An electric hotplate ring is a disc of diameter glowing dull red at about ; the…
PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Origins of quantum theory · Origins of quantum theory
Thermal Physics, Ch Photons and phonons: blackbody radiation and the heat capacity of solids
Problem
An electric hotplate ring is a disc of diameter 190mm glowing dull red at about 700K; the kitchen around it is at 293K. Treat the ring and the kitchen as black surfaces, treat the ring as a flat disc radiating from its upper face only, and ignore convection and conduction.
((a)) Estimate the net power the ring loses by radiation.
((b)) A lidded pan on the ring encloses about 0.50L of space. Treating that space as a cavity at 700K, estimate how many electromagnetic standing-wave modes it holds below 20THz, counting both polarisations, and estimate the total energy those modes would hold if each held kBT. Two significant figures are enough. Use σSB=5.67×10−8Wm−2K−4, c=2.998×108ms−1 and kB=1.381×10−23JK−1.