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How to convert a P-V diagram into T-S diagram?
Ref: https://edurev.in/question/701485/How-to-convert-a-P-V-diagram-into-T-S-diagram-

On P-V diagram, slope of an isotherm is more than the slope of an adiabatic curve.

Suppose, we have to draw curve ABCD(shown on P-V diagram) in T-s diagram

Now, DA is the first adiabatic curve.

Also, when we move towards A, Temperature increases. (See the first diagram --> we move from, say, T1 to T2)

Now, from A to B --> s increases and T increases as well !!!

So, B will be above A and also on the right of A....!!! (as above)

Now, BC is an adiabatic curve and when we move from B to C --> T decreases..!!!

But, T at C is above that of D.

Now, we shall join AB and CD by curves.

So, with the same logic we can convert any PV diagram into Ts diagram...!!!

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FAQs on P-V diagram and transform it into a T-S diagram - IITJAM - IIT JAM

1. What is a P-V diagram and how is it related to a T-S diagram?

Ans. A P-V diagram, also known as a pressure-volume diagram, is a graphical representation of the relationship between pressure and volume in a thermodynamic system. On the other hand, a T-S diagram, also known as a temperature-entropy diagram, represents the relationship between temperature and entropy in a system. Both diagrams are used to visualize the thermodynamic processes and properties of a system, but they focus on different variables. While a P-V diagram shows the changes in pressure and volume, a T-S diagram shows the changes in temperature and entropy.

2. How is a P-V diagram useful in understanding thermodynamic processes?

Ans. A P-V diagram is useful in understanding thermodynamic processes as it provides a visual representation of the changes in pressure and volume during different stages of a process. It helps in analyzing the work done by or on the system, the heat transfer, and the efficiency of the process. By studying the shape and characteristics of the P-V diagram, one can determine the type of process (isothermal, adiabatic, etc.) and gain insights into the behavior of the system.

3. How can a T-S diagram provide information about the efficiency of a thermodynamic cycle?

Ans. A T-S diagram provides information about the efficiency of a thermodynamic cycle by allowing us to analyze the heat transfer and work done during the cycle. The area enclosed by the cycle on the T-S diagram represents the net work done by the system. By comparing this area with the total heat added to the system, one can calculate the thermal efficiency of the cycle. Additionally, the shape and characteristics of the T-S diagram can indicate the presence of irreversibilities or losses in the cycle, which can affect its efficiency.

4. What are some common processes represented on a P-V diagram?

Ans. Some common processes represented on a P-V diagram include isothermal processes, adiabatic processes, constant volume processes, and constant pressure processes. In an isothermal process, the temperature remains constant, resulting in a curve that is a hyperbola on the P-V diagram. In an adiabatic process, there is no heat transfer, leading to a steeper curve on the diagram. A constant volume process is represented by a vertical line, indicating no change in volume, while a constant pressure process is represented by a horizontal line, indicating no change in pressure.

5. How can a T-S diagram be used to analyze the reversibility of a process?

Ans. A T-S diagram can be used to analyze the reversibility of a process by examining the shape of the curves representing the process. A reversible process is represented by a curve that is a smooth and continuous line on the T-S diagram. Any deviation from this smooth curve indicates irreversibilities in the process, such as heat transfer across a finite temperature difference or non-quasistatic behavior. The presence of irreversibilities leads to a non-smooth curve or a broken line on the T-S diagram, indicating a less efficient or irreversible process.

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