a) Two thermal reservoirs are placed in contact with each other. Prove from the increase of entropy principle that heat transfer will be in the direction of high temperature to low temperature.
b) Prove using the increse in entropy principle that the maximum thermal efficiency for any heat engine is the Carnot efficiency.
c) Using the Tds equations to show that the polytropic exponent of an ideal gas undergoing an isentropic process is k( the ratio of specific heats).