Otto Cycle Efficiency

Question

A two-stroke engine equipped with a single cylinder having a bore of 12 cm and a stroke of 50 cm operates on an Otto cycle. At the beginning of the compression stroke air is at 100 kPa, 25 ℃. The maximum temperature in the cycle is 1100 ℃ . Use the PG model.

What would the efficiency be if the clearance volume were 1200 cc?

Using the Eqn: $$1-\frac{1}{r^{0.4}}$$ I keep getting 50.2%, but Mastering Engineering is telling me I'm wrong. Does anyone see an error with this? I'm lost.

I have V₁=6854.84 which gives me a compression ratio of 5.71239 because V₂ is 1200. I must not have the right compression ratio because from there it should just be plug and chug but I can't see what I'm doing wrong.

Answer 1

According to my reference book on thermodynamics, the efficiency is given by:

$$\eta = 1-\frac{1}{\varepsilon^{\varkappa-1}}.$$

The heat capacity ratio is given by $\varkappa$ and $\varepsilon$ is the compression ratio. The compression ratio is given by $\varepsilon =\frac{V_k+V_h}{V_k}$, in which $V_k$ is the volume after the isentropic compression and $V_k+V_h$ is the initial volume. Assuming $\varepsilon = r$ and $\varkappa = 1.4$ gives exactly your result. But $\varkappa$ does depend on temperature and pressure. So it might be that in the exercise they used another $\varkappa$ value or another fluid at all. It would help us if you could provide the full exercise statement and the solution, with which you compared your solution.