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Chapter 3: Q6E (page 677)

Question: (a) Calculate the theoretical efficiency for an Otto-cycle engine with \(\gamma = 1.4\) and \(r = 9.50\) . (b) If this engine takes in \(10,000\;{\rm{J}}\) of heat from burning its fuel, how much heat does it discard to the outside air?

Short Answer

Expert verified

The theoretical efficiency for the otto cycle is \(59.36\% \).

Step by step solution

01

Write the given data from the question.

Ratio of heat capacity,\(\gamma = 1.4\)

Compression ratio of otto cycle,\(r = 9.50\)

02

Determine the formulas to calculate the theoretical efficiency for the otto-cycle.

The expression to calculate the theoretical efficiency for otto cycle 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 theoretical efficiency for the otto-cycle.

Calculate the theoretical efficiency for otto cycle.

Substitute \(9.50\) for \(r\) and \(1.4\) for \(\gamma \) into equation (i).

\(\begin{array}{l}\eta = 1 - \frac{1}{{{{9.5}^{\left( {1.4 - 1} \right)}}}}\\\eta = 1 - \frac{1}{{{{9.5}^{0.4}}}}\\\eta = 1 - 0.4063\\\eta = 0.5936\end{array}\)

Hence the theoretical efficiency for the otto cycle is \(59.36\% \).

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