Physics- Pressure Problem , help

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The discussion revolves around a physics problem involving two gas containers at different temperatures and pressures, which are connected to equalize conditions. The small container has a volume of 1 L and the large container has a volume of 2 L, with a final temperature of 321 K. Participants are attempting to derive the final pressure using the ideal gas law, but some are struggling with the calculations. The equation provided relates the pressures, volumes, and temperatures of the gases before and after equalization. The conversation emphasizes the need to correctly apply the ideal gas law to solve for the final pressure in the combined volume of 3 L.
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Two containers contain the same gas at different temperatures and pressures, as indicated in the figure. The small container has a volume of 1 L, and the large container has a volume of 2 L. The two containers are then connected to each other using a thin tube, and the pressure and temperature in both containers are allowed to equalize. If the final temperature is 321 K, what is the final pressure? Assume that the connecting tube has negligible volume and mass.


Attempt : Pf Vf / 321 =( 3 x 10^5 )(2L) / 600 + (2 X 10^5)(1L) / 200


I am stuck here , can't solve it . I tried solving for the variable didn't get the right answer.


Here is the diagram :
 

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\frac{(Pf)(V)}{T} = \frac{(P1)(V1)}{T1} + \frac{(P2)(V2)}{T2}

Got it from there?
 
Yeah, how do I go about it?
 
Did you use 3L as the final volume.

Looks like you get one eq. w/ one variable.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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