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. `t prop ((1)/(T_(2))-(1)/(T_(1)))`
B. `t prop ((1)/(T_(2)^(2))-(1)/(T_(1)^(2)))`
C. `t prop ((1)/(T_(2)^(3)) -(1)/(T_(1)^(3)))`
D. `t prop ((1)/(T_(2)^(4))-(1)/(T_(1)^(4)))`

Answer

A

Explanation

Power radiated `P = 4 pi r^(2) sigma T^(4)=-(ms(dT)/(dt))`
`-(dT)/(T^(2))=(4 pi r^(2)sigma dt)/(m)=c dt`
`-underset(T_(1))overset(T_(2))(int) =ct rArr t=K[(1)/(T_(2)^(3))-(1)/(T_(1)^(3))]`.