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 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

C

Explanation

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