The equations of state for electromagnetic radiation in thermodynamic equilibrium with a cavity of volume V at temperature T (blackbody radiation) are P=a T^4/3 and U=a T^4 V, where a=4(segma)/c is the radiation constant, c is speed of light in vacuum, and (segma) is the Stefan-Boltzmann constant.
a. Find the equation of an adiabatic process V (T). That is, write down a function of V and T that is constant during an adiabatic process.
b. Find the heat capacity for an isochoric (i.e., constant volume) process.
c. Find the amount of heat needed in order to raise the temperature of a blackbody cavity of constant volume equal to 1 L from 400K to 500K.