# Thermal efficiency of a given complete cycle

I am answering the following question:

Gas initially at a pressure of 101.325 kPa and temperature of 60 °C undergoes the following cycle:

• 1-2: Adiabatic Compression through compression ratio of 4.5:1
• 2-3: Heating at constant volume through a pressure ratio of 1.35:1
• 3-4: Constant entropy expansion to initial pressure
• 4-1: Constant pressure cooling to initial volume

If $Cp = 1\ \mathrm{\frac{kJ}{kg\ K}}$ and $Cv = 0.678\ > \mathrm{\frac{kJ}{kg\ K}}$ for the gas, determine the thermal efficiency for the cycle.

Since it sounds pretty much like the Otto cycle, I try using the formula with compression ratio $r_k = 4.5$:

$$k = Cp/Cv = 1.47$$

$$e = 1-(1/(r_k^{k-1})) = 50.68\%$$

What am I doing wrong? Is it not an Otto cycle?

This should be the $$P-v$$ diagram of your engine (sorry for the lousy image):
Side note: compression ratio in Otto cycle $$r$$ is not $$\frac{P_2}{P_1}$$ as in your calculations, it's defined as the ratio between maximum and minimum volume in the cycle $$\frac{V_{max}}{V_{min}} = \frac{V_4}{V_3}$$