Why Use Constant Volume for This Adiabatic Equation?

In summary, using constant volume in the adiabatic equation simplifies calculations by eliminating the need to account for changes in pressure and temperature that occur during volume changes. This approach allows for a more straightforward analysis of thermodynamic processes, particularly in closed systems where the volume remains unchanged. By maintaining a constant volume, the relationship between pressure and temperature can be easily derived, aiding in the understanding of adiabatic processes and their applications in various scientific and engineering fields.
  • #1
abdossamad2003
68
4
Why is this equation (red sign) written in constant volume and not in constant pressure?
Screenshot 2023-11-07 20.46.13.png
 
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  • #2
Because this is what counts for the internal energy of the gas.
 
  • #3
I was not convinced why internal energy should be written for heat capacity in constant volume. This process does not take place in constant volume, and if it is in constant volume, the change in internal energy must be zero.
 
  • #4
The work is done on the adiabatic system, that is, it is not in constant volume, in my opinion, constant pressure seems more reasonable
 
  • #5
What is your understanding of the effect of volume on the internal energy of an ideal gas?
 
  • #6
The effect of volume on the internal energy is meaningful only in diabatic processes, for example, when heat is added to the system at a constant volume and the internal energy increases, but in adiabatic processes, when the volume is constant, the work done on the system is zero and the incoming heat is zero, as a result of the change in energy Internal is zero.
 
  • #7
abdossamad2003 said:
The effect of volume on the internal energy is meaningful only in diabatic processes, for example, when heat is added to the system at a constant volume and the internal energy increases, but in adiabatic processes, when the volume is constant, the work done on the system is zero and the incoming heat is zero, as a result of the change in energy Internal is zero.
This is totally incorrect. Irrespective of the process, the internal energy of an ideal gas depends only on temperature, and not volume.
 
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  • #8
abdossamad2003 said:
I was not convinced why internal energy should be written for heat capacity in constant volume. This process does not take place in constant volume, and if it is in constant volume, the change in internal energy must be zero.
See, e.g., here: https://en.wikipedia.org/wiki/Internal_energy#Internal_energy_of_the_ideal_gas. ##C_V## is the coefficient of proportionality between internal energy on one hand and number of moles and temperature of the gas on the other hand.
 

FAQ: Why Use Constant Volume for This Adiabatic Equation?

What is an adiabatic process?

An adiabatic process is a thermodynamic process in which there is no heat exchange between the system and its surroundings. This means that all the energy transfer is in the form of work, and the total heat energy of the system remains constant.

Why is constant volume used in some adiabatic process equations?

Constant volume is used in some adiabatic process equations to simplify the analysis of the system. When volume is constant, there is no work done by the system (since work is a product of pressure and volume change), making it easier to focus on changes in internal energy and temperature.

Why is constant pressure not typically used in adiabatic process equations?

Constant pressure is not typically used in adiabatic process equations because, in an adiabatic process, the system's pressure and volume are interdependent and change dynamically. Using constant pressure would not accurately reflect the behavior of the system, as it would imply heat exchange to maintain constant pressure, which contradicts the definition of an adiabatic process.

How does the first law of thermodynamics apply to adiabatic processes?

The first law of thermodynamics states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. In an adiabatic process, since there is no heat exchange (Q = 0), the change in internal energy is equal to the negative of the work done by the system (ΔU = -W).

Can adiabatic processes occur at constant pressure under any circumstances?

Adiabatic processes at constant pressure are theoretically possible but highly impractical in real-world scenarios. To maintain constant pressure in an adiabatic process, the system would need to perform or have work done on it in a manner that precisely compensates for changes in volume and internal energy without any heat exchange, which is extremely challenging to achieve.

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