Thermal radiation from black and white spheres · CAP 2005 #18
Physics · thermodynamics
Problem
Two spheres are identical except that sphere A is white whereas sphere B is black. After they have been in thermal contact long enough with each other and their surroundings, in the visible range, (a) A radiates less than B; (b) both emit the same amount of radiation; (c) A radiates more than B; (d) A radiates more than B only if its temperature is high enough.Intuitive explanation
At thermal equilibrium, both spheres reach the same temperature as their surroundings. The key insight is distinguishing between absorption and emission: while color affects how much radiation each sphere absorbs from the environment, thermal equilibrium means both spheres must emit exactly the same total power to maintain that balance. A black surface absorbs more but also must emit more to stay in equilibrium; a white surface absorbs less but emits proportionally less too. The color difference matters for how they get there, not for what happens once they've settled.
Intuitive explanation
At thermal equilibrium, both spheres reach the same temperature as their surroundings. The key insight is distinguishing between absorption and emission: while color affects how much radiation each sphere absorbs from the environment, thermal equilibrium means both spheres must emit exactly the same total power to maintain that balance. A black surface absorbs more but also must emit more to stay in equilibrium; a white surface absorbs less but emits proportionally less too. The color difference matters for how they get there, not for what happens once they've settled.