In an engine working on an ideal Otto cycle, the temperature at the beginning and at the end of compression are 300 K and 600 K respectively. What will be the air-standard efficiency of the engine? [Consider $γ = 1.4$ ]

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SJVN ET Mechanical 2019 Official Paper

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Answer 1

Concept:

The air-standard efficiency of an ideal Otto cycle is:

$ \eta = 1 - \frac{1}{r^{\gamma - 1}} $

Given:

$ T_1 = 300~K $, $ T_2 = 600~K $, $ \gamma = 1.4 $

Step 1: Find Compression Ratio

$ \frac{T_2}{T_1} = r^{\gamma - 1} \Rightarrow \frac{600}{300} = 2 = r^{0.4} $

$ r = 2^{1/0.4} = 2^{2.5} \approx 5.66 $

Step 2: Efficiency

$ \eta = 1 - \frac{1}{5.66^{0.4}} \approx 1 - \frac{1}{2} = 0.5 = 50\% $