3. (20 points) Heat Engine. Consider an engine working in a reversible cycle and using an ideal gas with constant heat capacity cp? as the working substance. The cycle consists of two processes at constant pressure, joined by two adiabatics. (a) (10 points) Find the efficiency e of this engine only in terms of P1? and P2?. (b) (5 points) Which of

Question

3. (20 points) Heat Engine. Consider an engine working in a reversible cycle and using an ideal gas with constant heat capacity

c_{p}

as the working substance. The cycle consists of two processes at constant pressure, joined by two adiabatics. (a) (10 points) Find the efficiency

e

of this engine only in terms of

P_{1}

and

P_{2}

. (b) (5 points) Which of the temperatures,

T_{a}, T_{b}, T_{c}

, or

T_{d}

, is the highest, and which is the lowest? (c) (5 points) What is the efficiency of a Carnot engine

e_{Carnot}

with the same gas working between the highest and lowest temperatures. Prove that

e_{Carnot}

is greater than

e

found in part (a).

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