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12 . kinetic theory of gases — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics12 . kinetic theory of gases1 Mark
MCQ
Consider the following statements for air molecules in an air tight container :

$(I)$ The average speed of molecules is larger than root mean square speed.

$(II)$ Mean free path of molecules is larger than the mean distance between molecules.

$(III)$ Mean free path of molecules increases with temperature.

$(IV)$ The rms speed of nitrogen is smaller than oxygen molecule.

Which of the above statements are correct?

  • ✓
    Only statement $II$ is correct
  • B
    Statements $II$ and $III$ are correct
  • C
    Statements $II$ and $IV$ are correct
  • D
    Statements $I, II$ and $IV$ are correct
✓

Answer

Correct option: A.
Only statement $II$ is correct
a
$(a)$ Average speed is related to the rms speed as

$\bar{c}=\sqrt{\frac{8}{3 \pi}} \cdot c_{ rms }$

$\Rightarrow \bar{c} < c_{ rms }$

So, statement $1$ is incorrect.

Mean free path of molecules is larger than mean distance between molecules.

So, statement $II$ is correct.

Mean free path decreases with temperature as collision frequency increases with temperature. So, statement $III$ is incorrect.

As, $c_{ rms } \propto \frac{1}{\sqrt{M}} \Rightarrow rms$ speed of nitrogen molecule is higher than that of oxygen molecule at same temperature. So, statement $IV$ is incorrect.

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