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The molecules of a given mass of a gas have rms velocity of 200m.s^-^1 at 27^0C and 1.0 \times 10^5 \mathrm{~N} \mathrm{~m}^{-2}  pressure, When the temperature and pressure of a gas are respectively, 127^0C and 0.05 \times 10^5 \mathrm{~N} \cdot \mathrm{m}^{-2}, the rms velocity of its molecules in  M.s^-^1 is - 

Option: 1

\frac{400}{\sqrt{3}}


Option: 2

\frac{100 \sqrt{2}}{3}


Option: 3

\frac{100}{3}


Option: 4

100 \sqrt{2}

 


Answers (1)

best_answer

rms speed of gas molecules, c \propto \sqrt{T}

\therefore \frac{c_1}{c_2}=\sqrt{\frac{T_1}{T_2}}=\sqrt{\frac{27+273}{\left.127+273\right)}}=\sqrt{\frac{300}{400}}=\frac{\sqrt{3}}{2}

\text { or, } c_2=\frac{2}{\sqrt{3}} c_1=\frac{2}{\sqrt{3}} \times 200=\frac{400}{\sqrt{3}} \mathrm{~m} / \mathrm{s}

 

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shivangi.bhatnagar

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