Thermo Exam Question: Estimate Temp & Pressure After Compression

[bruce999]

Hello.
I have a thermodynamics exam tomorrow. This is a past exam question and I'm not doing very well with it. If anyone has any ideas please help!

A charge enters a spark ignition engine at 330K and 1 bar, and is isentropically compressed through a ratio of 7:1. Estimate the temp and pressure at the end of the compression, taking the charge to be:
a) pure air with constant specific heat.
b) a stoichiometric mixture of air and octane(C8H18) with variable specific heats (neglect residual gases).

 

[Astronuc]

Well, I guess the test was yesterday. How'd you do?

Anyway:

1) First of all, you must understand the significance of isentropic.

Then the compression is 7:1 so the charge, air, is compressed to 7 bar.

Then solve the temperature using the appropriate equation.

2) similar to 1) but now a mixture of stoichiometric mixture of air and octane(C8H18) - so determine the partial pressures and composition, which influences specific heat. Same compression ratio.

 

[minger]

Well, I guess the test was yesterday. How'd you do?

Anyway:

1) First of all, you must understand the significance of isentropic.

Then the compression is 7:1 so the charge, air, is compressed to 7 bar.

Then solve the temperature using the appropriate equation.

2) similar to 1) but now a mixture of stoichiometric mixture of air and octane(C8H18) - so determine the partial pressures and composition, which influences specific heat. Same compression ratio.

That's not true. You need to use the isentropic relations. Compression ratio is a ratio of volumes, not pressures. The three isentropic relations are:
(T2/T1) = (v1/v2)^(k-1)
(T2/T1) = (P2/P1)^(k-1)/k
(P2/P1) = (v1/v2)^k
These are estimations based on constant specific heats. To be more accurate and use variable specific heats, you will need to use vr and Pr, relative specific volume and relative pressure. However, since the question says estimate, using the isentropic relations should be good. So, if (v1/v2) = 7, then P2 = P1*7^1.4 (k = 1.4 for air). Likewise, T2 = T1*7^0.4

As said in the other thread, I'm not 100% sure how to do part b off the top of my head.

 

[Astronuc]

Thanks for the correction minger, and my apology to bruce999

A good discussion of compression and expansion is found at:

http://www.grc.nasa.gov/WWW/K-12/airplane/compexp.html