JEE Main & Advanced Sample Paper JEE Main - Mock Test - 9

  • question_answer
    Given is the graph between \[\frac{PV}{T}\]and P for 1 g of oxygen gas at two different temperatures \[{{T}_{1}}\] and \[{{T}_{2}}\] as shown in figure. Given, density of oxygen\[=1.427\text{ }kg\,{{\text{m}}^{-3}}\]. The value of \[PV/T\]at the point A and the relation between \[{{T}_{1}}\] and \[{{T}_{2}}\]are respectively

    A) \[0.259\,J{{K}^{-1}}\] and \[{{T}_{1}}<{{T}_{2}}\]

    B) \[8.314\,J\,mo{{l}^{-1}}{{K}^{-1}}\]and \[{{T}_{1}}>{{T}_{2}}\]

    C) \[0.259\,J\,{{K}^{-1}}\] and \[{{T}_{1}}>{{T}_{2}}\]

    D) \[4.28\,J\,{{K}^{-1}}\] and \[{{T}_{1}}<{{T}_{2}}\]

    Correct Answer: C

    Solution :

    \[PV=\mu RT=\frac{m}{M}RT,\] where w = mass of the gas
    and \[\frac{m}{M}=\mu =\] number of moles.
    \[\frac{PV}{T}=\mu R=\] a constant for all values of P.
    That is why, ideally it is a straight line.
    \[\therefore \,\,\frac{PV}{T}=\frac{1g}{32\,g\,mo{{l}^{-1}}}\times 8.31J\,mo{{l}^{-1}}{{K}^{-1}}=0.259J{{K}^{-1}}\]Also, \[{{T}_{1}}>{{T}_{2}}\]


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