How can the internal energy and pressure of a gas per unit volume be represented?

  • A
    $P = \frac{2}{3}E$
  • B
    $P = \frac{3}{2}E$
  • C
    $P = \frac{1}{2}E$
  • D
    $P = 2E$

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Which of the following is correct about collision frequency $(Z_{11})$ of an ideal gas participating in an isobaric process?

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$X$ and $Y$ are two volatile liquids with molar weights of $10 \ g \ mol^{-1}$ and $40 \ g \ mol^{-1}$ respectively. Two cotton plugs,one soaked in $X$ and the other soaked in $Y$,are simultaneously placed at the ends of a tube of length $L = 24 \ cm$. The tube is filled with an inert gas at $1 \ atmosphere$ pressure and a temperature of $300 \ K$. Vapours of $X$ and $Y$ react to form a product which is first observed at a distance $d \ cm$ from the plug soaked in $X$. Take $X$ and $Y$ to have equal molecular diameters and assume ideal behaviour for the inert gas and the two vapours.
$1.$ The value of $d$ in $cm$,as estimated from Graham's law,is:
$(A) \ 8 \ (B) \ 12 \ (C) \ 16 \ (D) \ 20$
$2.$ The experimental value of $d$ is found to be smaller than the estimate obtained using Graham's law. This is due to:
$(A)$ larger mean free path for $X$ as compared to that of $Y$.
$(B)$ larger mean free path for $Y$ as compared to that of $X$.
$(C)$ increased collision frequency of $Y$ with the inert gas as compared to that of $X$ with the inert gas.
$(D)$ increased collision frequency of $X$ with the inert gas as compared to that of $Y$ with the inert gas.
Give the answer for question $1$ and $2$.

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