A solid metallic sphere of radius 5.0 cm behaves like a perfect blackbody
PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Modern Physics · Modern Physics
Problem
A solid metallic sphere of radius 5.0 cm behaves like a perfect blackbody. The sphere can be heated electrically in a laboratory where the ambient (room) temperature remains steady at 300 K.
(i) Show that the total power P radiated by the sphere at an absolute temperature T may be written in the form P=4πr2σT4, where the symbols have their usual meanings.
(ii) If the temperature of the sphere is raised from 300 K to 600 K, by what percentage does the power emitted by the sphere increase? (Take the room temperature to remain 300 K and ignore radiation received from the surroundings.)
(iii) Keeping the surroundings at 300 K, calculate the net rate of loss of thermal energy from the sphere when its surface is at 600 K. Use σ=5.67×10−8W m−2K−4 to express your answer in watts to an appropriate number of significant figures.