The root mean square velocity of an ideal gas in a closed container of fixed volume is increased from `5xx10^(4)cms^(-1)` to `10xx10^(4)cm s^(-1)`. Which of the following statements correctly explains how the change is accomplished?

Options

A. By heating the gas, the temperature is doubled.
B. By heating the gas, the pressure is quadrupled.
C. By heating the gas, the temperature is quadrupled.
D. By heating the gas, the pressure is doubled.

Explanation

Hint: `mu_(rms)=sqrt((3RT)/(M))` or `sqrt((3PV)/(M))`
`(mu_(rms))_(1)=5xx10^(4)cm s^(-1)`
`(mu_(rms))_(2)=10xx10^(4) cm s^(-1)`
`P_(1)=((mu_(rms))_(1)^(2)xxM)/(3V)=(5xx10^(4))^(2)xx(M)/(3V)`
`P_(2)=((mu_(rms))_(2)^(2)xxM)/(3V)=(10xx10^(4))^(2)xx(M)/(3V)`
or `(P_(2))/(P_(1))=((10xx10^(4))^(2))/((5xx10^(4))^(2))=(100)/(25)=4`
`:. P_(2)=4xxP_(1)`
Similarily, `T_(2)=4xxT_(1)`