A block is kept in a room which is at `20^(@)C`. To raise the temperature of the block, heat is given to it at a constant rate of 600 watt (using an electric heater). The temperature of the block rises with time as shown in the graph. The slope of the graph at time `t = 0` is `3^(@)C s^(-1)`. Once the temperature rises to `60^(@)C`, the heater is switched off and another heater is switched on to maintain the temperature of the block at `60^(@)C`. This new heater supplies heat at a constant rate of 100 watt. Assume that heat capacity of the block remains constant for the range of temperature involved.
(a) Explain why the slope of the given graph is decreasing with time.
(b) Calculate the heat capacity of the block.
(c) If the 100 W heater is also switched off, what will be initial rate of cooling of the block?
(d) Assuming that rate of heat loss by the block to the surrounding is proportional to difference in its temperature with surrounding, calculate the heat radiated per second by the block when it was at `30^(@)C`.

Answer

(b) `200J^(@)C_(-1)` (c) `0.5^(@)C^(-1)` (d) 25W