In the compression stroke of a Diesel engine air is compress

In the compression stroke of a Diesel engine, air is compressed from atmospheric pressure and room temperature to about 1/15 of its original volume. Find the final temperature, assuming a reversible adiabatic compression. (Take air=1.4.)

Solution

For reversible adiabatoc compression,

P V^Y = constant

atmospheric pressure, P = 1 atm = 101325 Pa

room temperature, T = 20 deg C   = 293.15 K

Vf = Vi/15   (Given)

Hence,

(101325 ) ( Vi)^1.4   = (Pf) (Vf)^1.4

Pf = 101325 ( Vi / Vf)^1.4

and Vi / Vf = 15

Pf = 101325 (15)^1.4 = 4489979.675 Pa

Now using Gas equation,

PV = nRT

PV / T = constant

(101325) ( Vi ) / ( 293.15)   = (4489979.675)(Vi/15) / (Tf)

Tf = 866.02 K Or 592.87 deg C