First slide

Gaseous state

Question

A flask has 10 gas particles, out of which four particles are moving at 7 ms^-1 and the remaining are moving at the same speed of 'X' ms^-1. If the r.m.s. of the gas is 5 ms^-1, what is the value of X ?

Moderate

Solution

$\begin{array}{l} u_{rms} = \sqrt{\frac{u_{1}^{2} N_{1} + u_{2}^{2} N_{2}}{N_{1} + N_{2}}} \Rightarrow u_{rms}^{2} = \frac{u_{1}^{2} N_{1} + u_{2}^{2} N_{2}}{N_{1} + N_{2}} \\ 25 = \frac{4 \times 7^{2} + u_{2}^{2}}{10} \Rightarrow u_{2} = \sqrt{\frac{54}{6}} = 3 {ms}^{- 1} \end{array}$

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