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)

 

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

 

Vrms= 200 m/s at T = 270C = 300K

p = 105 Nm-2

Vrms\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

Preparation Products

Rank Booster NEET 2021

This course will help student to be better prepared and study in the right direction for NEET..

₹ 13999/- ₹ 9999/-
Buy Now
Knockout NEET May 2021

An exhaustive E-learning program for the complete preparation of NEET..

₹ 22999/- ₹ 14999/-
Buy Now
Knockout NEET May 2022

An exhaustive E-learning program for the complete preparation of NEET..

₹ 34999/- ₹ 24999/-
Buy Now
Test Series NEET May 2021

Take chapter-wise, subject-wise and Complete syllabus mock tests and get in depth analysis of your test..

₹ 6999/- ₹ 4999/-
Buy Now
Test Series NEET May 2022

Take chapter-wise, subject-wise and Complete syllabus mock tests and get an in-depth analysis of your test..

₹ 6999/-
Buy Now
Exams
Articles
Questions