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

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In the discussion about Planck's radiation law, the focus is on the term hv/kt, which is asserted to be dimensionless. The variables are defined as follows: h is Planck's constant (Js), k is the Boltzmann constant (J/K), t is temperature (K), and v, clarified as frequency (ν), has units of 1/time. The participant initially struggled with the dimensional analysis but confirmed that the units cancel out correctly when ν is considered. This understanding resolves the confusion regarding the dimensionless nature of the expression. The discussion highlights the importance of correctly identifying the units involved in physical equations.
noreally
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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*
 
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What are the units of h, k, v, and t, separately?
 
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!
 
noreally said:
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
 
Thanks for the clarification, that makes sense and also in terms of the dimensional analysis which now cancels. Many thanks!
 

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