For an adiabatic expansion of an ideal gas, the fractional change in its pressure is equal to (where γ is the ratio of specific heats):

Question

For an adiabatic expansion of an ideal gas, the fractional change in its pressure is equal to (where &gamma; is the ratio of specific heats): (A) -&gamma; ( dV / V ) (B) -&gamma; ( V / dV ) (C) -(1/&gamma;) ( dV / V ) (D) ( dV / V )

Tardigrade Admin · Accepted Answer

PV &gamma;= constant Differentiating ( d P / dV )=-(&gamma; P / V ) ( dP / P )=-(&gamma; d V / V )

Q. For an adiabatic expansion of an ideal gas, the fractional change in its pressure is equal to (where $γ$ is the ratio of specific heats):

$- γ \frac{d V}{V}$

$- γ \frac{V}{d V}$

$- \frac{1}{γ} \frac{d V}{V}$

$\frac{d V}{V}$

$P V^{γ} =$ constant Differentiating
$\frac{d P}{d V} = - \frac{γ P}{V}$
$\frac{d P}{P} = - \frac{γ d V}{V}$

Q. For an adiabatic expansion of an ideal gas, the fractional change in its pressure is equal to (where γ is the ratio of specific heats):

−γVdV​

−γdVV​

−γ1​VdV​

VdV​