General Thermodynamic Properties of FRW Universe and Heat Engine

Abstract

In this work, the Friedmann–Robertson–Walker (FRW) Universe is considered a thermodynamic system, where the cosmological constant generates the thermodynamic pressure. Using a unified first law, we have determined the amount of energy dE crossing the apparent horizon. Since heat is one of the forms of thermal energy, so the heat flows δQ through the apparent horizon = amount of energy crossing the apparent horizon. Using the first law of thermodynamics, on the apparent horizon, we found TdS=A(ρ+p)Hr˜hdt+Aρdr˜h where T,S,A,H,r˜h,ρ,p are respectively the temperature, entropy, area, Hubble parameter, horizon radius, fluid density and pressure. Since the apparent horizon is dynamical, so we have assumed that dr˜h cannot be zero in general, i.e., the second term Aρdr˜h is non-zero on the apparent horizon. Using Friedmann equations with the unified first law, we have obtained the modified entropy-area relation on the apparent horizon. In addition, from the modified entropy-area relation, we have obtained modified Friedmann equations. From the original Friedmann equations and also from modified Friedmann equations, we have obtained the same entropy. We have derived the equations for the main thermodynamical quantise, such as temperature, volume, mass, specific heat capacity, thermal expansion, isothermal compressibility, critical temperature, critical volume, critical pressure and critical entropy. To determine the cooling/heating nature of the FRW Universe, we have obtained the coefficient of Joule–Thomson expansion. Next, we have discussed the heat engine phenomena of the thermodynamical FRW Universe. We have considered the Carnot cycle and obtained its completed work. In addition, we studied the work completed and the thermal efficiency of the new heat engine. Finally, we have obtained the thermal efficiency of the Rankine cycle.