# Adiabatic process - Diesel engine

1. Oct 15, 2011

### ibysaiyan

1. The problem statement, all variables and given/known data
A diesel engine requires no spark plug. The air in a cylinder is compressed so
highly that the fuel spontaneously ignites when sprayed into cylinder. If the air is
initially at 20°C and is then compressed by a factor of 15 in volume, what final
temperature is attained (before fuel injection)? Assume the compression is adiabatic,
and treat the air as an ideal gas. Take delta = 1.4 for air. By what factor does the
pressure increase?

2. Relevant equations
PV^ delta = constant
TV ^delta-1 = constant.
Delta = Cp/Cv.

Internal energy = Work done.
3. The attempt at a solution

I am totally lost with this problem, I know what an adiabatic process is, how to derive the delta, etc but I can't seem to match that with the above question.

Any tips ?

Last edited: Oct 15, 2011
2. Oct 16, 2011

### ibysaiyan

I think I have got an idea...
We know TV^delta -1 = constant...
Could I use the following relation :
T1 V1 ^delta -1 = T2 V2 ^delta-1

To get my t2 value?

No that doesn't seem right...

T$V^{\gamma-1}$ = k.

So if I plug in my initial temperature value as : 293.15 k and volume assumed to be at 1 , that will give me a value = k.

For the final temperature:
$T_{2}$$V^{\gamma-1}$ = k
so t2 * (1/15)^ 1.4-1 = 5863/20
which gives me t2 = 866k.

=] ?

Last edited: Oct 16, 2011
3. Oct 16, 2011

### LawrenceC

T2/T1 = (V1/v2)^(k-1)

You know the volume ratio, T1, and you know k.

4. Oct 16, 2011

### ibysaiyan

thanks you very much! : ))))))))))))))))))))))))))))))

5. Oct 16, 2011

### ibysaiyan

Also at the end of the question it asks by how much factor has hte pressure risen.. which according to my calculations is ~ 44 times.

Is this correct too ?

6. Oct 16, 2011

### LawrenceC

Yes, that is what I get for two significant figures.

7. Oct 16, 2011