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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
A cylinder of capacity $20$ litres is filled with ${H_2}$ gas. The total average kinetic energy of translatory motion of its molecules is $1.5 \times {10^5}\,J$. The pressure of hydrogen in the cylinder is
  • A
    $2 \times {10^6}\,N/{m^2}$
  • B
    $3 \times {10^6}\,N/{m^2}$
  • C
    $4 \times {10^6}\,N/{m^2}$
  • ✓
    $5 \times {10^6}\,N/{m^2}$
✓

Answer

Correct option: D.
$5 \times {10^6}\,N/{m^2}$
d
$E = \frac{3}{2}PV$$ \Rightarrow P = \frac{{2E}}{{3V}}$$ = \frac{2}{3} \times \frac{{1.52 \times {{10}^5}}}{{20 \times {{10}^{ - 3}}}}$

 $ = \frac{{{{10}^5}}}{{20 \times {{10}^{ - 2}}}} = 5 \times {10^6}N/{m^2}$

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