Question

If n is the degree of freedom of gas then the ratio of two principal specofic heats Cv/Cp os given by what ?

Answer 1

suppose a polyatomic gas molecule has n degree of freedom .

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Internal energy of one gram mole of the gas ,

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U= n x 1/2 x kb x Tx Na 
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n/2 x R x T
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AS,  Cv = dU / dT

Cv= d(U)/ dT

Cv= d / dT ( n/2 RT)

Cv= n/2 R

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Cp= Cv + R

Cp= n/2 R+R

Cp= (n/2 +1 ) R

γ=Cp/Cv 

γ=  (n/2 +1 ) R
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     n/2 R
γ= (1 + 2/n)

γ is way to express ratio.