A diesel engine works at a high compression ratio to compress air until it reach

Question

A diesel engine works at a high compression ratio to compress air until it reaches a temperature high enough to ignite the diesel fuel. Suppose the compression ratio (ratio of volumes) of a specific diesel engine is 21 to 1. If air enters a cylinder at 1 atm and is compressed adiabatically, the compressed air reaches a pressure of 71 atm. Assuming that the air enters the engine at room temperature (25.0 °C) and that the air can be treated as an ideal gas, find the temperature of the compressed air.

Explanation / Answer

first finding the exponent of equation in adiabatic process (gamma = ln(P_{2}/P_{1})/(ln(V_{1}/V_{2}))

(gamma = 1.40)

now we have (T_{2} = T_{1}* (V_{1}/V_{2})^{gamma - 1})

(T_{2} = 1007.679 K)

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