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A vehicle powered by a spark-ignition engine follows air standard Otto cycle (γ = 1.4). The engine generates 70 kW while consuming 10.3 kg/hr of fuel. The calorific value of fuel is 44,000 kJ/kg. The compression ratio is _______ (correct to two decimal places).

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Concept:

A spark-ignition engine works upon Otto cycle

Air standard, efficiency for an Otto cycle is given by \({\eta = 1 - \frac{1}{{{r^{\gamma - 1}}}}} \)

Where ‘r’ is compression ratio, γ = 1.4 for air

Efficiency is also given by 

\(\eta = \frac{{Power\;output}}{{Heat\;input}}\)

Heat inpur = Q = (mass flow rate of fuel) × (calorific value of fuel) = ṁ × cv

Calculation:

Given, ṁ = 10.3 kg/hr, cv =  44,000 kJ/kg, Power output = 70 kW

\(Q = \left( {\frac{{10.3}}{{3600}} × {44,000}} \right)kW = \;125.89\;KW\)

\(\eta = \frac{{70}}{{125.89}} = 0.556\)

Now, 

\(0.556 = 1 - \frac{1}{{{r^{\left( {1.4 - 1} \right)}}}} \Rightarrow \frac{1}{{{{\text{r}}^{0.4}}}} = 0.444\)

⇒ r = 7.61

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