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NEET Sample Paper NEET Sample Test Paper-92

  • question_answer
    Two closed bulbs of equal volume (V) containing an ideal gas initially at pressure \[{{P}_{i}}\] and temperature \[{{T}_{1}}\] are connected through a narrow tube of negligible volume as shown in the figure below. The temperature of one of the bulbs is then raised to \[{{T}_{2}}.\] The final pressures \[{{P}_{f}}\] is :

    A) \[2{{p}_{i}}\left( \frac{{{T}_{2}}}{{{T}_{1}}+{{T}_{2}}} \right)\]

    B)        \[2{{p}_{i}}\left( \frac{{{T}_{1}}{{T}_{2}}}{{{T}_{1}}+{{T}_{2}}} \right)\]

    C) \[{{p}_{i}}\left( \frac{{{T}_{1}}{{T}_{2}}}{{{T}_{1}}+{{T}_{2}}} \right)\]    

    D)        \[2{{p}_{i}}\left( \frac{{{T}_{1}}}{{{T}_{1}}+{{T}_{2}}} \right)\]

    Correct Answer: A

    Solution :

    [a]  For a given mass of an ideal gas, the volume and amount (moles) of the gas are directly proportional if the temperature and pressure are constant, i.e. \[V\propto n\] Hence in the given case. Initial moles and final moles are equal \[{{({{n}_{T}})}_{i}}={{({{n}_{T}})}_{f}}\] \[\frac{{{P}_{i}}V}{R{{T}_{1}}}+\frac{{{P}_{i}}V}{R{{T}_{1}}}=\frac{{{P}_{f}}V}{R{{T}_{1}}}+\frac{{{P}_{f}}V}{R{{T}_{2}}}\] \[2\frac{{{P}_{i}}}{{{T}_{1}}}=\frac{{{P}_{f}}}{{{T}_{1}}}+\frac{{{P}_{f}}}{{{T}_{2}}}\] \[{{P}_{f}}=\frac{2\,\,{{P}_{i}}{{T}_{2}}}{{{T}_{1}}+{{T}_{2}}}\]


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