Page 230 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 18] HEAT 215

When an amount of heat Q is transferred to or from a mass m of a substance whose specific heat capacity
is c, the resulting temperature change T is related to Q, m, and c by the formula

Q = mc T
Heat transferred = (mass)(specific heat capacity)(temperature change)

SOLVED PROBLEM 18.5
How much heat must be added to 3 kg of water to raise its temperature from 20 to 80 C?
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The temperature change is T = 80 C − 20 C = 60 C. Hence
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Q = mc T = (3kg)[4.185 kJ/(kg· C)](60 C) = 753 kJ
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SOLVED PROBLEM 18.6
From a 50-lb block of ice initially at 25 F, 200 Btu of heat is removed. What is its final temperature?
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Q = mc T
Q 200 Btu
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T = = = 8 F
mc (50 lb)[0.5 Btu/(lb· F)]
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The final temperature is therefore 25 F − 8 F = 17 F.
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SOLVED PROBLEM 18.7
To a 1-kg sample of wood 40 kJ of heat is added, and its temperature is found to rise from 20 to 44 C.
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What is the specific heat capacity of the wood?

Q = mc T
Q 40 kJ
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c = = = 1.67 kJ/(kg· C)
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m T (1kg)(24 C)
SOLVED PROBLEM 18.8
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A total of 0.8 kg of water at 20 C is placed in a 1.2-kW electric kettle. How long a time is needed to raise
the temperature of the water to 100 C?
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The required heat is

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Q = mc T = (0.8kg)[4.185 kJ/(kg· C)](100 C − 20 C) = 268 kJ
Since P = E/t and P = 1.2kW = 1.2 kJ/s,
E 268 kJ
t = = = 223 s = 3.7 min
P 1.2 kJ/s
SOLVED PROBLEM 18.9

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In preparing tea, 600 g of water at 90 C is poured into a 200-g china pot [c pot = 0.84 kJ/(kg· C)]at20 C.
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What is the final temperature of the water?
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If T is the final temperature, then the 600 g = 0.6 kg of water initially at 90 C undergoes a temperature change
of T water = 90 C − T . At the same time the 200 g = 0.2 kg pot initially at 20 C undergoes a temperature change
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