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JEE Main 2026 (Online) 24th January Morning Shift

MCQ+4 / -12026

\(\text { Match the LIST-I with LIST-II }\)
































































List-I Isothermal process for ideal gas systemList-II Work done ( 

<mi>V</mi>

<mi>f</mi>



>

<mi>V</mi>

<mi>i</mi>





<mi>V</mi>

<mi>f</mi>



>

<mi>V</mi>

<mi>i</mi>



V_(f) > V_(i) )
A.Reversible expansionI.

<mi mathvariant="normal">w</mi>



=

0



<mi mathvariant="normal">w</mi>



=

0

w=0
B.Free expansionII.

<mi mathvariant="normal">w</mi>



=

−

<mi data-mjx-auto-op="false">nR</mi>



T

ln

⁡

<msub>

  <mrow data-mjx-texclass="ORD">

    <mtext> </mtext>

    <mi mathvariant="normal">V</mi>

  </mrow>

  <mrow data-mjx-texclass="ORD">

    <mrow data-mjx-texclass="ORD">

      <mi mathvariant="normal">f</mi>

    </mrow>

  </mrow>

</msub>

<msub>

  <mrow data-mjx-texclass="ORD">

    <mi mathvariant="normal">V</mi>

  </mrow>

  <mrow data-mjx-texclass="ORD">

    <mrow data-mjx-texclass="ORD">

      <mi mathvariant="normal">i</mi>

    </mrow>

  </mrow>

</msub>





<mi mathvariant="normal">w</mi>



=

−

<mi data-mjx-auto-op="false">nR</mi>



T

ln

⁡

<msub>

  <mrow data-mjx-texclass="ORD">

    <mtext></mtext>

    <mi mathvariant="normal">V</mi>

  </mrow>

  <mrow data-mjx-texclass="ORD">

    <mrow data-mjx-texclass="ORD">

      <mi mathvariant="normal">f</mi>

    </mrow>

  </mrow>

</msub>

<msub>

  <mrow data-mjx-texclass="ORD">

    <mi mathvariant="normal">V</mi>

  </mrow>

  <mrow data-mjx-texclass="ORD">

    <mrow data-mjx-texclass="ORD">

      <mi mathvariant="normal">i</mi>

    </mrow>

  </mrow>

</msub>



w=-nRT ln((V_(f))/(V_(i)))
C.Irreversible expansionIII.

<mi mathvariant="normal">w</mi>



=

−

<mrow data-mjx-texclass="ORD">

  <mi mathvariant="normal">p</mi>

</mrow>

<mrow data-mjx-texclass="ORD">

  <mrow data-mjx-texclass="ORD">

    <mi data-mjx-auto-op="false">ex</mi>

  </mrow>

</mrow>



<mo data-mjx-texclass="OPEN">(</mo>

<msub>

  <mrow data-mjx-texclass="ORD">

    <mi mathvariant="normal">V</mi>

  </mrow>

  <mrow data-mjx-texclass="ORD">

    <mrow data-mjx-texclass="ORD">

      <mi mathvariant="normal">f</mi>

    </mrow>

  </mrow>

</msub>

<mo>−</mo>

<msub>

  <mrow data-mjx-texclass="ORD">

    <mi mathvariant="normal">V</mi>

  </mrow>

  <mrow data-mjx-texclass="ORD">

    <mrow data-mjx-texclass="ORD">

      <mi mathvariant="normal">i</mi>

    </mrow>

  </mrow>

</msub>

<mo data-mjx-texclass="CLOSE">)</mo>





<mi mathvariant="normal">w</mi>



=

−

<mrow data-mjx-texclass="ORD">

  <mi mathvariant="normal">p</mi>

</mrow>

<mrow data-mjx-texclass="ORD">

  <mrow data-mjx-texclass="ORD">

    <mi data-mjx-auto-op="false">ex</mi>

  </mrow>

</mrow>



<mrow>

  <msub>

    <mrow data-mjx-texclass="ORD">

      <mi mathvariant="normal">V</mi>

    </mrow>

    <mrow data-mjx-texclass="ORD">

      <mrow data-mjx-texclass="ORD">

        <mi mathvariant="normal">f</mi>

      </mrow>

    </mrow>

  </msub>  

  <mo>−</mo>  

  <msub>

    <mrow data-mjx-texclass="ORD">

      <mi mathvariant="normal">V</mi>

    </mrow>

    <mrow data-mjx-texclass="ORD">

      <mrow data-mjx-texclass="ORD">

        <mi mathvariant="normal">i</mi>

      </mrow>

    </mrow>

  </msub>  

</mrow>



w=-p_(ex)(V_(f)-V_(i))
D.Irreversible compressionIV.

<mi mathvariant="normal">w</mi>



=

−

<mrow data-mjx-texclass="ORD">

  <mi mathvariant="normal">p</mi>

</mrow>

<mrow data-mjx-texclass="ORD">

  <mrow data-mjx-texclass="ORD">

    <mi data-mjx-auto-op="false">ex</mi>

  </mrow>

</mrow>



<mo data-mjx-texclass="OPEN">(</mo>

<msub>

  <mrow data-mjx-texclass="ORD">

    <mi mathvariant="normal">V</mi>

  </mrow>

  <mrow data-mjx-texclass="ORD">

    <mrow data-mjx-texclass="ORD">

      <mi mathvariant="normal">i</mi>

    </mrow>

  </mrow>

</msub>

<mo>−</mo>

<msub>

  <mrow data-mjx-texclass="ORD">

    <mi mathvariant="normal">V</mi>

  </mrow>

  <mrow data-mjx-texclass="ORD">

    <mrow data-mjx-texclass="ORD">

      <mi mathvariant="normal">f</mi>

    </mrow>

  </mrow>

</msub>

<mo data-mjx-texclass="CLOSE">)</mo>





<mi mathvariant="normal">w</mi>



=

−

<mrow data-mjx-texclass="ORD">

  <mi mathvariant="normal">p</mi>

</mrow>

<mrow data-mjx-texclass="ORD">

  <mrow data-mjx-texclass="ORD">

    <mi data-mjx-auto-op="false">ex</mi>

  </mrow>

</mrow>



<mrow>

  <msub>

    <mrow data-mjx-texclass="ORD">

      <mi mathvariant="normal">V</mi>

    </mrow>

    <mrow data-mjx-texclass="ORD">

      <mrow data-mjx-texclass="ORD">

        <mi mathvariant="normal">i</mi>

      </mrow>

    </mrow>

  </msub>  

  <mo>−</mo>  

  <msub>

    <mrow data-mjx-texclass="ORD">

      <mi mathvariant="normal">V</mi>

    </mrow>

    <mrow data-mjx-texclass="ORD">

      <mrow data-mjx-texclass="ORD">

        <mi mathvariant="normal">f</mi>

      </mrow>

    </mrow>

  </msub>  

</mrow>



w=-p_(ex)(V_(i)-V_(f))

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