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

Options

A. `"log"_(e)(T_(2))/(T_(1))`
B. `((1)/(T_(2)^(2))-(1)/(T_(1)^(2)))`
C. `((1)/(T_(2)^(3))-(1)/(T_(1)^(3)))`
D. `((1)/(T_(2)^(4))-(1)/(T_(1)^(4)))`

Answer

C

Explanation

As the body is isolated so, the rate of cooling
`-ms(d theta)/(dt)=Asigmatheta^(4)or,(d theta)/(theta^(4))=-(Asigma)/(ms)dt,tprop(1)/(T_(2)^(3))-(1)/(T_(1)^(3))`