- #1

Somali_Physicist

- 117

- 13

## 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 don't acquire a unitless solution