A gas is formed of molecules each molecule possessing f degrees of freedom, then the value of γ = 
is equal to :
Text Solution
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According to law of equipartition of energy, the internal energy associated per degree of freedom is 
kT, where k is the Boltzmann's constant.
Thus, internal energy associated per molecule = f 
kT
If N A is Avagadro's number, then internal energy of one mole of an ideal gas is
U = N A f 
kT = 
f (N A k)T = 
f RT
where R = N A k = gas constant
Molar heat capacity at constant volume
C V = 
= 
= 
Molar heat capacity at constant pressure
C p = C v + R (Mayor's relation)
= 
= 
R
Hence, y = 
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