Concept Questions (a) A real (irreversible) engine operates between hot and cold reservoirs whose temperatures are $T_{\mathrm{H}}$ and $T_{\mathrm{C}}$. The engine absorbs heat of magnitude
$Q_{\mathrm{H}} \mid$ from the hot reservoir and performs work of magnitude $|W| .$ What is the expression
that gives the change in entropy $\Delta S_{\text {universe }}$ of the universe associated with the operation of this engine? Express your answer in terms of $T_{\mathrm{H}}, T_{\mathrm{C}},\left|Q_{\mathrm{H}}\right|,$ and $\left|Q_{\mathrm{C}}\right|$
Would you expect the change in the entropy of the universe to be greater than, less than, or equal to zero? Provide a reason for your answer. (c) Suppose that a reversible engine (a Carnot engine) operates between the same hot and cold temperatures as the irreversible engine described above. For the same input heat $\left|Q_{\mathrm{H}}\right|,$ would the reversible
engine produce more, less, or the same work as the irreversible engine? Justify your answer. (d) In terms of $\Delta$ S universe and $T_{\mathrm{C}}$, how could one determine the difference, if any, between the work done by the reversible engine and that done by the irreversible engine?
Problem (a) An irreversible engine operates between temperatures of 852 and $314 \mathrm{~K}$. It absorbs $1285 \mathrm{~J}$ of heat from the hot reservoir and does $264 \mathrm{~J}$ of work. What is the change $\Delta S_{\text {universe }}$ in the entropy of the universe associated with the operation of this engine? (b) If the engine were reversible, what is the magnitude $|W|$ of the work it would have done, assuming it operated between the same temperatures and absorbed the same heat as the irreversible engine? (c) Using the results of parts (a) and (b), find the difference between the work produced by the reversible and irreversible engines.