How Does Thermodynamics Apply to Jet Engine Functionality?

[anony]

Homework Statement

http://img183.imageshack.us/img183/3628/jetlf0.jpg


http://img393.imageshack.us/img393/1759/jet2iu4.jpg

Homework Equations

The Attempt at a Solution

H = U + pV is the enthalpy, and hence the enthalpy per unit mass is h = U/m + pV/m which I have simplified to 7/2 RT/M

I am then able to derive the expression in part b).

Part c) though I'm very confused about, and then moving onto d) I'm pretty lost. I realize that in part say, to get change in T = 2Mq/7R, I can either set vf = vi = 0, or just simply vf = vi works too (where vf is final velocity and vi initial velocity). If someone could just point me in the right direction, that'd be awesome.

For part d) dQ = 0 as its adiabatically compressed. Work done on the gas is p dV, and so dU = dQ + dW = pdV. p isn't constant, so I tried to rewrite as dU = nR dT (going for the long shots here hoping it will take me somewhere). Seeing as I seem to be going completely along the wrong lines, I'm not going to carry on..

Any help is appreciated, thanks.

 

[Jhero]

Thank you for sharing your attempt at solving the problem. It seems like you have a good understanding of the concept of enthalpy and how to derive the expression in part b). However, I can see where you might be getting stuck in parts c) and d). Let me offer some guidance that might help you progress in your solution.

For part c), you are correct in saying that the change in temperature can be calculated using the equation ΔT = 2Mq/7R. However, you need to consider the initial and final velocities of the gas in order to calculate the change in internal energy. Remember that internal energy is a state function, meaning it only depends on the initial and final states of the system, not the path it takes to get there. Therefore, you can use either the initial or final velocity to calculate the change in internal energy, but not both.

For part d), you are on the right track by considering the work done on the gas and the change in internal energy. However, you need to consider the specific heat capacity at constant volume (Cv) instead of the ideal gas constant (R). This is because the gas is being compressed adiabatically, meaning there is no heat exchange and therefore no change in entropy (ΔS = 0). This leads to the equation dU = Cv dT. From there, you can use the equation for work done on the gas, dW = -p dV, to solve for the change in temperature.

I hope this helps guide you in the right direction. Remember to always think about the physical meaning of the equations and how they relate to the problem at hand. Good luck with your solution!