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JEE Main 202118 MarchEvening Shift
Exam
JEE Main
Year
2021
Date
18 March
Shift
Evening Shift
Subject
Physics
Chapter
Thermodynamics

JEE Main 2021 · 18 March · Evening Shift · Physics · Thermodynamics

For an adiabatic expansion of an ideal gas, the fractional change...

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

Options

  1. A−γdVV- \gamma\dfrac{dV}{V}
  2. B−γVdV- \gamma\dfrac{V}{dV}
  3. C−1γdVV- \dfrac{1}{\gamma}\dfrac{dV}{V}
  4. DdVV\dfrac{dV}{V}

Correct answer

A. −γdVV- \gamma\dfrac{dV}{V}

Step-by-step solution

⇒PVγ=⇒ P{V}^{\gamma} = constant

Differentiating,

⇒dPdV=−\gammaPV⇒ \dfrac{dP}{dV} = - \dfrac{\gammaP}{V}

⇒dPP=−\gammadVV⇒ \dfrac{dP}{P} = - \dfrac{\gammadV}{V}

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