Problem with ideal gas pressure

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SUMMARY

The discussion centers on calculating the equilibrium pressure of two bulbs containing ideal gases at different temperatures and pressures. Bulb A has a volume of 100 cm³, filled with gas at 10°C and 3.0 x 105 Pa, while Bulb B has a volume of 50 cm³, filled with gas at 100°C and 1.0 x 105 Pa. The ideal gas law, PV = nRT, is utilized to derive the necessary equations for pressure and molar quantities. The solution requires establishing three equations to solve for the final pressure and molar numbers in the system.

PREREQUISITES
  • Understanding of the Ideal Gas Law (PV = nRT)
  • Basic knowledge of thermodynamics and gas laws
  • Familiarity with A-level Physics concepts
  • Ability to manipulate algebraic equations
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  • Study the Ideal Gas Law applications in different thermodynamic processes
  • Learn about the concept of gas mixtures and partial pressures
  • Explore the relationship between temperature, pressure, and volume in ideal gases
  • Investigate advanced topics in thermodynamics, such as the laws of thermodynamics
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A-level Physics students, educators teaching thermodynamics, and anyone interested in understanding the behavior of ideal gases under varying conditions.

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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 10oC to a pressure of 3.0 x 105 Pa. Bulb B is filled with an ideal gas at 100oC to a pressure of 1.0 x 105 Pa. The two bulbs are connected with A maintained at 10oC and B at 100oC. 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.
 
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Initially you have [itex]P_A V_A=n_A R T_A[/itex] and [itex]P_B V_B=n_B R T_B[/itex]. You can figure out all of those numbers, right? Finally you have a new pressure [itex]P[/itex] and new molar numbers [itex]n'_A[/itex] and [itex]n'_B[/itex], 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 [itex]n_A+n_B=n'_A+n'_B[/itex].
 

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