Rigorous Definition of Kelvin?

Hi all,
I'm reading through Zwiebach's String Theory text on my own and am thinking about one of his very elementary exercises on "units." We are asked to define temperature in Kelvin with reference to the fundamental units of mass, length, and time. My thought is the following:

We take kT=hf where here f is the frequency of oscillation of Cs-133 radiation at that temperature since that is how the "second" is defined. Then we will have defined the temperature T (in Kelvin) in terms of only numerical quantities whose value we know (k and h) and f.

I'm not very confident about this at all but I'm not sure how else to do it.

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mfb
Mentor
That is the usual way to make units less dependent on specific setups, indeed. I think "fundamental units of mass, length and time" are the planck units here, not specific transition in some specific isotope.

Ah okay, so how would I go about constructing the Kelvin that way?

mfb
Mentor
You can just use kT=hf as definition, with fixed values for k and h (in Planck units, h has a known value anyway). The value of k is arbitrary.

hmm okay. But then what would "f" be? I thought you said we ought not refer to a specific isotope or anything like that.

mfb
Mentor
The planck units have something you can use there.