Question

hi

i am working on trying to derive KE (or Etrans)=3/2nRT

so i know these steps

that

___________

pV= nRT

and pV= 1/3 NmV2

and combining them, we get

nRT= 1/3Nmv2

also, we know that for translational motion, KE= 1/2Nmv2


______

i don't know how

2/3 (1 /2 Nmv2) = nRT


where did that 2/3 come from??!!

i know that subsequently, it will be 2/3KE= nrt

and i will get KE=3/2 nRT

i just don't KNOW WHERE THE 2/3 came from in the first place!

Answer 1

2/3 x 1/2 is another way of writing 1/3. The equations

nRT= (1/3)Nmv^2

and

nRT = (2/3)(1/2)NmV^2

are equivalent.