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Some amount of oxygen gas contained in a vessel has a density of 1.429 \mathrm{~kg} \cdot \mathrm{m}^{-3} at STP. The temperature is increased until the pressure is doubled. Neglecting the change in volume of the vessel, Find the rms speed of the oxygen molecules.

Option: 1

65215 \mathrm{~cm} \cdot \mathrm{s}^{-1}


Option: 2

65215


Option: 3

65251 \mathrm{cm}


Option: 4

65215 \mathrm{~cm}


Answers (1)

best_answer

Mass and Volume of the gas remain the same; So the density also remains the same.

\text { So, } p=1.429 \mathrm{~kg} \cdot \mathrm{m}^{-3}=1.429 \times 10^{-3} 8 \cdot \mathrm{cm}^{-3}

in the first care, s ms speed of oxygen molecules,

C_{1}=\sqrt{\frac{3 P_{1}}{P}}=\sqrt{\frac{3 \times(76 \times 13.6 \times 980)}{1.429 \times 10^{-3}}}=46114 \mathrm{~cm} \cdot \mathrm{s}^{-1}

in the second case, P_{2}=2 P_{1} \therefore \frac{c_{2}}{C_{1}}=\sqrt{\frac{P_{2}}{P_{1}}=\sqrt{2}}$ or $c_{2}=\sqrt{2} c_{1}=46114 \times \sqrt{2}=65215 \mathrm{~cm} \cdot \mathrm{s}^{-1}.

Posted by

Kuldeep Maurya

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