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QJEEM19Phacc6: JEE Main 2019 Physics - Class 11 JEEM19Phacc6 Solution: An HCl molecule has rotational, translational and vibrational…

An HCl molecule has rotational, translational and vibrational motions. If the rms velocity of HCl molecules in its gaseous phase is v‾\overline v , m is its mass and kB is Boltzmann constant, then its temperature will be :

Multiple Choice Options

  • A mv‾25kB{{m{{\overline v }^2}} \over {5{k_B}}}
  • B mv‾26kB{{m{{\overline v }^2}} \over {6{k_B}}}
  • C mv‾27kB{{m{{\overline v }^2}} \over {7{k_B}}}
  • D mv‾23kB{{m{{\overline v }^2}} \over {3{k_B}}}

Step-by-Step Verified Solution

An HCl molecule, being diatomic, has:

  • 3 translational degrees of freedom
  • 2 rotational degrees of freedom
  • 2 vibrational degrees of freedom

The total number of degrees of freedom is 3+2+2=73 + 2 + 2 = 7 .

According to the equipartition theorem, each degree of freedom contributes 12kBT\frac{1}{2} k_B T to the total energy. So the total energy is given by: 72kBT\frac{7}{2} k_B T

The translational kinetic energy is related to the root-mean-square (rms) speed v‾\overline{v} by: 12mv‾2=72kBT\frac{1}{2} m \overline{v}^2 = \frac{7}{2} k_B T

Rearranging to solve for the temperature, we find: T=mv‾27kBT = \frac{m \overline{v}^2}{7k_B}

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