For adiabatic expansion of an ideal gas- the fractional change in its pressure is equal to - is the ratio of specific heats and V is the volume of the gas

For adiabatic process, PV^γ = constant ⇒ln P+γln V= constant Differentiating both sides, dPP+γdVV=0 ⇒dPP= γdVV Hence, option (A) is the correct answer. ...

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Standard XII

Chemistry

Heat Capacity at Constant Pressure

For adiabatic...

Question

For adiabatic expansion of an ideal gas, the fractional change in its pressure is equal to :

$(γ$ is the ratio of specific heats and $V$ is the volume of the gas $)$

- γ \frac{d V}{V}

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\frac{d V}{V}

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- \frac{1}{γ} \frac{d V}{V}

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- γ \frac{V}{d V}

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Solution

The correct option is A $- γ \frac{d V}{V}$
For adiabatic process,

$P V^{γ} =$ constant

$\Rightarrow ln P + γ ln V =$ constant

Differentiating both sides,

$\frac{d P}{P} + γ \frac{d V}{V} = 0$

$\Rightarrow \frac{d P}{P} = - γ \frac{d V}{V}$

Hence, option $(A)$ is the correct answer.

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

The correct option is A −γdVVFor adiabatic process, PVγ= constant ⇒lnP+γlnV= constant Differentiating both sides, dPP+γdVV=0 ⇒dPP=−γdVV Hence, option (A) is the correct answer.

For adiabatic expansion of an ideal gas, the fractional change in its pressure is equal to :

$(γ$ is the ratio of specific heats and $V$ is the volume of the gas $)$

The correct option is A $- γ \frac{d V}{V}$
For adiabatic process,

$P V^{γ} =$ constant

$\Rightarrow ln P + γ ln V =$ constant

Differentiating both sides,

$\frac{d P}{P} + γ \frac{d V}{V} = 0$

$\Rightarrow \frac{d P}{P} = - γ \frac{d V}{V}$

Hence, option $(A)$ is the correct answer.