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  3. In a gas, 5 molecules have speed 150 m/s, 170 m/s, 170 m/s, 180 m/s, 190 m/s. Ratio of V_r_m_s to V_m_e_a_n is nearly
# Engineering

In a gas, 5 molecules have speed 150 m/s, 170 m/s, 170 m/s, 180 m/s, 190 m/s. Ratio of V_r_m_s to V_m_e_a_n is nearly

Answers (1)
S Satyajeet Kumar

Root mean square velocity -

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

= \sqrt{\frac{3P}{\rho }}
 

- wherein

R = Universal gas constant

M = molar mass

P = pressure due to gas

\rho = density

 

 

Average speed of molecule of a gas -

V_{av}= \sqrt{\frac{8KT}{\pi m}}

        = \sqrt{\frac{8RT}{\pi m}}
 

- wherein

K = Boltzmann's Constant

m = mass of a molecule

R = Universal gas constant

T = temperature

 

 V_{rms}=\sqrt{\frac{V{_{1}}^{2}+V{_{2}}^{2}+V{_{3}}^{2}+V{_{4}}^{2}+V{_{5}}^{2}}{5}}= 172.51\ m/s

V_{mean}=\frac{150+170+170+ 180+190}{5}=\frac{860}{5}=172\ m/s

Ratio = 1

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