A metal block of heat capacity 80 J/ ºC placed in a room at 20 ºC is heated electrically. The heater is switched off when the temperature reaches 30 ºC. The temperature of the block rises at the rate of 2 ºC/s just after the heater is switched on and falls at the rate of 0.2 ºC/s just after the heater is switched off. Assume Newton’s law of cooling to hold.
Text Solution
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Given:
Heat capacity of the metal block, 
Heat absorb by the metal block is,
Rate of rise in temperature of the block 
Rate of fall in temperature of the block 
The negative sign indicates that the temperature is falling with time.
Energy 
Power 
Energy per unit time
Power of the heater 
Heat capacity 
Power Radiated = Energy lost per unit time.
heat capacity 
Here, 
represents the rate of decrease in temperature.
c) 16 W of power is radiated when the temperature of the block decreases from 
to 
.
From newton's law of cooling,
As we know, that power given by the heater is 
now we can use energy equations
Energy given by heater 
Heat absorbed by block + heat loss
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