Choose the correct relation, when the temperature of an isolated black body falls from `T_(1)` to `T_(2)` in time `'t'` and assume `'c'` to be a constant.

Options

A. `t=c(1/(T_(2))-1/(T_(1)))`
B. `t=c(1/(T_(2)^(2))-1/(T_(1)^(2)))`
C. `T=C(1/(T_(2)^(3)-1/(T_(1)^(3))))`
D. `t=c(1/(T_(2)^(4))-1/(T_(1)^(4)))`

Explanation

(c) We know `P=4pir^(2) sigma T^(4)=ms(-(dT)/(dt))`
`=-4/3pir^(3) rho (dT)/(dt)` and `R=(dT)/(dt)`
`PpropT^(2)` and `Rprop1/`
`int_(T_(1))^(T_(2)) (dT)/(T^(4))=` constant `int_(0)^(1)dt`
`t=c[1/(T_(2)^(3)-1/(T_(1)^(3))]`