The temperature of isolated black body falls from `T_(1) "to "T_(2)` in time t. Assuming Stefan’s law to hold, time t is proportional to :

Options

A. `tprop((1)/(T_(2))-(1)/(T_(1)))`
B. `tprop((1)/(T_(2)^(2))-(1)/(T_(1)^(2)))`
C. `tprop((1)/(T_(2)^(3))-(1)/(T_(1)^(3)))`
D. `tprop((1)/(T_(2)^(4))-(1)/(T_(1)^(4)))`

Explanation

Power radiated `P=4pir^(2)sigmaT^(4)=(ms(dT)/(dt))`
`-int_(T_(1))^(T_(2))(dT)/(T^(4))=ctimpliest=K[(1)/(T_(2)^(3))-(1)/(T_(1)^(2))]`