When a body is placed in surroundings at a constant temperature of 20°C, and heated by a 10-W heater, its temperature remains constant at 40°C. If the temperature of the body is now raised from 20°C t

Question

When a body is placed in surroundings at a constant temperature of 20°C, and heated by a 10-W heater, its temperature remains constant at 40°C. If the temperature of the body is now raised from 20°C to 80°C in 5 minutes at a uniform rate, the total heat it will lose to the surroundings will be- (Assume rate of heat loss is directly proportional to excess teperature over surrounding).

TestHub · Accepted Answer

Let T be the body temperature in degrees Celsius and t the time in seconds. The surroundings remain at 20 degrees Celsius. Heat-loss power is proportional to excess temperature:

$P_{loss} = k (T - 20)$

At 40 degrees Celsius, the heater power balances heat loss:

$10 = k (40 - 20)$

$k = 0.5 W K^{- 1}$

The uniform temperature rise takes 300 seconds:

$T - 20 = \frac{60}{300} t = \frac{t}{5}$

$P_{loss} = \frac{t}{10} W$

Integrating the lost power over the heating interval gives:

$Q = \int_{0}^{300} \frac{t}{10} d t$

$Q = \frac{30 0 ^{2}}{20} = 4500 J$

Therefore the answer is C.

Physics - Heat & Thermo Question with Solution | TestHub

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