An ideal simple gas turbine has a compression ratio of 5. What is its

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Discussion Overview

The discussion revolves around a homework problem involving an ideal simple gas turbine with a specified compression ratio of 5. Participants explore how to calculate the efficiency, work ratio, and heat rejection based on given parameters, including the turbine's power output and the compressor's power requirement.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant expresses uncertainty about how to find the ratio of specific heats, γ, and mentions the need to use the provided equations.
  • Another participant questions whether additional information about the compressor is available beyond the pressure ratio.
  • A later reply provides additional context, stating that the turbine produces 6 MW and the compressor requires 2 MW, suggesting these values are relevant for calculations.
  • One participant asserts that the pressure ratio alone is insufficient to determine the ratio of specific heat capacities.
  • Another participant requests the full problem statement to clarify what is being asked after "What is its ...".
  • After receiving the complete problem statement, a participant identifies the ratio of specific heats for air as 1.4 and indicates they have made progress in solving the problem.
  • A participant raises a question about how to calculate the heat rejected by the turbine.
  • One participant notes that the turbine's efficiency is not 1.0 and explains that the efficiency relates the work output to the total heat input.

Areas of Agreement / Disagreement

Participants do not reach a consensus on how to approach the problem, with some expressing uncertainty about the necessary parameters and calculations. Multiple viewpoints on the sufficiency of the provided information and the calculation methods remain evident.

Contextual Notes

The discussion highlights limitations in the information provided, particularly regarding the assumptions needed to calculate the efficiency and heat rejection. The dependence on the specific heat ratio and the implications of turbine efficiency are also noted as unresolved aspects.

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Homework Statement


An ideal simple gas turbine has a compression ratio of 5. What is its


Homework Equations


c=r(γ-1/γ)
η=1-(1/c)

The Attempt at a Solution


I'm stuck, I think I need to use the above equations and possibly more. I just don't know how to find a value for the ratio of specific heats,γ.
 
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Do you have any other information about the compressor apart from its pressure ratio?
 


rock.freak667 said:
Do you have any other information about the compressor apart from its pressure ratio?

Yeah:
"The turbine
produces 6 MW (gross) and the compressor requires 2 MW to drive it."
It's just put after the question, so I assumed I need to use the compression ratio which is 5.
 


Given the pressure ratio alone, I don't think you can find the ratio of the specific heat capacities.

I am assuming that is what you were asked to find.
 


Can you post the entire text of the problem? It looks like something is missing after
"What is its ..."
 


SteamKing said:
Can you post the entire text of the problem? It looks like something is missing after
"What is its ..."

An ideal simple gas turbine has a compression ratio of 5. What is its efficiency? If the turbine
produces 6 MW (gross) and the compressor requires 2 MW to drive it, what is the work ratio and how much heat is
rejected?
 


The ratio of specific heats is that for air, which is 1.4
 


SteamKing said:
The ratio of specific heats is that for air, which is 1.4

I've done it now thanks!

But how do I calculate the heat rejected? :/
 


I assume that the efficiency for the turbine was not 1.0. You know how much work output was obtained from the turbine. The efficiency of the turbine relates the output to the total heat input.
 

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