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Methane gas within a piston–cylinder assembly is compressed in a quasiequilibrium process. Is this process internally reversible? Is this process reversible?

Water within a piston–cylinder assembly cools isothermally at 100 C from saturated vapor to saturated liquid while interacting thermally with its surroundings at 20 C. Is the process an internally reversible process? Is it reversible? Discuss.

To increase the thermal efficiency of a reversible power cycle operating between reservoirs at TH and TC, would you increase TH while keeping TC constant, or decrease TC while keeping TH constant? Are there any natural limits on the increase in thermal efficiency that might be achieved by such means?