Question

A system $S$ receives heat continuously from an electrical heater of power $10W$. 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

• A. 750 $J{/}^{0}C$
• B. 1500 $J{/}^{0}C$
• C. 3000 $J{/}^{0}C$
• D. 6000 $J{/}^{0}C$

Answer 1

The correct option is B 1500 $J{/}^{0}C$

Rate of heat received is proportional to the temp difference between the system and surrounding. Thus at ${50}^{o}C$ we have
$\frac{dQ}{dt}=a(T_{system}-T_s)$ where a is a proportionality constant.
$\therefore 10=a(50-20)=30a$
$\therefore a=\frac{1}{3}$
Now S cools from ${35.1}^{o}C$ to ${34.9}^{o}C$ in 60 sec.
We take the average temperature here as ${35}^{0}C$ and evaluate the rate of heat transfer during this stage
$\frac{dQ}{dt}=a(35-20)=5J{s}^{-1}$
$\therefore Q_{total}=5\ast 60=300J$
Heat Capacity $C=\frac{Q_{total}}{fallintemperature}$
or
$C=\frac{Q_{total}}{35.1-34.9}=1500J{(}^{0}C{)}^{-1}$