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 2 W
B. The rate of loss of heat of the cylinder to surrounding at `45^(@)C` is l2 W
C. The rate of loss of heat of the cylinder to surrounding at `20^(@)C` is 5 W
D. The rate of loss of heat of the cylinder to surrounding at `45^(@)C` is 30 W

Answer

A, B

Explanation

At `45^(@)C` we use
`|(dQ)/(dt)|_(l ess)=k(45-75)=12`
at `20^(@)C |(dQ)/(dt)|_(less) =k(20-15)=0.4xx5=2W`
`implies k=(12)/(30)=0.4`
hence option (A) and (B) are correct.