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 the 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 the 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 sun, then Q falls uniformly over the inner surface of the sphere of radius d. Rate of gain of heat by unit area of radius d. Rate of gain of heat by unit area of planet $$=$$ $$Q4$$$$π$$$$d2For$$ steady temperature of plant σ$$T4$$ $$=$$ $$Q4$$$$π$$$$d2T4$$ $$=$$ $$Q4$$πσ$$d2$$ or   T $$=$$ $$(Q4$$πσ$$d2)14or$$ 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 the exactly equal amount of heat received from the sun then which of the following statement is true?

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