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Re: [Phys-L] new kilogram, ampere, kelvin, and mole



Regarding JD’s comment:



This is progress. This is a Good Thing™



And it's about time.



The SI overhaul is far more extensive in its conceptual impact than is commonly let on in many popular new releases about it (although there is, by design, no effective discernable quantitative impact yet with the current state of the art of metrological technology).


With the redefinition of the kilogram so that h = 6.62607015*10-34 Js this means that the properties of a Cs-133 atom effectively determine all of our usual mechanical units because the second is still defined in terms of such an atom, and the other universal constants are now to be just defined numbers. For instance, if we write the energy splitting between F = 3 and F=4 hyperfine states of the electronic ground state of a 133Cs atom as δeCs133 then 1 joule is effectively indirectly defined to be 1 J = δeCs133/(9192631770*6.62607015*10-34). Likewise, if we write δmCs133 as the mass difference between a 133Cs atom at rest in its F=3 hyperfine state in its electronic ground state and when it is in its F=4 hyperfine state in its electronic ground state. Then one kilogram is effectively defined to be 1 kg = δmCs133*2997924582/(9192631770*6.62607015*10-34).

Also, if we write e = 1 elementary charge then a coulomb is effectively defined as 1 C = e/(1.602176634*10-19), and the supposed base unit of the ampere is now effectively defined in terms of the coulomb and the second, rather defining the coulomb in terms of the base units of the ampere and the second, as has been traditionally the case. Also, this redefinition means that both μ0 and ε0 no longer have their previously defined values, but now become (again) experimentally measurable being determined by the value of the fine structure constant. But the relationship μ0*ε0 = 1/c2 still holds exactly.

With the redefinition of the kelvin so that Boltzmann’s constant is exactly k = 1.380649*10-23 J/K This means the kelvin scale of thermodynamic temperature is now to be fully disconnected from all the properties of water. No longer is the triple point temperature of pure water with mean terrestrial isotopic composition exactly 273.16 K. Instead, rather, a thermodynamic system now has a thermodynamic temperature of exactly 1 K if its entropy increases by exactly 1 nat (i.e. the number of accessible microscopic states of the system increases by a factor of e, the Naperian base of logarithms) when it absorbs exactly 1.380649*10-23 J of heat in a reversible process.

With the redefinition of Avogadro’s number this means the concept of a mole is now (finally) disconnected from both the mass of a 12C atom in its ground state and the mass of the IPK in Sèvres. Now a mole of things is simple exactly NA ≡ 602,214,076,000,000,000,000,000 of those things (much more like a dozen, a score or a gross). BTW, the redefinitions of both NA and k mean that the ideal gas constant, R also now has an exactly defined value of R ≡ 8.31446261815324 J K-1 mol-1.



Dave Bowman