The ratio of the heat capacities C_p / C_V fo | vedclass

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(A) The ratio of molar heat capacities at constant pressure $(C_p)$ to that at constant volume $(C_V)$ is represented by the adiabatic index $\gamma =

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$He$

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(A) The ratio of molar heat capacities at constant pressure $(C_p)$ to that at constant volume $(C_V)$ is represented by the adiabatic index $\gamma = C_p / C_V$.For a monoatomic gas,the degrees of freedom $f = 3$,so $\gamma = 1 + (2/f) = 1 + 2/3 \approx 1.67$.For a diatomic gas,the degrees of freedom $f = 5$,so $\gamma = 1 + 2/5 = 1.40$.For a non-linear triatomic gas,the degrees of freedom $f = 6$,so $\gamma = 1 + 2/6 \approx 1.33$.Given that $C_p / C_V = 1.67$,the gas must be monoatomic.Among the given options,$He$ (Helium) is a noble gas and is monoatomic,while $H_2$,$CO_2$,and $CH_4$ are polyatomic.Therefore,the correct option is $A$.

The ratio of the heat capacities $C_p / C_V$ for one mole of a gas is $1.67$. The gas is

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