Which Thermodynamic Process Governs Gas Filling an Evacuated Space?

[gfd43tg]

I am not sure what assumption I can make for this problem and why it's valid. It certainly isn't isochoric. Since the volume changes, I conclude its not isobaric either (P should decrease). I don't think it's adiabatic because the part (b) clearly hints that it is not reversible in part (a). That leaves me with isothermal. But if a gas expands, it's temperature should decrease.

Therefore, I don't know which of these processes I could use to solve for the final temperature.

 

[SteamKing]

What about PV = nRT?

If you expanded some gas into an evacuated chamber, can you think of a way the gas would 'unexpand' itself back to its original state?

 

[gfd43tg]

Right. Well, if I do

P1V1 = RT1
P2V1 = RT2

then I get P1/T1 = P2/T2.

However, I only have P1 and T1.

 

[Chestermiller]

If you think of the tank as a black box, then no heat enters or leaves the tank, and no work is done on it. So what does that tell you about the change in internal energy of its contents?

Chet

 

[gfd43tg]

The internal energy is constant, so it is isothermal.

It is a bit troubling to think about gas expanding at constant temperature without having heat removed or added in order to maintain the constant T.

 

[Chestermiller]

The internal energy is constant, so it is isothermal.

It is a bit troubling to think about gas expanding at constant temperature without having heat removed or added in order to maintain the constant T.

In the dynamic transient process that occurs in the tank before the system finally equilibrates, several things are happening, including local expansion against adjacent gas (tendency to cool), local recompression in some regions (tendency to heat), local acceleration to develop kinetic energy, and viscous dissipation of kinetic energy (tendency to heat). The overall final net effect is no temperature change.

Chet