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Q.

A system $S$ receives heat continuously from an electrical heater of power $10 W .$ The temperature of $S$ becomes constant at $50^{0} C$ when the surrounding temperature is $20^{0} C .$ After the heater is switched off, $S$ cools from ${35.1}^{0} C$ to ${34.9}^{0} C$ in 1 minute. The heat capacity of $S$ is

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a

$100 J /^{0} C$

b

$750 J /^{0} C$

c

$300 J /^{0} C$

d

$1500 J /^{0} C$

answer is D.

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Detailed Solution

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Rate of cooking $= m s (- \frac{d θ}{d t}) = 4 σ A T_{0}^{3} Δ T$
$\Rightarrow 4 σ A \times T_{0}^{3} (50 - 20) = 10$
and $4 σ A \times T_{0}^{3} (35 - 20) = m s (- \frac{d θ}{d t}) = m s (\frac{0.2}{60})$
$\Rightarrow m s = \frac{60}{0.2} \times (\frac{15 \times 10}{30}) = 1500 J /^{0} C$

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