The total energy radiated from a block body source at constant temperature is collected for one minute and is used to heat a quantity of water. The temperature of water is found to increase from `20^(@)C` to `20.5^(@)C`. If the absolute temperature of the blackbody is doubled and the experiment is repeated with the same quantity of water of `20^(@)C`, the temperature of water will be:

Options

A. `21^@C`
B. `22^@C`
C. `24^@C`
D. `28^@C`

Answer

D

Explanation

Energy radiated –
`Q prop T^4 implies (Q_2)/(Q_1)=((2T)/(T))^4=16 implies Q_2=16Q_1`
Now, `Q_1=mcDeltaT=`mc(20.5-20)
and `Q_2=mc(T-20)`
`implies (Q_2)/(Q_1)=(T-20)/(0.5) implies (16)/(1)=(T-20)/(0.5) implies T = 28^@C`.