JEE Main & Advanced Chemistry States of Matter Question Bank Ideal gas equation and Related gas laws

  • question_answer Two closed vessels of equal volume containing air at pressure \[{{P}_{1}}\] and temperature \[{{T}_{1}}\] are connected to each other through a narrow tube. If the temperature in one of the vessels is now maintained at \[{{T}_{1}}\] and that in the other at \[{{T}_{2}}\], what will be the pressure in the vessels

    A)                 \[\frac{2{{P}_{1}}{{T}_{1}}}{{{T}_{1}}+{{T}_{2}}}\]             

    B)                 \[\frac{{{T}_{1}}}{2{{P}_{1}}{{T}_{2}}}\]

    C)                 \[\frac{2{{P}_{1}}{{T}_{2}}}{{{T}_{1}}+{{T}_{2}}}\]             

    D)                 \[\frac{2{{p}_{1}}}{{{T}_{1}}+{{T}_{2}}}\]

    Correct Answer: C

    Solution :

               \[\frac{{{P}_{1}}}{{{T}_{1}}}+\frac{{{P}_{1}}}{{{T}_{1}}}=\frac{P}{{{T}_{1}}}+\frac{P}{{{T}_{2}}}\]                                 \[\frac{2{{P}_{1}}}{{{T}_{1}}}=P\left( \frac{{{T}_{1}}+{{T}_{2}}}{{{T}_{1}}{{T}_{2}}} \right)\];  \[\therefore P=\frac{2{{P}_{1}}({{T}_{1}}{{T}_{2}})}{{{T}_{1}}({{T}_{1}}+{{T}_{2}})}=\frac{2{{P}_{1}}{{T}_{2}}}{{{T}_{1}}+{{T}_{2}}}\]

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