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Homework Statement
Basically the units of the Canonical Partition Function within the logarithms should be zero
Homework Equations
The Attempt at a Solution
N here is a number so we ignore the left logarithms, applying a "Unit function " for the terms within the logarithm.
(F_{u}((mk_{b}TV^{2/3})/(2πħ^{2})) ) ^{3/2} :
The above function can work on each individual portion and spit out the unit values , assuming all the operations act in the same way.
k_{b}T => J (Thermal Energy)
m => Kg
ħ^{2} => J^{2}s^{2}
V^{2/3} => J^{2/3}
Now ignoring the power to 3/2 =>
Kg*J*J^{2/3}*s^{2}*J^{2}
=> kg*s^{2}*J^{1/3}
=> kg^{2/3}s^{8/3}m^{2/3}
Now Even if we introduce 3/2 we dont acquire a unitless solution
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