A metal cylinder of mass `0.5` kg is heated electrically by a 12 W heater in a room at `15^(@)` C. The cylinder temperature rises uniformly to `25^(@)` C in 5 min and finally becomes constant at `45^(@)` C Assuming that the rate of heat losss is proportional to the excees 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 12W
C. the rate of loss of heat of the cylinder to surrounding at `20^(@)` C is 5W
D. the rate of loss of heat of the cylinder to surrounding at `45^(@)` C is 30W.

Answer

A, B

Explanation

Rate of heat loss `((dQ)/(dt))_(loss)=k(theta-theta_(0))`
At `45^(@)` C Rate of heat loss = Rate of heat supplied =12W
`k(45-15)=12`
`Rightarrow k=2//5 W//^(@)C`
`((dQ)/(dt))_(loss)=k(20-15)=2W`