Question

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

Answer 1

So, do you know that pV = NKT ?!

Answer 2

no that is what i am trying to prove

Answer 3

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

Answer 4

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.

Answer 5

http://en.wikipedia.org/wiki/Ideal_gas_law

Answer 6

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

Answer 7

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 :)

Answer 8

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.