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12 . kinetic theory of gases — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics12 . kinetic theory of gases1 Mark
MCQ
If $10^{22}$ gas molecules each of mass $10^{-26}\, kg$ collide with a surface (perpendicular to it)elastically per second over an area $1\, m^2$ with a speed $10^4\,m/s$, the pressure exerted by the gas molecules will be of the order of
  • A
    ${10^8}\,\frac{N}{{{m^2}}}$
  • B
    ${10^3}\,\frac{N}{{{m^2}}}$
  • C
    ${10^4}\,\frac{N}{{{m^2}}}$
  • ✓
    None of this
✓

Answer

Correct option: D.
None of this
d
Pressure is defined as normal force per unit area.

Force is calculated as change in $ momentum/time.$

By this answer is $2 \mathrm{N} / \mathrm{m}^{2}$

None of the option matches so this question must be Bonus.

Detailed solution is as following:

$Magnitude\, of\, change\, in\, momentum \,per\, collision$ $=2$ $mv$

Pressure $=\frac{\text { Force }}{\text { Area }}=\frac{N(2 m v)}{1}$

${=\frac{10^{22} \times 2 \times 10^{-26} \times 10^{4}}{1}} $

${=2 \mathrm{N} / \mathrm{m}^{2}}$

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