For a polyatomic gas, how is cv (specific heat at constant volume) = 4 + degree of freedom and cp(specific heat at constant pressure) = 4 + degree of freedom

Asked by Avijit Gupta | 13th Feb, 2012, 08:15: PM

Expert Answer:

Actually every degree of freedom contributes 1/2 kB T energy.
 
One mole of a gas has U=(3/2 kB T+ 3/2 kB T+ f kB T) NA
 
3/2 kB T--Due to three translational degree of freedoms.
 
3/2 kB T---Due to three rotational degree of freedom.
 
f-- No of vibrationals mode.
 
f kB T--Due to f vibrational degree of freedoms.
 
Cv=dU/dt= (3+f) R       ( kB NA=R)
 
Cp-Cv=R
 
Cp= (4+f) R

Answered by  | 14th Feb, 2012, 08:01: PM

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