Adiabatic process - Diesel engine

[ibysaiyan]

Homework Statement

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?

Homework Equations

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

Internal energy = Work done.

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 ?

 

[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...

How about this :
TV^{\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.

=] ?

 

[LawrenceC]

Your answer is correct. Assume isentropic so exponent is specific heat ration. Your equation is:

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

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

 

[ibysaiyan]

your answer is correct. Assume isentropic so exponent is specific heat ration. Your equation is:

T2/t1 = (v1/v2)^(k-1)

you know the volume ratio, t1, and you know k.

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

 

[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 ?

 

[LawrenceC]

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

 

[ibysaiyan]

Thanks for your help!