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Question
An isolated chamber with rigid walls is divided into 2 equal compartments, one contains gas and other in vacuum. The partition between compartment ruptures. After some time, the temperature and pressure are found uniform through out the chamber.

a) If the filled compartment initially contained an ideal gas of constant heat capacity at 1MPa and 500K. What are final temp. and press. in the chamber.

b) If the filled compartment initiallly contains steam at 1MPa and 500K. What is the final temp. and press. in the compartment.

c)  Repeat part a) if the 2nd compartment initially contains ideal gas, but at half the pressure and 100K higher temperature.

d) Repeat part b), if the 2nd compartment initially contains steam, but half the pressure and 100K higher temperature.


i need you to give atleast the formula to solve.. I can't find it.. Please

Answer
Free expansion is an irreversible process in which a gas expands into an insulated evacuated chamber.

Real gases experience a temperature change during free expansion. For an ideal gas, the temperature doesn't change, and the conditions before and after adiabatic free expansion satisfy

   pi*Vi = pf*Vf,

where p is the pressure, V is the volume, and i and f refer to the initial and final states.

Therefore, the final temperature of the gas will be Tf=500K and the final pressure will be:

   Pf=Pi*Vi/Vf   but  Vf=2*Vi  therefore  Pf=Pi*Vi/(2*Vi)=Pi/2=1MPa/2=0.5MPa

During free expansion, no work is done by the gas. The gas goes through states of no thermodynamic equilibrium before reaching its final state, which implies that one cannot define thermodynamic parameters as values of the gas as a whole. For example, the pressure changes locally from point to point, and the volume occupied by the gas (which is formed of particles)
is not a well defined quantity.

For additional information regarding a real gas go to http://en.wikipedia.org/wiki/Joule%E2%80%93Thomson_effect  

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James J. Kovalcin

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I am teaching or have taught AP physics B and C [calculus based mechanics & electricity and magnetism] as well as Lab Physics for college bound students. I have a BS in Physics from the University of Pittsburgh and a Master of Arts in Teaching from same. I have been teaching physics for 34 years. I am constantly updating my skills and have a particular interest in modern physics topics.

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