A system `S` receives heat continuously from an electric heater of power `10 W`. The temperature of `S` becomes constant at `50^(@)C` when the surrounding temperature is `20^(@)C`. After the heater is switched off, `S` cools from `35.1^(@)C` to `34.9^(@)C` in `1 minute`. the heat capacity of `S` is

Options

A. `100J//"^(@)C`
B. `300J//"^(@)C`
C. `750J//"^(@)C`
D. `1500J//"^(@)C`

Answer

D

Explanation

Rate of cooling
= ms`(-(d theta)/(dt)) = 4 sigma AT_(0)^(3) DeltaT`
`implies 4sigmaA xx T_(0)^(3)(50-20) = 10` and `4sigmaA xx T_(0)^(3)(35-20) = "ms"(-(d theta)/(dt)) = ms((0.2)/(60))`
`implies ms= (60)/(0.2) xx ((15 xx10)/(30)) = 1500J//^(@)C`