A planet radiates heat at a rate proportional to the fourth power of its surface temperature T. If such a steady temperature of the planet is due to an exactly equal amount of heat received from the sun then which of the following statement is true?

Options

A. (a)The planet’s surface temperature varies inversely as the distance of the sun
B. (b)The planet’s surface temperature varies directly as the square of its distance from the sun
C. (c)The planet’s surface temperature varies inversely as the square root of its distance from the sun
D. (d)The planet’s surface temperature is proportional to the fourth power of distance from the sun

Answer

C

Explanation

Total energy received per second
`P_("sun")/(4pir^(2))(piR^(2)),(esigma)4piR^(2)T^(4)=(ppiR^(2))/(4pir^(2))a`
or `T^(4)=K(R^(2))/(r^(2)),Talpha(1)/(sqrt(r))`