Question

3. For diatomic ideal gases at room temperature, find out the change in entropy due to mixing using the following partition functions hv expl2kT T V( h2 Ztranslation rotation vibration h2 hv 1 exp 4. For solids, Einstein the vibrational levels given energy are as hv, j-0,1,2,.. Assuming that the N 2 strongly coupled atoms are +=3 equivalent to 3N simple harmonic independent oscillators, find out the followings (a) Equation for the vibrational energy as a function of temperature (b) Specific heat at constant volume.

Answer 1

Given axmKTY/2 Zioylation 2 8x TKT otation h2 Zvibatien e Lalay latitien quenolion have puitijeicative pofuly frsto-tal Pandilion fenctiom 3/2 87 RærkT. V Ehuliet h2 Fe-KTlyz Z yC-her) TxtKTIEuleT) S= OTVN 2 27mK 2MKT+ 2. KlvtklypKTzTx S = CS Scanned CamScahne + KTx to 2

- KT (0-T -X 1-hlkT S= KDgV+홀eg스 3 K h2 tk-kay-T) t T-EhET (4) Eimstein Salics E =(i)hu j- 0,1, 2, -- e |- e 1- e Phu y3NEOh l-e Phu Ch (1-EC- _e (1-é Pho e Phu Scanned withe CS CamScanner

E = (1- Fho hv 1-Pho 3N C (Unt high dembunet 3N phv + 2 LT 3N h KT 3NK T 7INE SA). (i) At louw temperatme -Bhv hv e Eニ X k メー! T2 3MMVR e KT2 Cv 3NK/L2hv KT CS Scannedwith CamScanner