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Uttarakhand PMT Uttarakhand PMT Solved Paper-2010

  • question_answer
    A vessel has 6 g of hydrogen at pressure p and temperature 500 K. A small hole is made in it so, That hydrogen leaks out. How much hydrogen leaks out if the final pressure is \[\frac{P}{2}\] and temperature falls to 300 K?

    A)  2 g             

    B)  3 g

    C)  4 g             

    D)  1 g

    Correct Answer: D

    Solution :

     From ideal gas equation, \[pV=\frac{m}{M}RT\] In\[I\]st condition, \[pV=\frac{6}{M}R(500)\]                ...(i) Let\[x\]gram of hydrogen leaks out, So,     \[\frac{P}{2}V=\frac{(6-x)}{M}R(300)\]         ...(ii) Dividing Eqs. (ii) by Eqs. (i), we have \[\frac{1}{2}=\frac{6-x}{6}.\frac{300}{500}\] \[\frac{1}{2}=\frac{6-x}{10}\] \[\Rightarrow \] \[6-x=5\] \[\therefore \] \[x=1g\]


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