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BCECE Engineering BCECE Engineering Solved Paper-2007

  • question_answer
    A gas expands isothermally against a constant external pressure of 1 atm from a volume of \[10\,d{{m}^{3}}\]to a volume of \[20\,d{{m}^{3}}.\] It absorbs 300 J of thermal energy from its surroundings. The \[\Delta U\]is

    A) \[-312\,J\]          

    B)        \[+\,123J\]

    C) \[-213\,J\]          

    D)                        \[+\,231\,J\]

    Correct Answer: C

    Solution :

    \[W=-\int_{{{V}_{1}}}^{{{V}_{2}}}{PdV}=-P({{V}_{2}}-{{V}_{1}})\] \[W=-1(20-10)=-10\,d{{m}^{3}}\text{atm}\] \[=-10\,d{{m}^{3}}\times \frac{8.314\,J{{K}^{-1}}\,mo{{l}^{-1}}}{0.0821\,d{{m}^{3}}\,{{K}^{-1}}\,mo{{l}^{-1}}}\] \[=-1013\,J\] From 1st law of thermodynamic \[\Delta U=q+W\] \[=800\,J+(-1013\,J)=-213\,J\]


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