The r.m.s velocity of the molecules of an ideal gas is C at a temperature of 100K. At what temperature is r.m.s. velocity will be doubled?

  • Option 1)

    200 K

  • Option 2)

    400 K

  • Option 3)

    300 K

  • Option 4)

    50 K

 

Answers (1)

As we learnt in 

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

 

 V_{rms} = \sqrt{\frac{3RT}{M}}

\Rightarrow V_{rms}\ \propto\ \sqrt{T}

V_{rms}  will be doubled when temperature increases four times.

\therefore  Temperature = 4 \times initial temperature

                           = 400 K


Option 1)

200 K

This option is incorrect

Option 2)

400 K

This option is correct

Option 3)

300 K

This option is incorrect

Option 4)

50 K

This option is incorrect

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