## anonymous 4 years ago I am trying to prove E(kin)=(3/2)RT (T in kelvin) in order to prove pV=nRT (so i cant use that equation) I have proved E(kin)=(1/2)mv^2

1. y2o2

So, do you know that pV = NKT ?!

2. anonymous

no that is what i am trying to prove

3. anonymous

or is N mole and K=R here or is it something else? Where R is molar gas constant = 8.314472 m2 kg s-2 K-1 mol-1

4. y2o2

Actually $E_{K.E} = {3 \over 2} KT \ \ Not \ \ {3\over2}RT$ where K is Boltzmann constant , not the Universal gas constant. and K = R/A where A is Avogadro's number.

5. y2o2
6. Mani_Jha

Do u know that PV=$mnc ^{2}/3$? From here u get K.E=3(PV/n)/2 per molecule. Combining boyle's and charle's law and avogadro's law, u will get $P1V1/nT1 = CONSTANT$ for any gas, which is called R. Thus PV=nRT. Put this value and u will get K.E=3RT/2 per molecule

7. anonymous

i wanted to prove it without thoose laws like avogadros law since to me it seems like they are based on empirical data and I wanted to prove it theorethically because I like it better :)

8. anonymous

we use Equipartition theorem to get E(k)=3KT/2, and use Boltzmann statistics to prove PV=nRT, and in this way we get Boltzmann Constant quantitatively ,namely K=AR, where A is Avergadro Constant.