A metal block with a heater in it is placed in a room at temperature \( 293 \mathrm{~K} \). When...

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A metal block with a heater in it is placed in a room at temperature \( 293 \mathrm{~K} \). When the heater is switched on it is observed that the temperature of the block rises at the rate of \( 2^{\circ} \mathrm{C} / \mathrm{s} \) and \( P \) when its temperature rises to \( 30^{\circ} \mathrm{C} \), it is switched off. Just after when heater is switched off, it is observed that the block cools W at \( 0.2^{\circ} \mathrm{C} / \mathrm{s} \). If Newtons law of cooling is assumed to be valid, find the power of the heater. Also find the thermal power radiated by the block when it was at \( 30^{\circ} \mathrm{C} \) and at \( 25^{\circ} \mathrm{C} \). Given that the heat capacity of the block is \( 80 \mathrm{~J} /{ }^{\circ} \mathrm{C} \).
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