Question

A system receives heat continuously at the rate of 10W. The temperature of the system becomes constant at ${70}^{\circ }C$ when the temperature of the surroundings is ${30}^{\circ }C$. After the heater is switched off, the system cools from ${50}^{\circ }C$ to ${49.9}^{\circ }C$ in 1 min. The heat capacity of the system is

• A. 1000 J/°C
• B. 1500 J/°C
• C. 3000 J/°C
• D. None of these

Answer 1

The correct option is C

3000 J/°C

At ${70}^{\circ }C$, the system attains steady state.

i.e., Rate of heat generated = Rate of heat loss

or, $10W$ = $k(70-30{)}^{\circ }C$

(From Newton's law of cooling)

Or, $k$ = $\left(\frac{1}{4}\right)W{/}^{\circ }C$

At ${50}^{\circ }C$, rate of heat loss should be $k(50-30{)}^{\circ }C$ = $5W$, But rate of heat loss = (heat capacity) $\times$ (rate of cooling)

i.e., $\frac{-dQ}{dt}$ = $c\left(\frac{-dT}{dt}\right)-5W$ = $c[\frac{49.9-50}{60}{]}^{\circ }C/s$

Or $3000J{/}^{\circ }C$