Question

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 statements is true?

• A. The planet's surface temperature varies inversely as the distance of the sun
• B. The planet's surface temperature varies directly as the square of its distance from the sun
• C. The planet's surface temperature varies inversely as the square root of its distance from the sun
• D. The planet's surface temperature is proportional to the fourth power of distance from the sun

Answer 1

The correct option is C The planet's surface temperature varies inversely as the square root of its distance from the sun