The adiabatic Bulk modulus of a diatomic gas | vedclass

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(D) The adiabatic bulk modulus $(B_{ad})$ of a gas is defined as $B_{ad} = -V \frac{dp}{dV}$.For an adiabatic process,the relation between pressure $(

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$1.4 	imes 10^5 \, Nm^{-2}$

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(D) The adiabatic bulk modulus $(B_{ad})$ of a gas is defined as $B_{ad} = -V \frac{dp}{dV}$.For an adiabatic process,the relation between pressure $(p)$ and volume $(V)$ is $pV^{\gamma} = 	ext{constant}$.Differentiating with respect to $V$,we get $\frac{dp}{dV} V^{\gamma} + p \gamma V^{\gamma-1} = 0$.This simplifies to $\frac{dp}{dV} = -\gamma \frac{p}{V}$.Substituting this into the bulk modulus formula,we get $B_{ad} = -V (-\gamma \frac{p}{V}) = \gamma p$.For a diatomic gas,the adiabatic index $\gamma = 1.4$.At atmospheric pressure,$p = 1.013 	imes 10^5 \, Nm^{-2}$.Therefore,$B_{ad} = 1.4 	imes 1.013 	imes 10^5 \, Nm^{-2} \approx 1.4 	imes 10^5 \, Nm^{-2}$.

Molecule type	$\frac{C_{P}}{C_{v}}$
$A$. Monoatomic	$I$. $\frac{7}{5}$
$B$. Diatomic rigid molecules	$II$. $\frac{9}{7}$
$C$. Diatomic non-rigid molecules	$III$. $\frac{4}{3}$
$D$. Triatomic rigid molecules	$IV$. $\frac{5}{3}$

The adiabatic Bulk modulus of a diatomic gas at atmospheric pressure is

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