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The molecules of a given mass of a gas have r.m.s. velocity of 200 ms^-1 at 27 °C and 1.0 x 10⁵ Nm^-2 pressure. When the temperature and pressure of the gas respectively, 127 °C and 0.05 x 10⁵ Nm^-2, the r.m.s. velocity of its molecules in ms^-1 is

Option 1)
$100\sqrt 2$

Option 2)
$\frac{{400}} {{\sqrt 3 }}$

Option 3)
$\frac{{100\sqrt 2 }} {3}$

Option 4)
$\frac{{100}} {3}$

Answers (1)

best_answer

Root mean square velocity -

$V_{rms}= sqrt{frac{3RT}{M}}$

$= sqrt{frac{3P}{ ho }}$

- wherein

R = Universal gas constant

M = molar mass

P = pressure due to gas

$ho$ = density

$V_{rms}=200 m/s$

at T= $27^{\circ}C=300k$

$p=10^{5}Nm^{-2}$

$V_{rms}=\sqrt{\frac{rRT}{M}}$

$V_{rms}$ is independent to pressure. $\therefore \frac{V_{1}}{V_{2}}=\sqrt{\frac{T_{1}}{T_{2}}}=\sqrt{\frac{300}{400}}$

$\left ( T_{2} \right =127^{\circ}=400k)$

or $V_{2}=V_{1}.\left ( \sqrt{\frac{2}{3}} \right )=\frac{200\times 2}{\sqrt{3}}$

$=\frac{400}{\sqrt{3}}$ m/s

V_rms= 200 m/s at T = 27⁰C = 300K

p = 10⁵ Nm^-2

V_rms= $\sqrt{\frac{rRT}{M}}$

Option 1)

$100\sqrt 2$

Incorrect option

Option 2)

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

Correct option

Option 3)

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

Incorrect option

Option 4)

$\frac{{100}} {3}$

Incorrect option

Posted by

prateek

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