Question

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

• A. $100J{/}^{\circ }C$
• B. $300J{/}^{\circ }C$
• C. $750J{/}^{\circ }C$
• D. $1500J{/}^{\circ }C$

Answer 1

The correct option is D $1500J{/}^{\circ }C$

According to Newton's law of cooling:

Rate of heat transfer $\propto$ temperature difference between temperature of body and temperature of surrounding

$\frac{dQ}{dt}\propto (T_{body}-T_{surrounding})$

$\frac{dQ}{dt}=\propto \Delta T(\propto$=constant

$10=\propto (20-20)$

$\propto =\frac{1}{3}$

Now s cools from 35.1° to 34.9°C in 60 seconds

Average temperature =35°C

$\frac{dQ}{dt}=\propto (35-20)=5$Joules/second

Total heat transfer = 300Joules in 60 second

Heat capacity $S=\frac{Q_{\text{total}}}{\text{fall in temperature}}$

=$\frac{300}{0.2}$

=$1500J/°C$