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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2011

  • question_answer
        Pressure p, volume V, and temperature T certain material are related by \[p=\frac{AT-B{{T}^{2}}}{V}\]where A and B are constants. Find an expression for the work done by the material if the temperature changes from\[{{T}_{1}}\]to\[{{T}_{2}}\]while the pressure remains constant.

    A)  \[W=A(T_{1}^{2}-T_{2}^{2})-B(T_{2}^{2}-T_{1}^{2})\]

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

    C)  \[W=A({{T}_{2}}-{{T}_{1}})-B\left( {{T}_{2}}-\frac{1}{2}{{T}_{1}} \right)\]

    D)  \[W=A({{T}_{2}}-{{T}_{1}})-B\left( T_{2}^{2}-T_{1}^{2} \right)\]

    Correct Answer: D

    Solution :

                    Work\[W=p({{V}_{2}}-{{V}_{1}})\]at constant p Initial volume \[{{V}_{1}}=(A{{T}_{1}}-BT_{1}^{2})/p\] Final volume \[{{V}_{2}}=(A{{T}_{2}}-BT_{2}^{2})/p\] \[\Rightarrow \]               \[W=A({{T}_{2}}-{{T}_{1}})-B(T_{2}^{2}-T_{1}^{2})\]


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