How Do You Calculate Gamma in Thermodynamics?

[VitaX]

Homework Statement

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.

 

[Andrew Mason]

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

 

[VitaX]

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?

 

[Andrew Mason]

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

 

[rwisz]

As a scientist, my first step would be to clarify any uncertainties or questions I have about the problem. I would start by reviewing the given equations and making sure I understand the variables and their meanings. I would also check if any additional information or context is provided in the homework statement.

Next, I would try to identify what type of problem this is and what approach would be best suited to solve it. In this case, it seems like a thermodynamics problem involving adiabatic processes and efficiency. I would then review my notes or textbook to refresh my understanding of these concepts and how they relate to each other.

Since the task is to find gamma, I would start by setting up the equation γ = Cp/Cv and plugging in the values given in the problem. If any values are missing, I would use the given equations and information to solve for them. For example, if the initial and final temperatures are not given, I could use the efficiency equation ε = W/Qh to solve for them.

If I am still unsure about how to approach the problem or how to interpret the given information, I would reach out to my peers or professor for assistance. Collaboration and discussion can often lead to a better understanding of the problem and potential solutions.

In summary, as a scientist, I would approach this problem by clarifying any uncertainties, reviewing the relevant concepts and equations, and seeking assistance if needed. By following a systematic and methodical approach, I would be able to solve the problem and provide a well-thought-out response.