What Happens to Gas Temperature in an Isothermal Expansion?

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Homework Help Overview

The problem involves a thermally isolated chamber that is initially at low pressure and is vented to fill with air up to atmospheric pressure. Participants are discussing the implications of this process on the temperature of the gas in the chamber immediately after the valve is closed, with specific reference to thermodynamic principles.

Discussion Character

  • Conceptual clarification, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are questioning whether the air surrounding the chamber is at atmospheric pressure and how this affects the temperature of the gas entering the chamber. There are discussions about the nature of the expansion, including whether it is reversible or adiabatic, and the implications of work done by the gas.

Discussion Status

The discussion is exploring various interpretations of the problem, particularly regarding the assumptions about the process being isothermal or adiabatic. Some participants express confusion about the conditions of the problem and the expected temperature change, while others suggest that the rapid free expansion indicates no temperature increase.

Contextual Notes

There is uncertainty regarding the initial conditions of the gas and the nature of the expansion, with references to the specific heat ratio and the implications of work done during the expansion process. Participants are also reflecting on the source of the problem and its context.

maurice2705
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Homework Statement


A thermally isolated chamber is pumped down to a very low pressure. At some point, the chamber is vented slowly so that it is filled with air up to atmospheric pressure, whereupon the valve is closed. The temperature of the air surrounding the chamber is T0=300 K. What is the temperature T of the gas in the chamber immediately after the valve is closed. γ=Cp/CV=7/5 for air. (ANS: 420K)


Homework Equations


Has the air done any work? Does low pressure means vacuum?


The Attempt at a Solution


T0/V0=T/V But what is V0?
 
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maurice2705 said:

Homework Statement


A thermally isolated chamber is pumped down to a very low pressure. At some point, the chamber is vented slowly so that it is filled with air up to atmospheric pressure, whereupon the valve is closed. The temperature of the air surrounding the chamber is T0=300 K. What is the temperature T of the gas in the chamber immediately after the valve is closed. γ=Cp/CV=7/5 for air. (ANS: 420K)
I am not clear on the facts. Is the air surrounding the chamber at atmospheric pressure (ie. open to the atmosphere)? If so, there is no change in temperature when it fills up the chamber. I don't see how the temperature of the gas entering the chamber will increase, in any event.

Where did you get this problem?

AM
 
Andrew Mason said:
I am not clear on the facts. Is the air surrounding the chamber at atmospheric pressure (ie. open to the atmosphere)? If so, there is no change in temperature when it fills up the chamber. I don't see how the temperature of the gas entering the chamber will increase, in any event.

Where did you get this problem?

AM

yeah it's a werid problem


P1V1gamma = P2V2gamma

if it is reversible and adiabatic, which it should be since you're given gamma?
 
Liquidxlax said:
yeah it's a werid problemP1V1gamma = P2V2gamma

if it is reversible and adiabatic, which it should be since you're given gamma?
But it is not reversible. This is a rapid free expansion as the outside air fills the empty chamber. In any event, it is an expansion. So if any work is done by the gas filling the chamber, the internal energy will decrease. I don't see how temperature can possibly increase.

AM
 
Andrew Mason said:
But it is not reversible. This is a rapid free expansion as the outside air fills the empty chamber. In any event, it is an expansion. So if any work is done by the gas filling the chamber, the internal energy will decrease. I don't see how temperature can possibly increase.

AM

whoops i missed that, so yeah you're right there is no way the temp could increase. It almost sounds like a similar process in which they liquify hellium
 

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