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Chapter 3: Q7E (page 677)

Question: The Otto-cycle engine in a Mercedes-Benz SLK230 has a compression ratio of \(8.8\). (a) What is the ideal efficiency of the engine? Use \(\gamma = 1.40\). (b) The engine in a Dodge Viper GT2 has a slightly higher compression ratio of \(9.6\). How much increase in the ideal efficiency results from this increase in the compression ratio?

Short Answer

Expert verified

The efficiency of the engine is \(58.10\% \).

Step by step solution

01

Write the given data from the question.

The compression ratio,\(r = 8.8\)

The het capacity ratio,\(\gamma = 1.40\)

02

Determine the formulas to calculate the efficiency of the engine.

The expression to calculate the efficiency of engine is given as follows.

\(\eta = 1 - \frac{1}{{{r^{\gamma - 1}}}}\) 鈥︹�� (i)

Here,\(r\)is the compression ratio and\(\gamma \)id the heat capacity ratio.

03

Calculate the efficiency of the engine.

Calculate the efficiency of the engine.

Substitute \(8.8\) for \(r\) and \(1.4\) for \(\gamma \) into equation (i).

\(\begin{array}{l}\eta = 1 - \frac{1}{{{{8.8}^{\left( {1.4 - 1} \right)}}}}\\\eta = 1 - \frac{1}{{{{8.8}^{0.4}}}}\\\eta = 1 - 0.4189\\\eta = 0.5810\end{array}\)

Hence the efficiency of the engine is \(58.10\% \).

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