Temperature & Pressure. Beginner Physics.

AI Thread Summary
In a rigid, insulated container divided by a membrane, a gas at initial temperature To and pressure Po leaks into an empty half after the membrane ruptures, doubling its volume. The Ideal Gas Law (PV=nRT) is applied to analyze the changes in pressure and temperature. As the gas expands into the new volume, the final pressure P2 and temperature T2 can be expressed in relation to the initial conditions. The derived relationship shows that the ratio of the final pressure to final temperature is half that of the initial state, resulting in P2/T2 = 0.5 * (Po/To). Ultimately, this indicates that both pressure and temperature decrease as the gas expands.
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Homework Statement


A rigid, perfectly insulated container has a membrane dividing its volume in half. One side contains a gas at an absolute temperature To and pressure Po, while the other half is completely empty. Suddenly a small hole develops in the membrane, allowing the gas to leak out into the other half until it eventually occupies twice its original volume. In terms of To and Po, what will be the new temperature and pressure of the gas when it is distributed equally in both halves of the container?

Homework Equations


None.


The Attempt at a Solution


I have no idea how to explain this answer. I don't know how to approach this. Please help.
 
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The box has a definite volume of V and a definite amount of mass inside (n). If the gas starts off with a volume of V, Pressure of Po, Temp of To, and mass of n, use the Ideal Gas Law to solve for a change in volume and respective pressure/temperature changes.

PV=nRT where R is the ideal gas constant.

Case 1, Po*V=n*R*To
Case 2 P2*V2=n*R*T2

Po/To=(nR)/V
P2/T2=nR/V2

Since V2=2*V then P2/T2=0.5(nR)/V or the ratio of the pressure to the temperature of the final volume of gas will be half that of the original. P2/T2=.5*Po/To
 

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