Q. 6

# Two identical metal balls one at T1 = 300 K and the other at T2 = 600 K are kept at a distance of 1m in vacuum. Will the temperatures equalize by radiation? Will the rate of heat gained by the colder sphere be proportional to as may be expected from the Stefan’s law?

Yes, both the metal balls will radiate since their temperature is greater than 0 K. The radiation heat transfer is irrespective the surrounding medium.

The thermal radiation from a body depends on its temperature, according to Stefan–Boltzmann law. The law states that the radiation heat transfer from a black body is proportional to the fourth power of its absolute temperature ().

Or,

Where,

Stefan–Boltzmann constant 5.67 x 10-8 W/m2 k4

Area of the black body

Hence, the rate of radiation heat loss from the body at 300K will be less compared to the rate of radiation heat loss from the body at 600K. Since the bodies are in vicinity of each other and the radiation is happening in all the directions, the interactions of thermal radiation can cause the equalization of the temperatures on the balls.

Also, the heat loss from the hotter ball to the cooler ball or the heat gained by the cooler ball will be proportional to according to Stefan’s law.

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