Consider the two engines coupled together to the same "hot" and "cold" reservoirs. The first engine runs some unspecified reversible cycle and the second runs the reversible Carnot cycle.

Some reversit engine

$7\mathrm{.}1$ Is it possible to pick the "unspecified" cycle in such a way that Engine #$1$ produces less useful work on the surroundings compared to Engine #$2($the Carnot cycle$)?$ Please explain your answer. $(5$ pts$)$

$7\mathrm{.}2$ Is it possible to run Engine #$1$ in an irreversible cycle and produce more useful work on the surroundings compared to Engine #$2($the Carnot cycle$)?$ Please explain your answer. $(5$ pts$)$