A cubical box of side 1 meter contains heluim gas (atomic weight 4) at a pressure of `100N//m^2.` During and obervation time of 1 second, an atom travelling with the root-mean-square speed parallel to one of the edges of the cube, was found to make 500 hits with a particular wall, without any collision with other atoms. Take `R=25/3 Jmole-K and k=1.38xx10^-23J//K`
(a) Evalute the temperature of the gas.
(b) Evalute the average kinetic energy per atom.
(c) Evalute the total mass of helium gas in the box.

Answer

A, B, C

Explanation

The distance travelled by an
atom of helium in `1/500sec` (time
between two succesive
collision) is 2m. Therefore root
mean square speed
`C_(rms)=distance/time=2/(1//500)=1000m//s`

(a) But `C_(rms)=sqrt((3RT)/M)`
`rArr1000=((3xx25//3xxT)/(4xx10^-3) rArr T=160K`
(b) Average kinetic energy of an atom of a monoatomic
gas =`3/2kT`
`:. E_(av)=3/2kT=3/2xx(1.38xx10^-23)xx160`
`=3.312xx10^-21 Joules`
(c) From gas equation `PV=m/MRT`
`m=(PVM)/(RT)=(100xx1xx4)/(25//3xx160) rArr m=0.3012gm`