A body of area `0.8xx10^-2m^2` and mass `5xx10^-4kg` directly faces the sun on a clear day. The body has an emissivity of 0.8 and specific heat of `0.8 cal//kg` K. The surroundings are at `27^@C`. (solar constant`=1.4 kW//m^(2)`).
The temperature that the body would reach if it lost all its heat by radiation is

Options

A. 396 K
B. `296^@C`
C. `85^@C`
D. `85K`

Answer

C

Explanation

At maximum temeprature `(dT)/(dt)=0`
Initially `(dT)/(dt)=(3.6^@C)/(s)`
`((dT)/(dt))_(av)=((3.6)/(2)^@C)/(s)`
Rate of loss of heat
`=ms((dT)/(dt))_(av)=sigmaAe(T^4-T_0^4)`
`T^4=((5xx10^-4xx0.8xx4.2xx10^3xx(3.6)/(2)))/(5.67xx10^-8xx0.8xx10^-2xx0.8)+300^4`
`T=358K=85^@C`