a Gas expansion Thermodynamoic problem?

Hi, i just have a little confusion on a homework question.

I assume we know that when most gas expand, it absorbs heat and cools down.

The problem is:
If you have a solid sealed container, initially evacuated (vacuum).
and you drill a hole on a wall, the gas diffuse inside until it reaches atmospheric pressure, what is the temperature of the gas inside?

I dont really need the exact answer, but whats the equation? can anyone help?
Assume that i have a table that list out the entropy, specifific heat, and all those values that cant be caculated by math.

?2007-10-19T16:34:20Z

Favorite Answer

The initial entering of the atmosphere into a vacuum will be at high velocity resulting in a rapid decrease in pressure across the inlet hole (orifice).
Due to the 'Joules-Thompson' refrigeration effect, the sudden decrease in pressure causes cooling (expansion of gases). The air entering the container will cool down rapidly.
As the pressure in the container builds up, the pressure drop across the orifice (inlet hole) will decrease and eventually the internal pressure will equal that of the atmosphere.
As the pressure is increasing, the cooling effect is decreasing. The pressure increase causes temperature increase (reverse 'Joules-Thompson' effect and, the system will quickly equalise in both pressure and temperature.
Due to the rapidly changing parameters, calculation of the temperature and pressure changes isn't feasible and, as stated, when the system pressure stabilises at 14.7psi (or 760mmHg if you like), the temperature will also stabilise at that of the atmospheric air.

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crewdog032007-10-19T09:20:10Z

The basic equation is PV=nRT
P=pressure
V=volume
n=number of moles
R=constant
T=tempurature

you will use "change in pressure" and "change in temperature" for your case:

deltaP * V = n * R * deltaT

Just remember to use the right units when you use this equation. Units are all in absolute (e.g., Kelvin not Celcius)

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lnfrared Loaf2007-10-19T07:38:30Z

since pressure is directly proportional to the temperature

P1T1=P2T2

the temperature should be higher. sorry im not so sure about this :)

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Anonymous2007-10-19T07:47:15Z

i'm not sure but all i know is:
PV=RT
P1/P2=T2/T1

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