How Do You Calculate Gamma in Thermodynamics?

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Homework Help Overview

The discussion revolves around calculating the gamma (γ) value in thermodynamics, specifically in the context of adiabatic processes and gas efficiency. The original poster is attempting to determine the type of gas present based on the gamma value, but expresses confusion regarding the setup due to a lack of given values and difficulty with graph interpretation.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the relationship between gamma and the specific heat capacities (Cp and Cv) and explore the use of adiabatic conditions to derive necessary values. Questions arise about the ideal gas law and how to calculate temperatures at various points (A, B, C, D) in terms of initial pressure and volume.

Discussion Status

Some participants have provided guidance on calculating efficiency and suggested methods for finding temperatures at different points. There is an ongoing exploration of relationships between these temperatures, but no consensus has been reached on the overall approach.

Contextual Notes

Participants note the absence of specific values and the challenge of interpreting graphs, which may impact their ability to proceed with calculations. The original poster's uncertainty about the setup indicates potential gaps in understanding the problem context.

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Homework Statement



259k8xz.png


Homework Equations



γ = Cp/Cv
ε = W/Qh
PiVi^γ = PfVf^γ

The Attempt at a Solution



I know I have to find the gamma firstly in order to determine what type of gas is present here. And to do that I have to pick one of the adiabatic processes. I chose to do AD. But I am literally lost at how to set this up because we aren't really given values and reading graphs is not one of my strong suits in physics.

Note - The green in picture means "Correct". I just input 1 for the gas and .25 for the efficiency off guessing.
 
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VitaX said:
γ = Cp/Cv
ε = W/Qh
PiVi^γ = PfVf^γ

The Attempt at a Solution



I know I have to find the gamma firstly in order to determine what type of gas is present here. And to do that I have to pick one of the adiabatic processes. I chose to do AD. But I am literally lost at how to set this up because we aren't really given values and reading graphs is not one of my strong suits in physics.
To calculate the efficiency use:

ε = W/Qh = (Qh-Qc)/Qh

First, find the temperatures at A, B, C and D in terms of P0, and V0.

Then using the adiabatic condition expressed in terms of T and V, work out Cp/Cv. You will then be able to find Qh and Qc from the graph (for the constant pressure processes dQ = nCpdT) in terms of P0 and V0.

AM
 
Last edited:
Andrew Mason said:
To calculate the efficiency use:

ε = W/Qh = (Qh-Qc)/Qh

First, find the temperatures at A, B, C and D in terms of P0, and V0.

Then using the adiabatic condition expressed in terms of T and V, work out Cp/Cv. You will then be able to find Qh and Qc from the graph (for the constant pressure processes dQ = nCpdT) in terms of P0 and V0.

AM
Do you mean using the ideal gas law PV = nRT?

Point A Temperature:
PoVo = 1.55*8.31*T
T = PoVo/12.8805

Point D Temperature:
(Po/32)*8Vo = 1.55*8.31*T
T = PoVo/51.522

Is this what you were saying?
 
VitaX said:
Do you mean using the ideal gas law PV = nRT?

Point A Temperature:
PoVo = 1.55*8.31*T
T = PoVo/12.8805

Point D Temperature:
(Po/32)*8Vo = 1.55*8.31*T
T = PoVo/51.522

Is this what you were saying?
Yes. Calculate T at B and C now using the same method. But show the relationships between them:

T_D = 8T_A/32 = T_A/4

AM
 

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