The temperature of an spherical isolated black body falls from `T_(1)` and `T_(2)` in time t them time t is

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)))`

Answer

C

Explanation

`ms(dT)/(dt)=-sigmaAT^(4),underset(0)overset(t)intdt=(ms)/(sigmaA)underset(T_(1))overset(T_(2))int(dT)/(T^(4))`