welcome to our second example video. Looking at the how the microscopic picture corresponds with our macroscopic picture here in the kinetic theory of and we want to ask ourselves what is the root, mean square velocity of the particles inside this box? Now we do have two equations for this, though I highly recommend the second it comes from the first via the ideal gas law and to solve for the first, we would use the ideal gas law. So let's go ahead and just type in our answer. Then we have V. R. M s is equal to the square root. We'll have three times 1.38 times 10 to the negative. 23 Jules per Calvin multiplied by 298. Calvin is our temperature here, a 25 degrees C and then we're going to divide by M where m is going to be our 0.28 Remember here we've got end, too. So it's two times nitrogen, which is normally ah 14, you so 0.28 kilograms per mole. Then we have to multiply by the number of moles. Well, that's going to be the number of particles, which is one we're only considering. One particle divided by avocados. Number just six point. 02 times 10 to the 23. Okay, so this will be the number of moles, so our units will all work out. We end up with units of meters per second and when you type all this in, you should come up with something on the order of a couple 100 m per second.

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## Video Transcript

welcome to our second example video. Looking at the how the microscopic picture corresponds with our macroscopic picture here in the kinetic theory of and we want to ask ourselves what is the root, mean square velocity of the particles inside this box? Now we do have two equations for this, though I highly recommend the second it comes from the first via the ideal gas law and to solve for the first, we would use the ideal gas law. So let's go ahead and just type in our answer. Then we have V. R. M s is equal to the square root. We'll have three times 1.38 times 10 to the negative. 23 Jules per Calvin multiplied by 298. Calvin is our temperature here, a 25 degrees C and then we're going to divide by M where m is going to be our 0.28 Remember here we've got end, too. So it's two times nitrogen, which is normally ah 14, you so 0.28 kilograms per mole. Then we have to multiply by the number of moles. Well, that's going to be the number of particles, which is one we're only considering. One particle divided by avocados. Number just six point. 02 times 10 to the 23. Okay, so this will be the number of moles, so our units will all work out. We end up with units of meters per second and when you type all this in, you should come up with something on the order of a couple 100 m per second.

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