The Otto cycle's thermodynamic efficiency is often described using the compression ratio:
$$\eta_{th} = 1 - \left( \frac{1}{CR} \right ) ^ {k-1},$$
(where CR is the compression ratio, and k the ratios of specific heat).
Now I tried describing this using a pressure ratio (So instead of $\frac{V_1}{V_2}$ using $\frac{p_1}{p_2}$. Taking into account the compression in a cycle is (in the ideal case) an isentropic process, one could use $$p_1V_1^k = p_2V_2^k$$ $$\frac{P_2}{P_1} = \left ( \frac{V_1}{V_2} \right ) ^ {k} = \Pi$$
Combining these I would get: $$\eta_{th} = 1 - \left( \frac{1}{\Pi ^ {\frac{k-1}{k}}} \right ) $$
However this is exactly the same as the Brayton efficiency.. While the cycles are different (Otto uses isochoric combustion, while Brayton uses an isobaric expansion during combustion). I wanted to compare those two, what did go wrong?
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does work for me. Can you give a specific example that doesn't work for you? $\endgroup$