Question

For a given gas at 1 atm pressure, rms speed of the molecules is 200 m/s at 127ºC. At 2 atm pressure and at 227ºC, the rms speed of the molecules will be:
(A) 80 m/s (B) 80√5 m/s
(C) 100 m/s (D) 100√5 m/s

Answer 1

Given :

The rms speed of the gas at 1 atm and 400 K ( 127 °C ) = 200 m/s

To find :

The rms speed of the gas at 2 atm and 500 K ( 227 °C ) .

Solution :

let rms speed at 500 K is v .

rms speed , v$_{rms}$ = √( 3 * R * T / M )

Now , at 1 atm and 400 K ,

200 = √( 3 * R * 400 / M )            .....(i)

at 2 atm and 500 K ,

v = √( 3 * R * 500 / M )                ......(ii)

dividing (ii) by (i) ,

v / 200 = √ ( 500 / 400 )

=> v = ( 200 * √5 ) / 2

=> v = 100√5 m/s  

The rms speed of the gas at 2 atm and 500 K ( 227 °C ) is 100√5 m/s  .