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 25 to 1. If air enters a cylinder at 1 atm and is compressed adiabatically, the compressed air reaches a pressure of 66.0 atm. Assuming that the air enters the engine at room temperature (24.5°C) and that the air can be treated as an ideal gas, find the temperature (in K) of the compressed air.

Explanation / Answer

PV^Y = constant

=> (P2/P1)(V2/V1)^Y = 1

=> 66/1 (1/25)^y = 1

=> 25^y = 66

=> y = log 66... base(25)

=> y = 1.3

=> P^1-y T^y = Constant

=> (1)^1-1.3 (297.5)^1.3 = (66)^1-1.3 (T)^1.3

=> T = ((297.5)^1.3 /(66)^-0.3)^(1/1.3)

=> T = 782.3 K

(or) 509.31 °C

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