MCQ
At a given temperature if ${V_{rms}}$ is the root mean square velocity of the molecules of a gas and ${V_s}$ the velocity of sound in it, then these are related as $\left( {\gamma = \frac{{{C_P}}}{{{C_v}}}} \right)$
  • A
    ${V_{rms}} = {V_s}$
  • ${V_{rms}} = \sqrt {\frac{3}{\gamma }} \times {V_s}$
  • C
    ${V_{rms}} = \sqrt {\frac{\gamma }{3}} \times {V_s}$
  • D
    ${V_{rms}} = \left( {\frac{3}{\gamma }} \right) \times {V_s}$

Answer

Correct option: B.
${V_{rms}} = \sqrt {\frac{3}{\gamma }} \times {V_s}$
b
${v_{rms}} = \sqrt {\frac{{3P}}{\rho }} ,$ and ${v_{/ofu}} = \sqrt {\frac{{\gamma P}}{\rho }} $

$\frac{{{v_{rms}}}}{{{v_{/ofu}}}} = \sqrt {\frac{3}{\gamma }} $

$\Rightarrow {v_{rms}} = \sqrt {\frac{3}{\gamma }}  \times {v_{/ofu}}$

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