$(30\%)3.$ A cylinder fitted with a piston contains $0\mathrm{.}5$ kg of R$-134$a at $60C,$ with a quality of $60$ percent. The R$-134$a now expands in an internally reversible polytropic process to ambient temperature, $20C$ at which point the quality is $100$ percent. Any heat transfer is with a constanttemperature source, which is at $60C.$ Find the polytropic exponent n and show that this process satisfies the second law of thermodynamics.