Thermodynamics - Temperature/Entropy diagram

[Jalo]

Homework Statement

If I have a diagram P-V how can I turn it into a T-S diagram? (Temperature-Entropy)

Homework Equations

The Attempt at a Solution

I know that Q=TdS <=> dS = Q/T

If a process is isothermic I'll just draw a line. If the process is adiabatic I'll draw a vertical line (constant S). For any other process I don't know what to do...

Any help would be highly appreciated! If you have a book that explains this it would be perfect!

 

[anathema]

Thank you for your question. Converting a P-V diagram to a T-S diagram can be done using the following steps:

1. Identify the process: First, you need to identify the type of process shown in the P-V diagram. Is it isothermal, adiabatic, isobaric, or some other type of process? This will help you determine the appropriate equations to use.

2. Use the ideal gas law: The ideal gas law, PV = nRT, can be used to calculate the temperature at different points on the P-V diagram. Simply rearrange the equation to solve for T: T = PV/nR. This will give you the temperature values for each point on the diagram.

3. Use the entropy equation: As you mentioned in your attempt at a solution, the equation dS = Q/T can be used to calculate the change in entropy for a process. If the process is isothermal, then the change in entropy (dS) will be equal to the heat transfer (Q) divided by the temperature (T). If the process is adiabatic, then dS will be equal to zero.

4. Plot the points on a T-S diagram: Using the temperature and entropy values calculated in step 2 and 3, plot the points on a T-S diagram. The temperature will be on the horizontal axis (S) and the entropy on the vertical axis (T). Connect the points to create a line, which will represent the process on the T-S diagram.

I hope this helps! If you need further clarification or have any other questions, please don't hesitate to ask. Additionally, any thermodynamics textbook should have more information and examples on converting between P-V and T-S diagrams. Best of luck with your studies!