Does an Irreversible Adiabatic Process Defy the Equation PV^(gamma)=constant?

In summary, an irreversible adiabatic process is not an isentropic process, and is not described by the equation PV^\gamma=constant.
  • #1
asdf1
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Why doesn't an irreversible adiabatic process follow the equation,
PV^(gamma)=constant?
 
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  • #2
asdf1 said:
Why doesn't an irreversible adiabatic process follow the equation,
PV^(gamma)=constant?

Although some people here (i.e. my friend Andrew Mason) are of another "school of knowledge", I must say an irreversible adiabatic process is not an isentropic one, and so it is not described by your equation.
 
  • #3
Clausius2 said:
Although some people here (i.e. my friend Andrew Mason) are of another "school of knowledge", I must say an irreversible adiabatic process is not an isentropic one, and so it is not described by your equation.
For [itex]PV^\gamma = constant[/itex] to apply, the ideal gas law must apply at all times during the process. But this assumes that the system is at perfect thermodynamic equilibrium at all times during the process.

For an adiabatic gas expansion to be reversible, it must occur with an arbitrarily small pressure difference between the gas pressure and the external pressure. If this is the case, the work done by the gas in expanding ([itex]\int P_{gas}dv[/itex])is equal to the work done on the gas by the external pressure to return it to its original state ([itex]\int P_{ext}dv[/itex]) - hence it is reversible.

Typically an "irreversible adiabatic process" for an ideal gas is a process that occurs without exchange of heat with the surroundings but too rapidly for the relationship PV=nRT to apply during the process. The reason PV=nRT does not apply is because of the kinetic energy factor in the rapidly expanding or contracting gas.

My (mild) disagreement with friend Clausius2 is in calling all such processes adiabatic where kinetic energy is lost from the gas to the surroundings. If the gas expands rapidly and the resulting kinetic energy of the gas is ultimately transferred to the surroundings, I would say that the process is not adiabatic: heat (molecular kinetic energy) is effectively transferred to the surroundings.

AM
 
  • #4
hmm... that makes sense~
thanks! :)
 

1. What is an adiabatic process?

An adiabatic process is a thermodynamic process in which there is no transfer of heat or matter between a system and its surroundings. This means that the system is completely isolated and does not exchange energy with its surroundings, resulting in a change in its internal energy.

2. How is an adiabatic process different from an isothermal process?

An adiabatic process differs from an isothermal process in that it does not involve any heat exchange, whereas an isothermal process occurs at a constant temperature. In an adiabatic process, the system's internal energy changes due to work done by or on the system, while in an isothermal process, the system's internal energy remains constant.

3. What is the first law of thermodynamics and how does it relate to adiabatic processes?

The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or converted. In an adiabatic process, since there is no heat transfer, any change in the system's internal energy must be due to work done on or by the system. This is in line with the first law of thermodynamics.

4. What are some examples of adiabatic processes?

Some examples of adiabatic processes include the expansion or compression of a gas in a perfectly insulated container, the free expansion of a gas into a vacuum, and the flow of air over a mountain range or through a nozzle. These processes do not involve any heat transfer and therefore can be considered adiabatic.

5. Why are adiabatic processes important in thermodynamics?

Adiabatic processes are important in thermodynamics because they allow us to study the behavior of systems that are completely isolated from their surroundings. These processes also play a crucial role in understanding the efficiency of various thermodynamic cycles, such as the Carnot cycle, which operates under adiabatic conditions.

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