Thermal Properties: Pressure, Volume, Temp question

[wcbryant87]

Homework Statement

A Jaguar XK8 convertible has an eight-cylinder engine. At the beginning of its compression stroke, one of the cylinders contains 499 cm cubed of air at atmospheric pressure (1.01E5 Pa) and a temperature of 27.0 degrees C. At the end of the stroke, the air has been compressed to a volume of 46.2 cm cubed and the gauge pressure has increased to 2.72E6.

What is the final temperature

Homework Equations

P1*V1/T1 = P2*V2/T2

The Attempt at a Solution

I followed the equation that I posted above. Here is what it looked like.

(1.01E5 * 499 cm cubed)/ 27 = (2.72E6 * 46.2)/x

Solving for x, I got x = (2.72E6*46.2)/1866629.63 = 66.8 degrees C

Problem is, that answer is apparently wrong. Am I missing something here?

Thanks for the help!

 

[Lambduh]

Try changing your temperature to kelvin :)

 

[wcbryant87]

well it wants the answer in celcius. Does that equation have to be done with Kelvin units?

 

[xxChrisxx]

Were you given that equation? As you won't find T2 like that. Even if you use kelvin as the pv/pv is a ratio, it won't make any difference.

Hint: Expansion and compression is isentropic.

 

[wcbryant87]

No I wasn't given any equation. I thought that that one would work though because I was only missing one variable.

Do I use pv=nrt?

 

[xxChrisxx]

If you've got a book, look up isentropic compression.

pv^gamma = constant.

where gamma is the polytropic constant you'll have to find the relationship between temperature and anther variable.

 

[Gorz]

If you've got a book, look up isentropic compression.

pv^gamma = constant.

where gamma is the polytropic constant you'll have to find the relationship between temperature and anther variable.

Thats the Adiabatic process.

Calculate the mass of air in the cylinder from pv=mRT

Constants for air Cp=1005J/kgK, Cv=718J/kgK R=287J/kgK, calculate gamma from these.

Reaarange the equation for an adiabatic process to find T

 

[xxChrisxx]

its both acutally, as isentropic is adiabatic and reversible. to find the temperatre after compression you don't need the mass in the cylinder as it comes out in the wash.

the relationships for isentropic processes for ideal gases are listed in any thermo textbook. but as this is homework help I am not going to just give them out.