The ideal gas law for an adiabatic process

[garyd]

Homework Statement

Hi can someone please have a look at this question and let me know if I am on the right track, thanks.

A diesel engine requires no spark plug; instead the air in the cylinder is compresses so highly the fuel ignites spontaneously on injection to the cylinder.

Q. If the air is initially at 293K and then is compressed adiabatically by a factor of 15, what final temperature is attained ?( Just prior to injection, also consider air as an ideal gas)
Variables:
T1=293K
V1= 1
V2=1/15
T2=?

Homework Equations

T1 *V1^(Ƴ-1) = T2* V2^(Ƴ-1)

The Attempt at a Solution

Above relationship applies as process is adiabatic?

293× (1^(1.4-1)/ (1/15^(1.4-1) ))=866K

 

[BvU]

Looks good to me. Why the doubtful question mark ?

 

[garyd]

Why the doubtful question mark ?

Confidence, I am learning to trust the equations.

Another part of the question is; by what factor has the pressure increased? Can I use P V^Ƴ=constant, with p1=1, multiplied by ratio of V1/V2, both to the power of Ƴ? ans=2.95

 

[BvU]

Re post 1: T1 *V1^(Ƴ-1) = T1* V1^(Ƴ-1) I read T1 *V1^(Ƴ-1) = T2* V2^(Ƴ-1) which looks good.

Re post 3: numerically I get something different, but then I use $\gamma$, not $\gamma -1$ as the exponent... Big difference !

 

[garyd]

Yes I was using wrong exponent, 44 is the correct factor, thanks.

 

[Andrew Mason]

Confidence, I am learning to trust the equations.

Another part of the question is; by what factor has the pressure increased? Can I use P V^Ƴ=constant, with p1=1, multiplied by ratio of V1/V2, both to the power of Ƴ? ans=2.95

Once you have the temperature worked out, just use the ideal gas law: PV=nRT

P1V1/T1 = P2V2/T2

P2/P1 = (V1/V2)(T2/T1)

AM