Consider a spherical shell of radius R at temperature T. Black-body radiation inside it behaves as a photon gas with energy density U/V proportional to T⁴ and pressure p=U/(3V). If the shell undergoes adiabatic expansion, which relation between T and R is correct?
Options

Question

Consider a spherical shell of radius R at temperature T. Black-body radiation inside it behaves as a photon gas with energy density U/V proportional to T⁴ and pressure p=U/(3V). If the shell undergoes adiabatic expansion, which relation between T and R is correct?

Options

G1 Physics · Accepted Answer

For photon gas, U=aVT⁴ and p=U/(3V). Using dU+p dV=0 for an adiabatic change gives 4aVT³dT+(4/3)aT⁴dV=0, so dT/T=-(1/3)dV/V. Since V∝R³, T∝V raised to -1/3∝1/R. Option A.