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NEET Sample Paper NEET Sample Test Paper-66

  • question_answer
    A gas expands with temperature according to the relation\[\operatorname{V} = k{{T}^{2/3}}\]. What is the work done Q when the temperature changes by\[30{}^\circ C\]?

    A) 10 R                             

    B) 20 R

    C) 30 R                 

    D) 40 R

    Correct Answer: B

    Solution :

    \[W=\int{PdV}\,\,=\,\,\int{\frac{RT}{V}dV}\] Since \[\operatorname{V}=k{{T}^{2/3}}\,\,\Rightarrow \,\,dV=\,\,\frac{2}{3}\,K{{T}^{-1/3}}\,dT\] Eliminating K, we find \[\frac{dV}{V}=\frac{2}{3}\,\frac{dT}{T}\] Hence \[W=\int_{{{T}_{1}}}^{{{T}_{2}}}{\frac{2}{3}}\,\,\frac{RT}{T}\,dT\] \[=\,\,\,\frac{2}{3}R({{T}_{2}}-{{T}_{1}})\,\,=\,\,\frac{2}{3}\,R(30)\,\,=\,\,20R\]


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