(d)Show that the ratio of the absolute magnitude of the heat transfer to the gas during the isothermal process to that during the isochoric process is RP P choric (e)In which process is the absolute magnitude of the change in the internal energy of the gas the greatest? Explain your reasoning Solution Isothermal process Adiabatic process P (b)See the area under the curve of the graph, the work done by the gas is zero in isochoric process (c) See the area under the curve of the graph, the work done by the gas is greatest in isothermal (d) For isothermal process: Pv=P/ So the heat transfer is O.m, =nRT In=nRT In P. For isochoric process P T P T P-P T Thus the ratio of the absolute magnitude of the heat transfer to the gas during the isothermal process to that during the isochoric process is(d) Show that the ratio of the absolute magnitude of the heat transfer to the gas during the isothermal process to that during the isochoric process is f i V i isochoric isothermal P P c P RP Q Q ln ∆ = (e) In which process is the absolute magnitude of the change in the internal energy of the gas the greatest? Explain your reasoning. Solution: (a) (b) See the area under the curve of the graph, the work done by the gas is zero in isochoric process. (c) See the area under the curve of the graph, the work done by the gas is greatest in isothermal process. (d) For isothermal process: Pi Vi = PfVf So the heat transfer is f i i i f isothermal i P P nRT V V Q = nRT ln = ln For isochoric process: f i f i T T P P = So the heat transfer is ( ) Qisochoric = nCV Tf −Ti f i f i T T P P Q = f i i f i i T T T P P P − = − ∴ i i f i isochoric V T P P P Q nC ⋅ − ∴ = ⋅ Thus the ratio of the absolute magnitude of the heat transfer to the gas during the isothermal process to that during the isochoric process is Pi Pf P V Isothermal process Adiabatic process Isochoric process