Question

1. Compute the following quantities for a system with 1.0 mol of Kr at 298 K and 1.0 atm. For this problem, assume that Kr is ideal gas (indistinguishable particles) and electronic contribution to the partition function can be ignored. For part (b)-(d). clearly indicate how each quantitiy is related to the partition function, Q. (a) Single-particle partition function, q. (b) Helmholtz free energy, A. (c) Average energy of the system, (E). (d) Entropy, S. (e) Constant volume heat capacity, Co.

Answer 1

Answers Given that, Compute the following quantities for a sysysteme with. n=1 mol T = 298 K p=latm (a) Single - particle partition function, a let, Boltzman population formulai, probability pj of finding the system is the whole collection of N interacting molecules) in its ith quantum state, where Ej is the energy of that quantum State iT ink, as is the degeneracy & Q is partition function. of ith state Pj = rj exp |-65 / (T) (a = Ei rj exp (-Es/KT) a=& exp 1 - 2 )

for ideal gas; Therefore, for indistinguishable particles (6) Helmholtz Energy, A. A =-KT tha A=E-Ts H = E +PU G=H-TS dE= Tds -pdu dH = Tas + Udy da = - ST-PdV dG = -sd I + dp Elo)=d at temp To E-f(0) = - (alna/aB) H-H(o) = -(olualaß), tkiv (a enalaula p=-(2A/audi -) A-A -kt en(e)

if Alo) = 0 Therefore, A=-kilna] (c) Average energy of the system (E) let, Average Energy, E-60= -(almalarlu (E) = EE;P; =&E; Ettila =r8 Le C) (6) Beer - black Trove fire. [2E) = 2 en (d) Entropy, S. let, A=E-Ts - Khunc = d.ge -TS

Therefore, Ts = Kiena - dena ӘР Therefore, s = k ln {QIBLES)