Problem with ideal gas pressure

[ttkingdom]

Homework Statement

Diagram here:
http://img99.imageshack.us/img99/7189/systemgk9.jpg

Two bulbs, A of volume 100cm³ and B of volume 50cm³ , are connected to a three way tap T which enables them to be filled with gas or evacuated. The volume of the tubes may be neglected.
Initially bulb A is filled with an ideal gas at 10^oC to a pressure of 3.0 x 10⁵ Pa. Bulb B is filled with an ideal gas at 100^oC to a pressure of 1.0 x 10⁵ Pa. The two bulbs are connected with A maintained at 10^oC and B at 100^oC. Calculate the pressure at equilibrium.

Homework Equations

PV = nRT

The Attempt at a Solution

I have the total Volume, total n but I can't find the final temperature of the system.

I'm learning A-level Physics and this problem comes from a book, the Advanced Level Physics by Michael Nelkon. Please help me. Thank you in advance.

 

[Dick]

Initially you have $P_A V_A=n_A R T_A$ and $P_B V_B=n_B R T_B$. You can figure out all of those numbers, right? Finally you have a new pressure $P$ and new molar numbers $n'_A$ and $n'_B$, three unknowns. So you need three equations to find them. You have two PV=nRT equations in the final state (one for each bulb) and $n_A+n_B=n'_A+n'_B$.

 

[baba89]

The problem with ideal gas pressure in this scenario is that the ideal gas law (PV = nRT) assumes that the gas particles are point masses with no volume and that there are no intermolecular forces between them. However, in reality, gas particles do have volume and there are intermolecular forces present, especially at high pressures and low temperatures. This can lead to deviations from the ideal gas law and can affect the accuracy of the calculated pressure at equilibrium.

To solve this problem, you can use the combined gas law, which takes into account the volume and temperature changes of the gases as they are mixed. The equation is P1V1/T1 = P2V2/T2, where P1 and T1 are the initial pressure and temperature of one gas, P2 and T2 are the final pressure and temperature of the mixture, and V1 and V2 are the initial and final volumes of the gas.

Using this equation, you can calculate the final temperature of the system by setting up two equations: one for the initial state (bulb A) and one for the final state (mixture of gases). Then, you can solve for the final pressure using the ideal gas law, using the final temperature that you calculated.

It's important to note that this solution is an approximation and may not be completely accurate due to the limitations of the ideal gas law. However, it should give you a reasonable estimate of the pressure at equilibrium.