# Expansion of a Gas into a Vacuum

1. Jan 24, 2008

### kurebo

1. The problem statement, all variables and given/known data
A stop-cock which connects an evacuated flask with the atmosphere is opened and
air at 1 atm and 17°C (290 K) enters. (a) What will be the temperature of the air in the flask
before any heat has been transferred to the walls of the flask? Assume air to be a perfect
gas and its molal heat capacity at constant pressure to be 7.00 calories per degree.
Answer=132 °C (405 K)

2. The attempt at a solution

I started working on this under the assumption that it was a throttling question with constant enthalpy:
H2-H1=0
but I'm stuck at the point where you define enthalpy for each state. You can define the work done by the gas as:
w=int(Cv dT,T,290,T2) where Cv=Cp-R (Cp=7 cal/K;Cv=5.013 cal/K)

Any ideas on where to go?

Last edited: Jan 24, 2008
2. Jan 25, 2008

### stewartcs

Sounds like a free expansion of an ideal gas problem so the temperature change will be zero, i.e. the final temp is the same as the initial temp.

CS