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?

Question

Infinity Learn · Accepted Answer

Rate of loss of energy by unit area of the planet  $$=$$σ$$T4$$, Where σ  is a Stefan’s constant. Let  Q be the total energy emitted by the sun in every second. If d  is the distance of the planet from the sun, then Q  falls uniformly over the inner surface of the sphere of radius  d. Rate of gain of heat by unit area of planet $$=Q4$$$$π$$$$d2$$  For steady temperature of planetσ$$T4=Q4$$$$π$$$$d2$$ $$T4=Q4$$πσ$$d2$$ or $$T=(Q4$$πσ$$d2)1/4$$ or T∝$$1d$$

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?

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