What is the Ideal Gas Law for a Two-Bulb System with Varying Temperatures?

[Jean2005]

1. Two equal glass bulbs are connected by a narrow tube and the whole is initially filled with a gas at a temperature of T₀ and pressure of P⁰. Then, one of the bulbs is immersed in a bath at a temperature, T1 and the other in a bath at a different temperature, T2. Show that in this problem, the overall pressure in the system changes to a value, P, give by this:

P= (2P₀(T₁/T₀)/(1+(T₁/T₂)).

-need to use three equations using the ideal gas law, where one is for the combined system at the initial temperature and then an equation for each system after being immersed in the bath
-total number of particles is constant

 

[DoItForYourself]

Please try to solve the problem by combining these three equations.

Also, have in mind that the sum of the moles of the two glass bulbs is constant as you said previously.