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# Thermodynamics part 4: Moles and the ideal gas law

Sal explains the concept of a mole. Then he derives the molar version of the ideal gas law PV=nRT, where the gas constant R=831 J/molK. Created by Sal Khan.

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• Why did you use 8.31 J/mol K instead of 0.821 L atm/ mol K ? • They're different values of the gas constant, it just depends on which units you're using.

8.31 J/mol K assumes you're in SI units, meaning you're using Pascals for pressure and meters^3 for volume.The joules unit comes from substituting F/A (aka Newtons per meter squared) in for the P (pascals) in PV=nRT.

After substitution, the units look like:

(Newtons/meters^2)(meters^3)= R (mols)(Kelvin)

So the remaining left side (Newtons x meters) becomes joules and R = joules/(mols x kelvin)

If you're using liters for volume and atm for pressure then you'd use the 0.0821 number you mentioned.
• This is actually a chapter in chemistry called states of matter.Where there's gas laws and stuff.And chem also has some chapter called thermodynamics.Whats the difference betweem the physics version and the chem one? •  Rather than thinking of the science as discrete sub-subjects as they are taught in school such as biology, chemistry, and physics, in the real world they are often all considered together as a whole, so thermodynamics is thermodynamics.

With that being said, you would probably focus on different aspects of thermodynamics in chemistry or physics classes. In the chemistry classes, you are more concerned with the states of matter as you mentioned, particularly the amount of energy required to change from one state to another. You look at the interactions between molecules in the condensed (liquid and solid) states, which give liquids and solids their properties. You also consider things such as change in enthalpy(delta H), entropy(delta S), and free energy (delta G) because these all shed light on EVERY chemical reaction (that is, every chemical reaction has a delta G,S, and H value). You can also look at equilibrium, as this is a thermodynamic property. Thermodynamics is one of the most important considerations of a chemical reaction.

In physics, you are more concerned with things such as cycles (adiabatic expansion/compression, isothermal and isobaric changes, etc.) and the efficiency of these process, as well as the theoretically most efficient process known as the carnot cycle. The treatment would probably be more mathematical.

They both, as you said, pay close attention to the behavior of gases. Gas behavior is quite complex. Depending on what the level of the class you are in, you might be introduced to the kinetic molecular theory of gas, which attempts to make some sense of the nature of gases. You will definitely look at ideal gas behavior (i.e. the ideal gas law) in both classes, as well as some common "reduced" forms of it such as Boyle's and Charles' laws. You might even get a glimpse of non ideal behavior.

In short, thermodynamics is one of the most fundamental subjects in nature, and is one of the most important in our attempt to understand the universe. Almost ALL natural phenomena can be looked at from a thermodynamic point of view, because it deals with the universal concept of energy.
• I'm wandering if temperatures of matter should have a reference point like velocity. From my understanding, the temperature of an substance is the average kinetic energy of it's molecules while the speed of the molecule is relative to a particular reference point (i.e the speed of the rotating earth). I hope my question is understood. :) • what is meant by "6 followed by roughly 230's of molecules" at ? • p1v1 / t1 = p2v2 / t2 ....this works only for ideal gas?
(1 vote) • • Why do we have to convert to kelvins in the equations given in the video? • I was wondering if temperatures of matter should have a reference point like velocity. From what I understand, the temperature of a substance is the average kinetic energy of its molecules while the speed of the molecule is relative to a particular reference point. I saw someone else asked this but I didnt understand the answer they were given • • It comes from pv=KNT , where N is number of molecules and K is some constant, T-temperature in Kelvins.

pv=nRT , here we have small n , and it means , how many mols we have 1 mol=6,022 * 10^23 beacuse if we write in N it will be a huge number and its easier with mol mass. And R is gas constant that applies to any gas. I hope this helps , and if I am wrong , someone please rewrite.

We got R from Boltzman constant * Avogardo number
(1 vote)
• At , Sal told that we got a relation between p,v,R,t,n and he told that in the relation n is no.of molecules but he clearly wrote it is no.of moles , so which one is correct the no.of molecules or moles?
(1 vote) 