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Question: For an isothermal expansion of a perfect gas, the value of \(\frac{\Delta P}{P}\) is equal...

For an isothermal expansion of a perfect gas, the value of ΔPP\frac{\Delta P}{P} is equal

A

−γ1/2ΔVV- \gamma^{1/2}\frac{\Delta V}{V}

B

−ΔVV- \frac{\Delta V}{V}

C

−γΔVV- \gamma\frac{\Delta V}{V}

D

−γ2ΔVV- \gamma^{2}\frac{\Delta V}{V}

Answer

−ΔVV- \frac{\Delta V}{V}

Explanation

Solution

Differentiate PV=PV =constant w.r.t V

⇒ PΔV+VΔP=0P\Delta V + V\Delta P = 0⇒ ΔPP=−ΔVV\frac{\Delta P}{P} = - \frac{\Delta V}{V}