A metal block is placed in a room which is at `10^(@)C`. It is heated by an electric heater of power `500 W` till its temperature becomes `50^(@)C`. Its initial rate of rise of temperature is `2.5^(@)C//sec`. The heater is switched off and now a heater of `100 W` is required to maintain the temperature of the block at `50^(@)C`. (Assume Newtons Law of cooling to be valid)
`(i)` What is the heat capacity of the block ?
(`ii`) What is the rate of cooling of block at `50^(@)C` if the `100W` heater is also switched off ?
`(iii)` What is the heat radiated per second when the block was `30^(@)C` ?

Explanation

`(i)` `P_(heater)=P_(given to block)+P_(Loss to surroundings)`
Initial `P_(Loss)=0`
`:. 500=ms(dT)/(dt)+0`
`500=C 2.5`
`:. C=200 J//^(@)C`
`(ii)` At `50^(@)C`, power loss to surroundings `=100W`
`0=ms(dT)/(dt)+100`
`(dT)/(dt)= -(100)/(200)=-0.5^(@)C//sec`
`(iii)` Given at `50^(@)C` : Newton's Law of cooling
`"Power Loss"=100=k(50-10)impliesk=(10)/(4)=(5)/(2)`
`:. "At" 30^(@)C P_(Loss)=k(30-10)=(5)/(2)xx20=50W`