Calculating diesel cycle efficiency

[newe999]

Homework Statement

given:
diesel cycle,
P1V1 P2V2 P3V3 P4V4 - all known
T1 = 20°c
specific heat capacity constant pressure = 1000j/kgk
specific gas constant = 287j/kgk
compression index = 1.4

Homework Equations

heres where i am stuck!

The Attempt at a Solution

Hi all, I am unsure where to go with this one. I am guessing that i need to work out T2.T3.T4, but can't find in any of my notes where any of the γ or R come into play or how to get T2T3T4?. i have already calculated the work done for each stage in a previous part of the question so i have that. Just not too sure on where to go from here to calculate the efficiency of the cycle?
Also sorry if the post isn't written correctly this is my first post on here

 

[KataKoniK]

Hello,

Thank you for reaching out for help with this problem. It seems like you are on the right track in trying to calculate the efficiency of the diesel cycle. Here are some steps you can follow to solve this problem:

1. Use the ideal gas law (PV = nRT) to calculate the number of moles (n) of gas in the system. You can use the given pressure and volume values to find the initial number of moles (n1) and final number of moles (n4). Note that the temperature at state 1 (T1) is also given.

2. Use the given specific gas constant (R) to find the specific heat capacity at constant volume (Cv). This can be done using the equation Cv = R/(γ-1), where γ is the compression index given in the problem.

3. Use the first law of thermodynamics (ΔU = Q - W) to find the change in internal energy (ΔU) for each stage of the cycle. You can use the calculated values of work done in the previous part of the question to find the heat added (Q) for each stage.

4. Use the definition of efficiency (η = W/Qh) to find the efficiency of the cycle. Qh represents the heat added during the isobaric (constant pressure) processes, which can be calculated using the values of specific heat capacity at constant pressure (Cp) and the change in temperature (ΔT).

I hope this helps guide you in the right direction. Let me know if you have any further questions. Good luck with your calculations!