OpenStax College Physics for AP® Courses, Chapter 13, Problem 26 (Problems & Exercises)

This is College Physics Answers with Shaun Dychko. We're going to show that the three different ways of writing the universal gas constant works out to units of this NRT - works out to units of energy anyway. So if we assume that the universal gas constant is 8.31 Joules mole kelvin when we plug that into our NRT formula, N has units of moles are as Joules per mole kelvin and then T is always in kelvin and the moles and the kelvins cancel leaving us with Joules. And so yes, this is energy. When R is 1.99 calories per mole kelvin NRT becomes moles times calories per mole kelvin times kelvin and we're left with units of calories and calories is another way of measuring energy and it can be converted to Joules. And so yes, we've shown that NRT works out to energy. And then when R is 0.08 to one liter atmospheres per mole kelvin we have moles multiplied by liter atmospheres per mole kelvin times kelvin leaving us with liters and atmospheres. Liters can be converted into cubic meters. This is the SI unit for volume and this is a different unit for volume but they're both volumes, and so they can be thought of in this term of cubic meters. And atmosphere is another way of measuring pressure which in SI terms is newtons per meter squared. And so we have meters cubed divided by meter squared is a meter times newtons and meters times newtons is abbreviated by J which is Joules and yes this is energy in other words.