A glass-annealing lehr has an interior cavity of volume held at
PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Condensed Matter, Materials & Soft Matter · Origins of quantum theory
Thermal Physics, Ch Photons and phonons: blackbody radiation and the heat capacity of solids
Problem
A glass-annealing lehr has an interior cavity of volume V=2.5L=2.5×10−3m3 held at T=1150K. A sight port of area A=1.5mm2 is opened in one wall. Treat the interior as a black cavity in thermal equilibrium, the port as so small that the equilibrium inside is undisturbed, and radiation as the only channel of interest. You may use ∫0∞x2/(ex−1)dx=2.404.
((a)) How many electromagnetic modes does the cavity hold with frequency below 40THz?
((b)) How many photons does the cavity hold in total? State in one sentence why you do not need to be told how many photons were put in.
((c)) Using the effusion result of Chapter 2 for a gas of number density n whose particles all move with speed c, find the rate at which photons leave through the port, and find the power leaving through it.
((d)) The lehr is watched by a pyrometer whose silicon detector chip (θD=645K) is cooled to 12K. Find the Debye heat capacity of the chip per mole of silicon, ignoring any electronic contribution.