Show that the free energy of an ideal monatomic gas of N 3 particles in a volume V can be written as F k B N 3 T (1 ln(N 3 3 V)) , where is a thermal length scale Show that a two dimensional ideal gas of N 2 particles moving in a bounded area A has free energy 1 3D V2 mk F2 KBN2T (1 In(N2x A))...

First consider three dimensions From eq And Z ideal V 3N 3 2 N 3 For a free mona ...

Show that the free energy of an ideal monatomic gas of N 3 particles in a volume

Question:

Show that the free energy of an ideal monatomic gas of N₃ particles in a volume V can be written as F =−k_BN₃T (1 − ln(N₃λ³/V))
, where 1%3D V2лћ?/mkвТ

is a thermal length scale. Show that a two-dimensional ideal gas of N₂ particles moving in a bounded area A has free energy F2 = -KBN2T (1 – In(N2x²/A))