Question

The Boltzmann distribution in thermodynamics involves the factor exp[-E/kT], where E represents energy,T is the temperature and K is the Boltzmann constant. Find the dimension of k

Answer 1

What is the unit of e^x ?

Answer 2

I am not given units for e^x.

Answer 3

e^x has no unit! So x should also have no unit. That is -E/kT has no unit which is possible if k has the dimensions of E/T i.e \(ML^2T^{-2}\Theta^{-1}\) .

Answer 4

Oh I get it! Take for instance Tan a=2m/3m, the 'm' will eventually cancel each other out. leaving Tan a with no units. So I should always take exponents,logs,tangents,etc, to have no units ,right?

Answer 5

Right!

Answer 6

thanks