Question

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

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

Answer 1

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

We know that,Rate of heat$\propto$difference in temperature with the surroundings.
At ${50}^{0}C$,$\frac{dQ}{dt}=k\left(50-30\right)=10$,where k is constant.
So $k=\frac{1}{3}$
now at an average temperature of ${35}^{0}C$
$\frac{dQ}{dt}=\frac{1}{3}\times \left(35-20\right)J/s=5J/s$
Heat loss in $1minute$=$\frac{dQ}{dt}\times 60J=5\times 60J=300J=Q$
Now, fall in temperature=${0.2}^{0}C=\Delta \theta$
and $Q=c\Delta \theta$
Heat capacity$=c=\frac{Q}{\Delta \theta }=\frac{300J}{0.2}=1500J/C$