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

Answer

D

Explanation

(4) Rate of loss of heat `prop` difference in temperature with the surroundings
At `50^(@)C, (dq)/(dt) = k_(0) (50 - 20) = 10`, where `k_(0)` constant
`k_(0) = (1)/(3)`
At an average temperature of `35^(@)C`
`(dQ)/(dt) = (1)/(3) (35 - 20) = 5 J//s`
Heat lost in min = `(dQ)/(dt) xx 60 xx 5 xx 60 = 300 J = Q`
Fall in temperature `= 0.2^(@)C`
`Q = (ms) (Delta theta)`
Hetat capacity `ms = (Q)/(Delta theta) = (300)/(0.2) = 1500 J//^(@)C`