An ideal gas is taken through a reversible cycle consisting of an isothermal expansion followed by an isothermal compression that brings it back to the initial state. Answer the following queries based on the cycle.
(i) Explain why the net change in internal energy of the gas over the complete cycle is zero.
(ii) If the two isothermal steps occur at the same temperature, show that the net entropy change of the gas after completing the cycle is zero.
(iii) Despite the result in part (ii), can heat flow into or out of the gas during the individual steps? Explain briefly.