Units are not compatible but they are unitless

[RR_10401466]

 so it says my units are incompatable but they are unitless

[DJNewman]

H₂, H₃, and H₄ are all unit'd, because they all incorporate T₀ in their definitions, and that has a unit of K. You also use τ, which you defined as T/T₀, and those are also unit'd.

[Werner_E]

You can always evaluate each summand one after the other to see that all of them are of different dimension - not even two of them have the same unit: