Prove that the comoving entropy density (or the total entropy) is conserved for a general radiation + dust system. Here quasistatic evolution is assumed. Hint: Step 1: using the energy continuity equation in lecture 5 and s=Trho+p​ to prove dtd(sa3)​=Ta3​dtdT​(dTdp​−s) Here s and rho are entropy and energy densities, respectively. Step 2: using the fundamental equation in thermodynamics dU=TdS−pdV to show dp=sdT.