Problem 3 (25 points) Two containers of identical volume V are kept...

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Problem 3 (25 points) Two containers of identical volume V are kept at the constant temperature T, and are filled with the same type of ideal gas. Initially, the gas pressure in container 1 was P0, and the pressure in container 2 was 5P0. Then a small hole of area A was opened at t=0 to allow gas molecules to exchange between containers. (a) What are the final values of pressures in the containers, P1(t=00) and P2(t=00)? Make a sketch of pressures as functions of time, P1(t) and P2(t). (b) Set up differential equations that could allow you to solve for P1 (t) and P2(t). Express your answers in terms of A, V, T, Po, and the mean particle speed i. (c) Find P1(t) and P2(t).

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