How Do You Calculate Temperature and Pressure in Isentropic Compression?

[bruce999]

Exam revision question. Help!

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).

 

[minger]

For part a: you will use the constant specific heat relationships. They are something like P1/P2 = (V2/V1)^k-1 note: That equation is probably not true, but the three formulas are in that same format. Knowing that compression ratio is V1/V2, you can easily plug that number into the formula given initial T and P to find final T and P.

for b: hmmmm...partial pressures and stuff...wow, I have no idea. I guess one would find the stoichiometric ratio, I believe it's ~14:1, then go from there. That's about all the help I got for that part.

 

[thepatientmental]

Hi there,

I can understand the stress and pressure of preparing for an exam, especially when facing a challenging question. Don't worry, I am here to help!

For part a), you can use the isentropic compression equation to solve for the final temperature and pressure. This equation is T2/T1 = (P2/P1)^((γ-1)/γ), where T is temperature, P is pressure, and γ is the ratio of specific heats (1.4 for air). You can plug in the given values and solve for T2 and P2.

For part b), you will need to use the specific heat ratio (γ) for a mixture of air and octane, which can be calculated using the mole fractions of each component. You can then use the same isentropic compression equation to solve for the final temperature and pressure.

Remember to pay attention to units and double-check your calculations. Also, make sure to review any relevant formulas and concepts before the exam. Good luck!