Thermodynamics gas turbine question

[bkh5074]

Homework Statement

Air enters a gas turbine at 1600K and exits at 100kPa and 830K. The turbine efficiency is 85%. Determine the turbine inlet pressure?

Homework Equations

(I used 3 different methods and got a similar answer. I just don't understand if I was correct in assuming something.)

P=pressure, T=temp, s=entropy

First I used the Relative Pressure to find P1. P1=P2*(Pr1/Pr2)

Second I used the entropy change approximate analysis. (s2=s1 this is what I assumed)

s2-s1=0=cp_avg*Ln(T2/T1)-R*Ln(P2/P1) : Rearrange to solve for P1

Third I used EES which is basically assuming s2=s1, and used T1 and s1 to find P1

The Attempt at a Solution

First method: P1=P2*(Pr1/Pr2) P2 is given = 100kPa, I used the table to find Pr1 and Pr2 from the Temperatures given. P1=100*(791.2/55.1) = 1435.93kPa


Second method: cp_avg = 1.163, R = 0.287
(1.163)*Ln(830/1600)-(0.287)*Ln(100/P1)
P1=1428.694kPa

Third using EES and I got P1=1435.048kPa

So basically I got the same answer each time, but I wasn't sure if I was correct to assume s2=s1. The problem doesn't specify it's an Isentropic process. Am I to assume that is this case? I don't think that the turbine efficiency is any help either.
Or maybe I'm doing this all totally wrong, My Thermo Professor goes through class so fast and I just try my best to follow along and understand stuff. That's why I joined this forum for some extra help.

Thanks to all,
BKH

 

[KataKoniK]

Hello BKH,

Based on the information given, it is reasonable to assume that the process is isentropic because the turbine efficiency is given. In an isentropic process, the entropy remains constant, which is why you were able to use the equation s2-s1=0 to solve for P1. Your methods and calculations seem correct, and it is good that you got similar answers each time. This shows that your calculations are consistent and accurate.

One thing to note is that the turbine efficiency is defined as the ratio of the actual work output to the ideal work output. So if you want to include the turbine efficiency in your calculations, you could use the equation W_actual = W_ideal * efficiency, where W_actual is the actual work output, W_ideal is the ideal work output, and efficiency is the turbine efficiency. This would give you a slightly different answer for P1, but it would still be in the same range as your previous calculations.

Overall, it seems like you have a good understanding of the concepts and your calculations are correct. Keep up the good work! If you have any further questions or need clarification, don't hesitate to ask.