A body cools in a surrounding of constant temperature `30^(@)C`. Its heat capacity is `2J//^(@)C`. Initial temperature of the body is `40^(@)C`. Assume Newton's law of cooling is valid. The body cools to `36^(@)C` in `10` minutes.
When the body temperature has reached `36^(@)C`. it is heated again so that it reaches to `40^(@)C` in `10` minutes. Assume that the rate of loss of heat at `38^(@)C` is the average rate of loss for the given time . The total heat required from a heater by the body is :

Options

A. `7.2J`
B. `0.728 J`
C. `16J`
D. `32J`

Answer

C

Explanation

`because (40-36)/(10) = k(38-30) implies k = (4)/(10xx8) = (1)/(20)`
when the block is at `38^(@)C` and temperature is at `30^(@)C` the rate of heat loss ms`xx(d theta)/(dt) = "ms" k (38-30)`
Total heat loss in `10` minutes `implies DeltaQ = "ms:k(38-30) xx 10 = 2 xx(1)/(20) xx 8 xx 10 = 8J`