Consider a sample containing 1.70 mol of an ideal diatomic gas. (a) Assuming the
ID: 1297479 • Letter: C
Question
Consider a sample containing 1.70 mol of an ideal diatomic gas.
(a) Assuming the molecules rotate but do not vibrate, find the total heat capacity of the sample at constant volume. nCv = J/K
(b) Assuming the molecules rotate but do not vibrate, find the total heat capacity of the sample at constant pressure. nCp = J/K
(c) Assuming the molecules both rotate and vibrate, find the total heat capacity of the sample at constant volume. nCv = J/K
(d) Assuming the molecules both rotate and vibrate, find the total heat capacity of the sample at constant pressure. nCp = J/K
Explanation / Answer
1)
given the molecules rotate but do not vibrate
moving along x,y,z directions = 3
rotating around axes = 2
so the degrees of freedom = 5
so internal energy dE = (5/2) nRT
nCv = dE/T
nCv = (5/2) nR
so
nCv= (5/2 ) x 1.7 x 8.314
nCv = 35.3345 J/K
2)
we know that
Cp= Cv + R
nCp = nCv + nR
nCp = 35.3345 + 1.7 x 8.314
nCp = 51.9625 J/K
3)
now there is vibration
so it gives two degress of freedom , vibrational and elastic energies
so
degress of freedom = 7
dE = ( 7/2) nRT
nCv = dE /T
nCv = ( 7/2) nR
nCv = (7/2) x 1.7 x 8.314
nCv = 49.4683 J/K
4)
we know that
nCp = nCv + nR
nCp = 49.4683 + 1.7 x 8.314
nCp = 63.6021 J/K