1.An ideal gas of N indistinguishable particles is in a volume, V with macro-state M = (T, V, N) and microstate, I = {Pi

[answerhappygod]

1 An Ideal Gas Of N Indistinguishable Particles Is In A Volume V With Macro State M T V N And Microstate I Pi 1 (106.43 KiB) Viewed 19 times

1.An ideal gas of N indistinguishable particles is in a volume, V with macro-state M = (T, V, N) and microstate, I = {Pi, qi} where i = {1,.. ,N}. Given the Hamiltonian, H and the probability of being in state I as Σ N if H= where U(q) = {." otherwise pl+U(4) 2 m N 1. for H= i=1 -0, otherwise Špil - if {q;} € V 2 m 1 22 PM(T) = (a)Prove using the information above that the partition function, Z for the system is VN (2m1kgT) 2 Z = N! h2 3N Hint: Note that Z has been made dimensionless by dividing by h3N where h is some quantity with units usually taken as the Planck's constant. (b)Use Z to derive the caloric equation for a monatomic ideal gas using the Maxwell's relation between free energy and entropy, S. Hint: SE OF - dT VN