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WB JEE Medical WB JEE Medical Solved Paper-2015

  • question_answer
    The pressure p, volume V and temperature T for a certain gas are related by \[p=\frac{AT-B{{T}^{2}}}{V},\] where A and B are constants. The work done by the gas when the temperature changes from \[{{T}_{1}}\]to \[{{T}_{2}}\]while the pressure remains constant, is given by

    A)  \[A({{T}_{2}}-{{T}_{1}})+B(T_{2}^{2}-T_{1}^{2})\]

    B)  \[\frac{A({{T}_{2}}-{{T}_{1}})}{{{V}_{2}}-{{V}_{1}}}-\frac{B(T_{2}^{2}-T_{1}^{2})}{{{V}_{2}}-{{V}_{1}}}\]

    C)  \[A({{T}_{2}}-{{T}_{1}})-\frac{B}{2}(T_{2}^{2}-T_{1}^{2})\]

    D)  \[\frac{A({{T}_{2}}-T_{1}^{2})}{{{V}_{2}}-{{V}_{1}}}\]

    Correct Answer: C

    Solution :

     Given, \[P=\frac{AT-B{{T}^{2}}}{V}\] \[\Rightarrow \]\[PV=AT-B{{T}^{2}}\Rightarrow P\Delta V=A\Delta T-BT\Delta T\]On integrating, we get \[\text{Work}\,\text{=}\,\int_{{}}^{{}}{PdV}=A\int_{{{T}_{1}}}^{{{T}_{2}}}{dT-}B\int_{{{T}_{1}}}^{{{T}_{2}}}{TdT}\] \[=A({{T}_{2}}-{{T}_{1}})-\frac{B}{2}[{{({{T}_{2}})}^{2}}-{{({{T}_{1}})}^{2}}]\]


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