Is hv/kt Dimensionless in Planck's Radiation Law?

[noreally]

Hi all!

It was stated that in planks radiation law by my lecturer thathv/kt is dimensionless but my mediocre brain can't do the analysis. Try as I might I also can't find the relevant units to prove it. If someone could help I would be eternally grateful.

p.s. This is my first post *virginity lost*

 

[HallsofIvy]

What are the units of h, k, v, and t, separately?

 

[noreally]

h is planks constant (Js), k is the Boltzmann constant (J/k), t is temp (k) and v I am unsure on, which is why I am struggling. Thus far i got that they cancel to leave s(then units for v). Confirmation on v would be maybe a part 2 to my question. thanks for the reply!

 

[phyzguy]

h is planks constant (Js), k is the Boltzmann constant (J/k), t is temp (k) and v I am unsure on, which is why I am struggling. Thus far i got that they cancel to leave s(then units for v). Confirmation on v would be maybe a part 2 to my question. thanks for the reply!

What you have written as v is actually nu (see below) which is a frequency and has units of 1/time.

$$\nu$$

 

[noreally]

Thanks for the clarification, that makes sense and also in terms of the dimensional analysis which now cancels. Many thanks!