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Standard XII

Chemistry

Root Mean Square Velocity

A flask has 1...

Question

A flask has 10 gas particles out of which four particles are moving at $7 {ms}^{- 1}$ and all the remaining ones are moving at the speed of $' x' {ms}^{- 1}$ . If the $V_{r m s}$ of the gas is $5 {ms}^{- 1}$ , what is the value of $‘ x^{'}$ ?

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Solution

$V_{r m s} = \sqrt{\frac{10 \sum i = 1 v_{i}^{2}}{10}} = 5$ (Given)
$\Rightarrow \frac{(7^{2} \times 4) + (x^{2} \times 6)}{10} = 25$
$\Rightarrow 196 + 6 x^{2} = 250$
$∴ x = \sqrt{\frac{250 - 196}{6}} = 3 m/s$

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A flask has 10 gas particles out of which four particles are moving at 7 ms−1 and all the remaining ones are moving at the speed of 'x' ms−1. If the Vrms of the gas is 5 ms−1, what is the value of ‘x′ ?

Vrms=   ⎷10∑i=1v2i10=5 (Given) ⇒(72×4)+(x2×6)10=25 ⇒196+6x2=250 ∴x=√250−1966=3 m/s

A flask has 10 gas particles out of which four particles are moving at $7 {ms}^{- 1}$ and all the remaining ones are moving at the speed of $' x' {ms}^{- 1}$ . If the $V_{r m s}$ of the gas is $5 {ms}^{- 1}$ , what is the value of $‘ x^{'}$ ?

$V_{r m s} = \sqrt{\frac{10 \sum i = 1 v_{i}^{2}}{10}} = 5$ (Given)
$\Rightarrow \frac{(7^{2} \times 4) + (x^{2} \times 6)}{10} = 25$
$\Rightarrow 196 + 6 x^{2} = 250$
$∴ x = \sqrt{\frac{250 - 196}{6}} = 3 m/s$