Adiabatic compression in a diesel engine

[pentazoid]

Homework Statement

In a diesel engine, atmospheric air is quickly compressed to about 1/20 of its original volume. Estimate the temperature of the air after compression , and explain why a Diesel engine does not require spark plugs.

Homework Equations

f/2*ln(T_f/T_i)=-ln(V_f/V_i)

The Attempt at a Solution

I will assume the temperature inside a diesel engine is room temperature or 300 K.

f=5 since air is a diatomic gas.
T_i=300 K
T_f=?
V_i=V_i
V_f=.05*V_i

2.5*ln(T_f/(300K)=-ln(.05)

ln(T_f/300 K)=3/2.5

In(T_f/300)=1.2

T_f/300=exp(1.2)

T_f=300*exp(1.2)

since this is an adiabatic compression , no heat escapes. I guess spark plugs are not required because they produced heat and heat production isn't required to compress air inside a diesel engine. OR . The compression must be so high that heat is produced and the engine ignites by itself that there is no need for spark plugs.

 

[pentazoid]

Anybody not understand my question?

 

[Mapes]

Your answer is a touch off (<1%) due to rounding errors, but the approach is fine.