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

Options

A. `1000 J//^(@)C`
B. `1500 J//^(@)C`
C. `3000 J//^(@)C`
D. none of these

Answer

C

Explanation

At `70^@C` the system attains steady state,
i.e.,Rate of heat generated`=`Rate of heat loss
or, `10W=k(70-30)^@C`
(from Newton's law of cooling)
or `k=(1//4)W//^(@)C`
`50^@C` rate of heat loss sould be `k(50-30)^@C=5W`, But rate of heat loss`=`(heat capacity)`xx`(rate of cooling)
i.e., `(-dQ)/(dt)=c((-dT)/(dt))-5W=c[(49.9-50)/(60)]^@C//s`
or `3000 J^(@)//C`