The ratio of the adiabatic to isothermal elas | vedclass

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(B) The adiabatic elasticity of a gas is given by $E_{	ext{adiabatic}} = \gamma P$,where $\gamma$ is the adiabatic index and $P$ is the pressure.The

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$4/3$

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(B) The adiabatic elasticity of a gas is given by $E_{	ext{adiabatic}} = \gamma P$,where $\gamma$ is the adiabatic index and $P$ is the pressure.The isothermal elasticity of a gas is given by $E_{	ext{isothermal}} = P$.The ratio of adiabatic to isothermal elasticity is $\frac{E_{	ext{adiabatic}}}{E_{	ext{isothermal}}} = \frac{\gamma P}{P} = \gamma$.For a triatomic gas (non-linear),the degrees of freedom $f = 6$. The adiabatic index $\gamma = 1 + \frac{2}{f} = 1 + \frac{2}{6} = 1 + \frac{1}{3} = \frac{4}{3}$.Therefore,the ratio is $\frac{4}{3}$.

Column-$I$	Column-$II$
$(a)$ Monoatomic gas	$(i)$ ${C_P} = \frac{3}{2}R$
$(b)$ Diatomic gas with vibration	$(ii)$ ${C_P} = \frac{5}{2}R$
	$(iii)$ ${C_P} = \frac{7}{2}R$
	$(iv)$ ${C_P} = \frac{9}{2}R$

The ratio of the adiabatic to isothermal elasticities of a triatomic gas is

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