What Happens to Gas Temperature in an Isothermal Expansion?

[maurice2705]

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?

 

[Andrew Mason]

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

 

[Liquidxlax]

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


P₁V₁^gamma = P₂V₂^gamma

if it is reversible and adiabatic, which it should be since you're given gamma?

 

[Andrew Mason]

yeah it's a werid problemP₁V₁^gamma = P₂V₂^gamma

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

 

[Liquidxlax]

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