Effusion

First off, let's take the equation for the internal energy of a gas.

We use the root-mean-square speed of a gas (the square root of the square of the average velocity) to give an average because the true average velocity of an ideal gas particle is 0 because its motion is random.

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So, why did we solve for this? Well, let's imagine a container split in the middle by a divider with a small hole in the center, like the one in the image below.

In this image, the gas goes through the small hole in the divider to reach the other side, one molecule at a time. Now, how exactly do we quantify the rates of exchange when there's two gases inside? We can use the ratio of their root-mean-square speeds to get some intuition through Graham's Law.

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Assuming the two gases have the same temperature(they have equal average kinetic energies):

The final equation is the quantified form of Graham's Law, which states that at constant temperature and pressure, the relative effusion rates of two gases is inversely proportional to the square roots of their masses.

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A good real life example of this is that helium balloons deflate faster than air balloons. Air is made up of numerous gases, most of which have higher molar masses than helium, which has a molar mass of about 4.00 g/mol. Since the air has a higher molar mass than helium, helium will deflate faster. That's why if you filled a balloon with helium and filled another balloon with air and had both at the same temperature, after a couple hours, the helium balloon would be smaller than the air balloon due to more helium escaping the helium balloon.​