What is the Efficiency of a Heat Engine?

[TFM]

I am also assuming that the nR can cancel, so:

$$P_1(v_1\frac{v_1^{\gamma - 1}}{v_3^{\gamma - 1}} - V_3)}{V_3(P_1 - P_3 \frac{V_3^{\gamma - 1}}{v_1^{\gamma - 1}})}$$

Does this look right?

 

[Redbelly98]

To be honest I have lost track. However, it would be desirable to simplify the term

v₁ v₁^γ-1​

The idea is, once you have an expression for the efficiency, for you to manipulate and simplify it algebraically and get

$$e = 1 - \frac{1}{\gamma}\left(\frac{1 - \frac{p_3}{p_1}}{1 - \frac{v_1}{v_3}}\right)$$​

which, as I had mentioned earlier, has a typo corrected from what was given in Post #1 (v1/v3 instead of v3/v1).

 

[TFM]

Oops, my Latex went a bit wrong. it should have been:

$$\frac{P_1(v_1\frac{v_1^{\gamma - 1}}{v_3^{\gamma - 1}} - V_3)}{V_3(P_1 - P_3 \frac{V_3^{\gamma - 1}}{v_1^{\gamma - 1}})}$$