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  • Which of the following statement is not true?  Option: 1  the ratio of the mean speed to the rms speed is independent of the tempera

Which of the following statement is not true?
 

Option: 1

 the ratio of the mean speed to the rms speed is independent of the temperature.
 


Option: 2

 the square of the mean speed of the molecules is equal to the square of rms speed at a certain temperature.
 


Option: 3

mean kinetic energy of the gas molecules at any giventemp is dependent of the mean speed.
 


Option: 4

 the difference between rms speed and mean speed at any temperature fer different gases diminishes as larger molar masses are considered.


Answers (1)

best_answer

\begin{aligned} \mathrm{(a)}&\mathrm{ V_{a v}=\sqrt{\frac{8 R T}{\pi M}} \quad V_{r m s}=\sqrt{\frac{3 R T}{M}}}\\ &\mathrm{\frac{V_{a v}}{V_{\text {rms }}}=\frac{\sqrt{8 / \pi}}{\sqrt{3}} \quad \therefore \text{ Independent of temperature.}}\\ &\text{It is true} \end{aligned}

\begin{aligned} \mathrm{(b) \frac{8 R T}{\pi M}=\frac{3 R T}{M} \Rightarrow \frac{T}{T}=\frac{3 \pi}{8} \quad \therefore T \neq T^{\prime}\quad \text{ false }} \end{aligned}

 (c) mean kinetic energy is  \begin{aligned} \mathrm{\frac{1}{2} m v^2, } \end{aligned} when the change \begin{aligned} \mathrm{V_{a v}, V_{rms}} \end{aligned} get effected.  True

(d) True. This is because molecular mass oc cums in the denominate of the expression.

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Divya Prakash Singh

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