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Haryana PMT Haryana PMT Solved Paper-2004

  • question_answer
    The thermodynamic co-ordinates of a jar filled with gas A are P, V and T and another jar B filled with another gas are 2P, V/4 and 2T, where the symbols have their usual meaning. The ratio of the number of molecules of jar A to those of jar B is :

    A)  4 : 1                                      

    B)  2 : 1

    C)  1:2                                        

    D)  1 : 1

    Correct Answer: A

    Solution :

                                             The gas equation Is                                                         \[PV=nRT\]       Suppose \[{{n}_{1}}\] and \[{{n}_{2}}\] moles of the gas be in jar A and jar B respectively         Then   \[{{P}_{1}}{{V}_{1}}={{n}_{1}}R{{T}_{2}}\]                                          \[{{P}_{2}}{{V}_{2}}={{n}_{2}}R{{T}_{2}}\]                                          \[\frac{{{n}_{2}}}{{{n}_{1}}}=\frac{{{P}_{2}}{{V}_{2}}{{T}_{1}}}{{{P}_{1}}{{V}_{1}}{{T}_{2}}}\] For jar A                                          \[{{P}_{1}}=P\]                                          \[{{V}_{1}}=V\] For jar B                 \[{{P}_{2}}=2P\]                               \[{{V}_{2}}=V/4\]                 \[{{T}_{2}}=2T\]                 \[\frac{{{n}_{2}}}{{{n}_{1}}}=\frac{2PVT}{PV\times 4\times 2T}\]                 \[=\frac{1}{4}\]                 \[\frac{{{n}_{1}}}{{{n}_{2}}}=\frac{4}{1}\]


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