If $C_{p}$ and $C_{v}$ are the molar specific heats of a gas at constant pressure and volume respectively then the ratio of adiabatic and isothermal modulii of elasticity will be

\frac{C_{p} - C_{v}}{C_{p}}

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C_{p} C_{v}

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\frac{C_{v}}{C_{p}}

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\frac{C_{p}}{C_{v}}

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Solution

The correct option is C $\frac{C_{p}}{C_{v}}$
We know that $\frac{C_{p}}{C_{v}}$ is $γ$ .

For isothermal process we have PV=constant
Differentiating
$P d V + V d P = 0$
or
$P = \frac{d P}{- d V / V} = \frac{S t r e s s}{s t r a i n} = E_{i s o}$ =Isothermal modulus of elasticity

For adiabatic process we have $P V^{γ} = c o n s t a n t$
Differentiating
$d P V^{γ} + P γ V^{γ - 1} d V = 0$
or
$γ P = \frac{d P}{- d V / V} = \frac{s t r e s s}{s t r a i n} = E_{a d i a}$ =Adiabatic modulus of elasticity.

Thus $\frac{E_{a d i a}}{E_{i s o}} = \frac{γ P}{P} = γ = \frac{C_{p}}{C_{v}}$

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If Cp and Cv are the molar specific heats of a gas at constant pressure and volume respectively then the ratio of adiabatic and isothermal modulii of elasticity will be

If $C_{p}$ and $C_{v}$ are the molar specific heats of a gas at constant pressure and volume respectively then the ratio of adiabatic and isothermal modulii of elasticity will be