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Chapter 11: Problem 17

Consider a container of gas with the pressure inside the container the same as the room pressure outside the container. If a tiny hole is punched in the side of the container, will the gas leak out? Explain your answer.

Short Answer

Expert verified
In this scenario, the gas will not "leak out" in a conventional sense, as the pressure inside and outside of the container is equal (\(P_{inside} = P_{outside}\)). This means there is no force pushing gas particles through the hole. However, due to the random motion of gas particles, some may pass through the hole in either direction (effusion), causing the overall amount of gas in the container to remain relatively constant as the rate of gas molecules escaping and entering the container is equal.

Step by step solution

01

Understand Pressure Variables

The problem states that the pressure inside the container (P_inside) is equal to the room pressure outside the container (P_outside). So we can write the equation: \(P_{inside} = P_{outside}\)
02

No pressure difference

Since the pressure inside and outside of the container is equal, there is no pressure difference between the two: \(P_{inside} - P_{outside} = 0\) No pressure difference means that there is no force pushing the gas particles either in or out through the tiny hole.
03

Observe gas particle behavior

Gas particles are in constant motion and move randomly in all directions. Because of this, gas particles inside the container have chances to pass through the tiny hole to the outside and vice versa, gas particles from outside can enter the container.
04

Conclude the result

Since there is no pressure difference between the container and the room, the gas particles are not forced to move out through the hole or move in. However, due to their random motion, some particles may pass through the hole in either direction, in a process called effusion. Thus, the overall amount of gas in the container will remain relatively constant since the rate of gas molecules escaping and entering the container is equal. Therefore, the gas will not "leak out" in a conventional sense, because its overall amount in the container stays practically the same.

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