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JEE Main 20244 AprilEvening Shift
Exam
JEE Main
Year
2024
Date
4 April
Shift
Evening Shift
Subject
Physics
Chapter
Thermodynamics

JEE Main 2024 · 4 April · Evening Shift · Physics · Thermodynamics

A sample of gas at temperature T is adiabatically expanded to...

A sample of gas at temperature TT is adiabatically expanded to double its volume. Adiabatic constant for the gas is γ=3/2\gamma=3 / 2. The work done by the gas in the process is: (μ=1 mole)(\mu=1 \mathrm{~mole})

Options

  1. ART[1−22]R T[1-2 \sqrt{2}]
  2. BRT[2−2]R T[\sqrt{2}-2]
  3. CRT[2−2]R T[2-\sqrt{2}]
  4. DRT[22−1]R T[2 \sqrt{2}-1]

Correct answer

C. RT[2−2]R T[2-\sqrt{2}]

Step-by-step solution

W=nRΔT1−γTVγ−1= constan t=Tf(2V)γ−1Tf=T(12)1/2=T2W=R(T2−T)1−32=2RT(2−1)2=RT(2−2)\begin{aligned} & \mathrm{W}=\frac{\mathrm{nR} \Delta \mathrm{T}}{1-\gamma} \\ & \mathrm{TV}^{\gamma-1}=\text{ constan } \mathrm{t}=\mathrm{T}_{\mathrm{f}}(2 \mathrm{ V})^{\gamma-1} \\ & \mathrm{ T}_{\mathrm{f}}=\mathrm{T}\left(\frac{1}{2}\right)^{1 / 2}=\frac{\mathrm{T}}{\sqrt{2}} \\ & \mathrm{ W}=\frac{\mathrm{R}\left(\frac{\mathrm{T}}{\sqrt{2}}-\mathrm{T}\right)}{1-\frac{3}{2}}=2 \mathrm{RT} \frac{(\sqrt{2}-1)}{\sqrt{2}} \\ & =\mathrm{RT}(2-\sqrt{2})\end{aligned}
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