OpenStax College Physics for AP® Courses, Chapter 13, Problem 46 (Problems & Exercises)

This is College Physics Answers with Shaun Dychko. Hydrogen molecules with the molar mass of 2.016 grams per mole have an RMS speed of 193 meters per second. And the question is what is their temperature? So V RMS is the square root of 3 times Boltzmann's constant times temperature divided by the mass of a single molecule. And we'll figure out what that mass is by taking 2. 016 grams per mole and converting it into kilograms per mole then multiplying by one kilogram for every one thousand grams, and then turn it into kilograms per atom by multiplying by one mole for every 6.02 times 10 to the 23 atoms. This works out to 3.3488 times ten to the minus 27 kilograms per molecule actually. Okay. So this is one mole for every this many bits. I mean it's just a counting way - it's a way of counting. So we can just write molecules instead here if we want. Okay. So we're going to solve this now for T by squaring both sides and that gives us V RMS squared on the left and on the right hand side we'll just get rid of the square root sign. So that's 3 K T over M and then we solve for T by multiplying both sides by M over three K and then switch the sides around. And we get temperature is mass times RMS speed squared divided by 3 times Boltzmann's constant. So we plug in the number for the mass we found before for a single molecule times 193 meters per second and we square that divided by 3 times Boltzmann's constant and this gives us 3.01 Kelvin is the temperature.