A metal cylinder of mass `0.5kg` is heated electrically by a `12 W` heater in a room at `15^(@)C` The cylinder temperature rises nuniformly to `25^(@)C` in 5 min and finally becomes constant at `45^(@)C` Asuming that the rate of heat loss is proporational to the excess temperature over the surroundings .

Options

A. The rate of loss of heat of the cylinder to surrounding at `20^(@)C` is `2W` .
B. The rate of loss of heat of the cylinder to surrounding at `45^(@)C` is `2W` .
C. Specific heat capacity of metal is `(240)/(In(3//2))J//kg^(@)C`
D. None of these

Answer

A, C

Explanation

In final `at 20^(@)C, (dQ_(e))/(dt) =k (20-15) =(2)/(5) xx =2 watt`
`m.s (dT)/(dt) =12 - (2)/(5) (T -15) rArr m.s (dT)/(dt) = 18 - (2)/(5)T`
`m.sunderset(15)overset(25)int(dT)/(18-(2)/(5)T)=underset(15)overset(25)int(dT)/(18-2(2)/(5)T)=underset(0)overset(300)intdtrArrs=(240)/(l n((3)/(2)))J//kg-^(@)C`
.