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Homework Statement
A hypothetical engine, with an ideal gas as the working substance, operates on the cycle shown in Figure 1. Show that the efficiency of this engine is
[tex] e = 1  \frac{1}{\gamma}\left(\frac{1  \frac{p_3}{p_1}}{1  \frac{v_3}{v_1}}\right) [/tex]
Where [tex] \gamma = \frac{c_p}{c_v} [/tex]
Homework Equations
Efficiency = Benefit/Cost
Benefit = Work out
Cost = Heat in
PV = nRt
[tex] \Delta U = Q_{hot}  Q_{cold}  Work [/tex]
Work = pdv
The Attempt at a Solution
The Graph is attached, but basically it has a Adiabatic curve, which at the bottom goes up vertically, then left horizontally, back to make a cycle.
So far I have:
E = Work/Cost
Work = pdv
Cost = Q
[tex] w = pdv [/tex]
Since p is not constant, use ideal law,
[tex] w = \frac{nRt}{v}dv [/tex]
thus
[tex] w = \frac{nRt}{v}dv [/tex]
[tex] w = nRt [ln(v)]^{v_1}_{v_2} [/tex]
I also have:
[tex] e = 1  \frac{Q_{cold}}{Q_{hot}}[/tex],
from
[tex] \Delta U = Q_{hot}  Q_{cold}  Work [/tex]
Which is cylci and this delta u = 0.
I am going the ruight way about this problem?
Many thanks,
TFM
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