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NEET Sample Paper NEET Sample Test Paper-69

  • question_answer
    The specific heat of hydrogen gas at constant pressure is \[{{\operatorname{C}}_{P}} =3.4 \times  1{{0}^{3}}cal/kg\,C\] and at constant volume is\[{{\operatorname{C}}_{V}} =2.4 \times  1{{0}^{3}}cal/kg C\]. If one kilogram hydrogen gas is heated from \[10{}^\circ C\,\,to\,\,20{}^\circ C\] at constant pressure, the external work done on the gas to maintain it at constant pressure is

    A) \[{{10}^{5}}\,cal\]                  

    B) \[{{10}^{4}}\,cal\]

    C) \[{{10}^{3}}\,cal\]                  

    D) \[5\,\,\times \,\,{{10}^{3}}\,cal\]

    Correct Answer: B

    Solution :

    From FLOT \[\Delta Q=\Delta U+\Delta W\] Work done at constant pressure \[{{\left( \Delta W \right)}_{P}}={{\left( \Delta Q \right)}_{P}}-\Delta U\] \[{{(\Delta Q)}_{P}}-\,\,{{(\Delta Q)}_{V}}\,(As\text{ }we\text{ }know{{\left( \Delta Q \right)}_{V}}=\Delta U)\] \[Also\,\,{{\left( \Delta Q \right)}_{P}}=m{{c}_{P}}\Delta T\,\,and\,\,{{(\Delta Q)}_{V}}=m{{c}_{V}}\Delta T\] \[\Rightarrow \,\,\,\,{{(\Delta W)}_{P}}=\,\,m\left( {{c}_{P}}-{{c}_{V}} \right)\Delta T\] \[\Rightarrow \,\,\,\,\,{{\left( \Delta W \right)}_{P}}=1\times (3.4\times 1{{0}^{3}}-2.4\times {{10}^{3}})\times 10\] \[=\,\,\,\,{{10}^{4}}\,cal\]


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