Question

A space probe operating in a deep space environment (near absolute zero) loses heat by radiation. When the probe is active, the probe's power source actively produces 500 Watts of energy, which ultimately becomes thermal energy and is radiated away at the probe's temperature of 100K. When put into a dormant mode, the power source produces only 50 Watts of energy, and the probe cools down. In this dormant mode, what is the temperature of the probe?

		10 K
		32 K
		56 K
		90 K

Answer 1

The power radiated by a body at temperature T is

where is Stefan's constant, and A is the surface area of the body.

For temperatures T₁ and T₂, the powers radiated are in ratio

Substituting P₁=500W, T₁=100K, P₂=50W, T₂=?