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Heat Capacity at Constant Volume

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Question

The compression ratio of a cold air-standard Otto cycle is 9. At the end of the expansion process the pressure is 655 kpa and the temperature is 550 K. The heat rejection from the cycle is $200 k J / k g$ of air. The mean effective pressure is _________ kPa (Assume $γ = 1.4$ )
1316.63

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Solution

The correct option is A 1316.63

$\begin{matrix} e t a & = 1 - \frac{1}{(r_{k})^{γ - 1}} & = 1 - \frac{1}{(9)^{0.4}} = 0.585 Q_{S} & = \frac{Q_{R}}{1 - η} = \frac{200}{1 - 0.585} = 481.93 k J / k g W_{n e t} & = Q_{S} - Q_{R} = 481.93 - 200 = 281.93 v_{1} & = v_{4} = \frac{0.287 \times 550}{655} = 0.2409 m^{3} / k g v_{2} & = \frac{v_{1}}{9} = \frac{0.2409}{9} = 0.02677 m^{3} / k g M E P & = \frac{Q_{S} - Q_{R}}{v_{1} - v_{2}} = \frac{W_{n e t}}{v_{1} - v_{2}} \frac{k J / k g}{m^{3} k g} = \frac{281.93}{0.2409 - 0.02677} = \frac{281.93}{0.21413} = 1316.63 k P a \end{matrix}$

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