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KVPY Sample Paper KVPY Stream-SX Model Paper-13

  • question_answer
    Consider the reversible isothermal expansion of an ideal gas in a closed system at two different \[{{\text{T}}_{1}}\] temperatures and \[{{\text{T}}_{2}}\,({{\text{T}}_{1}}<{{\text{T}}_{2}}).\] The correct graphical depiction of the dependence of work done (w) on the final volume (V) is:

    A)

    B)

    C)

    D)

    Correct Answer: B

    Solution :

    \[w\,=\,-n\text{RT}\,\text{In}\,\frac{{{V}^{2}}}{{{V}_{1}}},\] \[w\,=\,-n\text{RT}\,\text{In}\,\frac{{{\text{V}}_{b}}}{{{\text{V}}_{i}}}\]
    \[\left| w \right|\,=\,-n\text{RT}\,\text{In}\,\frac{{{\text{V}}_{b}}}{{{\text{V}}_{i}}}\]
    \[\left| w \right|\,=\,n\text{RT}\,(\text{In}\,{{\text{V}}_{b}}\,-\,\text{In}\,{{\text{V}}_{i}})\]
    \[\left| w \right|\,=\,n\text{RT}\,\text{In}\,{{\text{V}}_{b}}\,-\,n\text{RT}\,\text{In}\,{{\text{V}}_{i}}\]
    \[\text{Y}\,=\,m\,x\,-\,\text{C}\]
    So, slope of curve 2 is more than curve 1 and intercept of curve 2 is more negative than curve 1.


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