Q113 / 180 · NEET 2013 (Karnataka) · Physics

In a vessel, the gas is at pressure $P$, if the mass of all the molecules is halved of their speed is double, then the resultant pressure will be :

  • Correct answer
    A
    $2 P$
  • B
    $P$
  • C
    $P / 2$
  • D
    $4 P$

Solution

The equation of pressure is $$ P=\frac{1}{3} \frac{m \mathrm{~N}}{v^2} v_{r m s}^2 $$ where $m=$ mass of each molecules $$ \begin{aligned} & N=\text { number of molecules } \\ & V=\text { volume of the gas } \end{aligned} $$ According to the question: mass of all molecules is halved an velocity is double then $$ \begin{aligned} \mathrm{P}^{\prime}=\frac{1}{3}\left(\frac{m}{2}\right) \times \frac{\mathrm{N}}{\mathrm{V}} \times( & \left(2 \mathrm{~V}_{\mathrm{ras}}\right)^2 \\ & =\frac{2}{3} \frac{m \mathrm{~N}}{\mathrm{~V}} \mathrm{~V}_{\mathrm{ras}}^2 \\ & =2 \mathrm{P} \end{aligned} $$ compare with eq (i) $$ \begin{aligned} & \mathrm{P}^{\prime}=2 \mathrm{P} \\ & \mathrm{P}^{\prime}=2 \mathrm{P} \end{aligned} $$

Hence, the correct answer is option: 'A'.

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