The molecules of a given mass of gas have an rms velocity of 200 m s- 1 at 27 ° C and pressure 1 atm . When the temperature is 127 ° C and pressure is 2 atm , the rms velocity in m s- 1 will be?

Question

The molecules of a given mass of gas have an rms velocity of 200 m s- 1 at 27 ° C and pressure 1 atm . When the temperature is 127 ° C and pressure is 2 atm , the rms velocity in m s- 1 will be? (A) (100 √2/3) (B) 100√2 (C) (400/√3) (D) None of these

Tardigrade Admin · Accepted Answer

RMS velocity doesn't depend upon pressure, it depends upon temperature only,

i e ., v_{r m s} \propto T

.

\Rightarrow \frac{v _{1}}{v _{2}} = \frac{T _{1}}{T _{2}} \Rightarrow \frac{200}{v _{2}} = \frac{( 273 + 27 )}{( 273 + 127 )} = \frac{300}{400}

\Rightarrow v_{2} = \frac{400}{3} m s^{- 1}

Q. The molecules of a given mass of gas have an rms velocity of $200 m s^{- 1}$ at $27^{\circ} C$ and pressure $1 a t m$ . When the temperature is $127^{\circ} C$ and pressure is $2 a t m$ , the rms velocity in $m s^{- 1}$ will be?

$\frac{100 2}{3}$

$1002$

$\frac{400}{3}$

None of these

RMS velocity doesn't depend upon pressure, it depends upon temperature only,
$i e ., v_{r m s} \propto T$ .
$\Rightarrow \frac{v _{1}}{v _{2}} = \frac{T _{1}}{T _{2}} \Rightarrow \frac{200}{v _{2}} = \frac{( 273 + 27 )}{( 273 + 127 )} = \frac{300}{400}$
$\Rightarrow v_{2} = \frac{400}{3} m s^{- 1}$

Q. The molecules of a given mass of gas have an rms velocity of 200ms−1 at 27∘C and pressure 1atm . When the temperature is 127∘C and pressure is 2atm , the rms velocity in ms−1 will be?

31002​​

1002​

3​400​