Odd Conclusion About Specific Heat Capacity

Nov 2016
So, I was bored and started messing about with the units for all the equations we've learned in class thus far. I was most interested by the conclusion I reached about Specific Heat Capacity. My reasoning went something along the lines of the following:

Specific Heat Capacity = J/kg/K
J = Nm = (kg m/s^2)m = kg m^2/s^2

Specific Heat Capacity = (kg m^2/s^2)/kg/K = m^2/s^2/K

Specific Heat Capacity = k(Δv^2/θ)
where k = a constant, Δv = Change in velocity, θ = Change in temperature

Just wanted to know your thoughts on this, and on how to put this into context. My thoughts were that Δv may refer to the change in velocity of the particles of a substance (proportional to temperature), and so Specific Heat Capacity is the relationship between velocity of particles in a substance and the temperature. I would be interested to know whether this works or if it is even possible to test.

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