Polytropic Equation: Is Temperature Constant?

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In summary, the equation pV^n=c is used to describe polytropic thermodynamic processes, which do not necessarily have constant temperature or negligible heat transfer. This equation was derived by recognizing that there can be other processes besides isothermal and adiabatic that follow the same mathematical form, and the term "polytropic" was coined to describe these processes. This information is from "Thermodynamics" 5th Edition by Wark, page 664.
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jaredokie
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Is temperature constant in a polytropic thermodynamic process? The equation pv^n=c leads me to believe so. But logic tells me otherwise. Its not isothermal or adiabatic. Did they derive this equation from using log transforms when analyzing gas experiments?
 
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A polytropic process does not require the heat transfer to be negligible. The process is following a relationship between equilibrium states. The equation is restricted to a quasistatic process for a simple compressible gas system.

The above is taking from "Thermodynamics" 5th Edition by Wark. Page 664
 
  • #3
But how did they come up with the equation pV^n=c?
I can find any derivation for that equation. I'm trying to understand how the equation was formed.
 
  • #4
jaredokie said:
But how did they come up with the equation pV^n=c?
I can find any derivation for that equation. I'm trying to understand how the equation was formed.
People noted that, for an isothermal process, n=1 and for an adiabatic process, n=γ. So they figured that, if the temperature is controlled properly, there can be other processes which satisfy a p-v equation of the specified mathematical form. They coined the term "polytropic" to refer to such processes.
 
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The answer to whether temperature is constant in a polytropic thermodynamic process depends on the specific conditions and assumptions of the process. The polytropic equation, pv^n=c, does not necessarily imply that temperature is constant. It simply represents a relationship between pressure (p), volume (v), and a constant (c) raised to a power (n). The value of n determines the type of process (e.g. isothermal, adiabatic, polytropic) and can vary depending on the system and conditions.

In a polytropic process, temperature can change depending on the value of n. For example, if n=1, the process would be isothermal and temperature would remain constant. However, if n does not equal 1, temperature will change.

The derivation of the polytropic equation does not necessarily involve log transforms. It can be derived from the first law of thermodynamics and the ideal gas law. The specific values of n for different processes can also be derived from the second law of thermodynamics.

In conclusion, the polytropic equation does not necessarily imply that temperature is constant. The value of n must be considered to determine the behavior of temperature in a polytropic process.
 

What is the Polytropic Equation?

The Polytropic Equation is a mathematical equation used in thermodynamics to describe the relationship between pressure, volume, and temperature of a gas undergoing a process. It is often written as PV^n = constant, where n is the polytropic index.

What does it mean when the Polytropic Equation says "temperature is constant"?

When the Polytropic Equation says "temperature is constant", it means that the temperature of the gas undergoing the process remains the same throughout. This indicates that there is no transfer of heat into or out of the system.

How is the Polytropic Equation used in real-world applications?

The Polytropic Equation is used in various industries, such as in the design and analysis of compressors, turbines, and other mechanical systems. It is also used in the study of atmospheric processes and in the development of gas laws.

What is the polytropic index?

The polytropic index, represented by the symbol n, is a numerical value that describes the type of process a gas undergoes. It can have a range of values from 0 to infinity, with certain values having specific meanings. For example, a value of n = 1 represents an isothermal process, while n = 0 represents an isobaric process.

Are there any assumptions made in the Polytropic Equation?

Yes, the Polytropic Equation makes certain assumptions, such as the gas being ideal, the process being reversible, and the polytropic index remaining constant throughout the process. These assumptions may not hold true in all real-world scenarios, but the equation is still a useful approximation in many cases.

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