A cubical box of side `5m` contains helium gas at a pressure `320 N//m^(2)`. During an observation time of 1 second, an atom travelling with root mean square speed parallel to one of the sides of the cube was found to make 1000 hits with a particular wall, without any collision with the other atoms. (take `R=25/3J//"mol"-K`). Then

Options

A. The temperature of gas is `16xx10^(3)K`
B. The temperature of gas is `8xx10^(3)K`
C. The total mass of helium gas in the box is `1.2gm`
D. The total mass of helium gas in the box is `2.5 gm`

Answer

A, C

Explanation

Time between two consecutive collision `=1/1000`sec
So, `(2l)/(v_("rms"))=1/1000`
`V_("rms")=2000xx5=10000m//s`
`v_("rms")=sqrt((3RT)/M)=10000`
So, `T=(10^(8)xx4xx10^(-3))/(3xx(25/3))=16xx10^(3)K`
Mass of helium gas `implies PV=nRT`
`PV=m/M RT`
`m=(PVM)/(RT)=(320xx125xx(4xx10^(-3)))/((25/3)xx16xx10^(3))=1.2 gm`