Temperature Change in Partitioned Tank with Ideal Gas Upon Removal of Partition

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Discussion Overview

The discussion revolves around the temperature change in a partitioned tank containing an ideal gas when the partition is removed, contrasting this with the temperature drop observed when an aerosol spray can is discharged. The scope includes thermodynamic principles, specifically focusing on free expansion and energy conservation.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions why the temperature change is zero during the free expansion of an ideal gas when the partition is removed, suggesting it contradicts the cooling effect observed with aerosol cans.
  • Another participant explains that in free expansion, the gas does not perform work and there is no heat exchange with the environment, leading to no change in internal energy and thus no change in temperature.
  • A participant clarifies that the temperature drop in an aerosol can is due to the work done against atmospheric pressure, which causes the gas to lose kinetic energy and thus temperature.
  • Another participant challenges the previous explanation, stating that even in a vacuum, a can would still feel colder when sprayed, attributing this to the conservation of energy and the loss of heat energy from the remaining propellant molecules.
  • It is noted that if the propellant is a liquid, the cooling effect is more pronounced due to the latent heat of vaporization absorbing environmental heat.

Areas of Agreement / Disagreement

Participants express differing views on the mechanisms behind temperature changes in the scenarios discussed. While some agree on the principles of free expansion and energy conservation, others contest the explanations regarding the cooling effect of aerosol cans, indicating that multiple competing views remain unresolved.

Contextual Notes

The discussion includes assumptions about ideal gas behavior and thermodynamic principles that may not account for all real-world conditions, particularly in the case of aerosol cans and the effects of phase changes in propellants.

74baja
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Hi all,

Sorry if this is posted in the wrong place, I'm new here.
I have a thermodynamics question. Why is the temperature change 0 in the case of a partitioned tank containing an ideal gas when the partition is removed? This seems to run counter to the idea of an aerosol spray can getting cold when it is discharged.

Thank you
 
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74baja said:
Hi all,

Sorry if this is posted in the wrong place, I'm new here.
I have a thermodynamics question. Why is the temperature change 0 in the case of a partitioned tank containing an ideal gas when the partition is removed? This seems to run counter to the idea of an aerosol spray can getting cold when it is discharged.

Thank you

Welcome to PF, 74baja! :smile:

It is called "free expansion" (look it up).

The expanding gas does not do any work, since there is no counter pressure.
Since there is also no exchange of heat with the environment, the change in internal energy is zero (dU=dQ+dW=0).
This is conservation of energy.

Since the internal energy of an ideal gas depends only on T (U=nCvT), T must have remained constant.
 
I see, thank you. So, the change in temperature when a can is discharged into the atmosphere is due to the opposing pressure of the atmosphere, and the work that the can gas must do to overcome it?

Thanks
 
Yes.
The expanding gas from the can has to push the opposing air away.
As a consequence the molecules lose kinetic energy, which means that the temperature drops.
 
74baja said:
I see, thank you. So, the change in temperature when a can is discharged into the atmosphere is due to the opposing pressure of the atmosphere, and the work that the can gas must do to overcome it?

Thanks

No. Even if you sprayed into a vacuum, you would feel a colder can.

By conservation of energy the kinetic energy acquired by the ejected propellant molecules has to come from somewhere, and that somewhere is the loss of heat energy (3kT/2 per molecule) of the remaining pressurized propellant.

If the propellant is a liquid, the effect is much more pronounced since then the latent heat of vaporization is the major absorber of environmental heat. A can of freon (like you can't get any more) is a good example. So is butane lighter fluid.
 

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