A rigid, sealed, evacuated cavity of volume has walls held at . The only thing inside…
PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Quantum Mechanics · Origins of quantum theory
Thermal Physics, Ch Photons and phonons: blackbody radiation and the heat capacity of solids
Problem
A rigid, sealed, evacuated cavity of volume V=2.0L=2.0×10−3m3 has walls held at 300K. The only thing inside is thermal radiation in equilibrium with the walls. The cavity is then warmed until the walls are at 480K, the volume being unchanged and nothing being let in or out. A student says: "The cavity is sealed and nothing can get in, so the number of photons inside is fixed; warming the walls only raises the energy of the photons already there." The photon number density of cavity radiation follows from the mode count g(ν)=8πVν2/c3 with the mean occupation ⟨n⟩=1/(ehν/kBT−1) of each mode, and evaluates to VN=8π(hckBT)3×2.404, using the stated integral ∫0∞x2/(ex−1)dx=2.404.
((a)) Find the number of photons in the cavity at 300K and at 480K, and the factor by which the number changes.
((b)) Say in one or two sentences what is wrong with this reasoning, and name the property of the photon gas that the result illustrates. Take h=6.626×10−34Js, c=2.998×108ms−1, kB=1.381×10−23JK−1.