temperature by 1 C when 1 kcal of heat is added, but 1 kg of aluminum increases in temperature by 4.5 C when
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this is done. The specific heat capacity of a substance is the amount of heat needed to change the temperature of
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a unit quantity of it by 1 . The symbol of specific heat capacity is c; its SI unit is J/(kg· C) [although kcal/(kg· C)
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is still sometimes used], and its British unit is Btu/(lb· F).
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Among common materials, water has the highest specific heat capacity, namely,
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c water = 4185 J/(kg· C) = 4.185 kJ/(kg· C) = 1.00 kcal/(kg· C) = 1.00 Btu/(lb· F)
Ice and steam have lower specific heat capacities than water:
c ice = 2090 J/(kg· C) = 2.09 kJ/(kg· C) = 0.50 kcal/(kg· C) = 0.50 Btu/(lb· F)
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c steam = 2010 J/(kg· C) = 2.01 kJ/(kg· C) = 0.48 kcal/(kg· C) = 0.48 Btu/(lb· F)
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Metals usually have low specific heat capacities; thus lead and iron have c = 130 and 460 J/(kg· C), respectively.
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