Question

The Otto-cycle engine in a Mercedes-Benz SLK230 has a compression ratio of 8.8.

Part A. What is the ideal efficiency of the engine? Use γ=1.40.
Part 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?

Answer 1

58.1%

59.533%

1.433%

Step-by-step explanation:

`(V_1)/(V_2)` = Compression ratio

`\gamma` = Specific heat ratio = 1.4

Efficiency in the Otto cycle is given by

`\eta=1-(1)/(\left((V_1)/(V_2)\right)^(\gamma-1))\\\Rightarrow \eta=1-(1)/(\left(8.8\right)^(1.4-1))\\\Rightarrow \eta=0.581`

The ideal efficiency of the engine is 58.1%

`\eta=1-(1)/(\left((V_1)/(V_2)\right)^(\gamma-1))\\\Rightarrow \eta=1-(1)/(\left(9.6\right)^(1.4-1))\\\Rightarrow \eta=0.59533`

The ideal efficiency of the engine is 59.533%

Increase in efficiency is 59.533-58.1 = 1.433%