A gas is formed of molecules each molecules possessing f degrees of freedom, then the value of `gamma=(C_(P))/(C_(V))` is equal to

Options

A. ` f`
B. ` 1+(2)/(f)`
C. ` (f)/(2)`
D. ` f +(1)/(2)`

Answer

B

Explanation

According to law of equipartition of energy , the internal
Thus , internal energy associated per molecule
`If N_A ` is Avagadro's number , then internal energy mole of an ideal gas is
` U = N_A f (1)/(2) kT `
`= (1)/(2) f (N_A k) T `
` = (1)/(2) f RT`
Where ` R = N_A k ` = gas constant
Molar heat capacity at constant volume
` C_V = C_V + R " " ` (Mayor's relation)
`= (1)/(2) fR + R = ((1)/(2) f+1) R `
Hence , `y = (C_P)/( C_V) = ((1)/(2) f +1) R )/((1)/(2) fR) = ( (1)/(2) f+1) )/( (1)/(2) f)) =1 `