Cylinder with piston separating two sections containing two gases.

[sploder]

Homework Statement

A closed, insulated cylinder is divided into two equal parts by a piston. One compartment contains Nitrogen at T=300K, P1=5bar, the other Carbon Dioxide at T=300K, P2=20bar. The cylinder contents then reach mechanical and thermal equilibrium.

1. Assuming that the gases can be treated as ideal gases with heat capacities at constant volume of 5R/2 and 7R/2, obtain the final temperature and pressure.

2. Obtain the final temperature and pressure using accurate thermodynamic properties for N2 and C02

Homework Equations

PV=nRT
ΔU=Q-W
Q=Uf-Ui
Ui=m1u(T1)+m2u(T2)
Uf=(m1+m2)u(Tf)

The Attempt at a Solution

1. Usually for problems like this the first thing you do is find the mass. Since volume is not given, I'm not sure how to even start this problem.

 

[BvU]

Well, then all you can do is use a symbol, for example V, and express the mass (if needed at all) in V and the other variables. They do tell you, however, that the two volumes are equal...

 

[Chestermiller]

If the system reaches thermal and mechanical equilibrium, how do the temperatures and pressures in the two compartments compare at final equilibrium?

How much work do the two gases in the rigid container do on the surrounding environment outside the rigid container?

How much heat is transferred from the two gases inside the insulated container to or from the surrounding environment outside the container?

What is the change in total internal energy for the combination of the two gases inside the container?

Can you write an equation for this combined change in internal energy in terms of the number of moles in each compartment, the heat capacity of the gas in each compartment, and the initial and final temperatures in the compartments?

What is the final temperature?

If the container is rigid, how does the total volume of the two compartments compare between the initial and final equilibrium states?

How does the number of moles of gas in each of the two compartments change between the initial and final equilibrium states?

Chet