Given the connection between Aw and K (Aw=2k) could you use the ideal gas law and derive the Boltzmann constant. Water freezes at 546.3 Aw and absolute zero is at 0 Aw. (Aw is an arbitrary temperature scale.

Explanation:

The relation between new scale and absolute temperature scale is given as follows

Aw = 2 K

for K = 273.15 ( freezing point of water at absolute scale )

Aw = 2 x 273.15 = 546.3 K

So each division of new scale is half the each division of absolute scale

each division of new scale is small .

The value of R  = 8.314 J per mole per K

Here per K is equivalent to 2Aw

So the vale of R in new scale = 8.314/2 J per mole per Aw

=  4.157 J per mole per Aw

k = R / N

= 4.157 / 6.02 x 10²³

= .69 x 10⁻²³

= 6.9 x 10⁻²⁴ J per molecule per Aw .

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