An ideal gas in a closed container is heated so that the final rms speed of the gas particles increases by 2 times the initial rms speed. If the initial gas temperature is `27^(@)C`, then the final temperature of the ideal gas is :

Options

A. `1200^(@)C`
B. `927^(@)C`
C. `827^(@)C`
D. `1473^(@)C`

Answer

B

Explanation

As, rms velocity of ideal gas particles is given,
`v_(rms)=sqrt((3kT)/(m))`
`rArr v_(rms) prop sqrt(T)`
where, temperature T is measured in kelvin scale.
So, the ratio
`(v_(1 rms)^(2))/(v_(2rms)^(2))=(T_(1))/(T_(2))`
As given, `v_(2 rms)=2v_(1 rms)` and `T_(1)=27^(@)C=300K`
`rArr (v_(1rms)^(2))/(4v_(1 rms)^(2))=(300)/(x)`
`rArr x=300xx4=1200K`
Hence, `1200K=(1200-273)^(@)C=927^(@)C`
Hence, the correct option is (b).