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Consider a container of oxygen gas at a temperature of $20^{\circ} \mathrm{C}$ that is 1.00 $\mathrm{m}$ tall. Compare the gravitational potential energy of a molecule at the top of the container (assuming the potential energy is zero at the bottom) with the average kinetic energy of the molecules. Is it reasonable to neglect the potential energy?

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$8.58 \times 10^{-5}$

Physics 101 Mechanics

Chapter 18

Kinetic Theory of Gases

Temperature and Heat

Rutgers, The State University of New Jersey

Simon Fraser University

Hope College

McMaster University

Lectures

02:55

Consider a container of ox…

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01:31

Oxygen $\left(\mathrm{O}_{…

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03:34

Okay, so we're doing Chapter 18 problems. 63 here. So it says consider a container of gas at temperature degrees Celsius. That is one meter tall. Compare the gravitational potential G of a molecule at the top of the container. Assuming the potential energy is Europe bottom with the average kinetic energy of the molecules, is it reasonable to to neglect of the potential energy. So groups so potential energy you is given, as in G. H Oh, and the average kinetic energy is given as 1/2 in the R. M s square or 3/2 tbt. So if we want to find the ratio, you took kinetic average than this is given as MGH over pre ops K b t. So it's right this out and we see that this is 32 times two times 1.66 times 10 and eight of 27 kilograms for you times 9.8 meters per second, squared times one meter all over. Three times 1.38 comes to the negative 23 jewels Kelvin and times to 93 Copan. So this comes out to being 8.58 times 10 to the negative pop, and this is unit list. This is a ratio of two energies. So what this is saying is the kinetic energy is much smaller are much larger than you. You as 8.58 times 10 to the negative, five times the kinetic energy. So that means that's roughly four orders of ensued smaller than the kinetic energy. So, yes, it's pretty pretty reasonable to neglect the gravitation. That's four orders of magnitude lesson kinetic energy. Who cares?

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