If, at a given temperature, the totla kinetic energy of the molecules in unit volume of an ideal gas be E, show that the pressure of the gas, `P=2//3E`.

Explanation

According to kinetiic gas equation, `PV=(1)/(3)mnc^(2)`
suppose, m=mass of each molecule of the gas and n=number of molecules present in V volume of the gas, c=root mean square velocity of gas molecule.
`therefore PV =(2)/(3)xxnxx(1)/(2)mc^(2)` or, `P=(2)/(3)xx((n)/(V))xx(1)/(2)mc^(2)` ltBrgt Where `(n)/(V)`= the number of molecules per unit volume and `(1)/(2)mc^(2)=` the average kinetic energy of each molecule.
`therefore ((n)/(V))xx(1)/(2)mc^(2)`=the total kinetic energy of the molecules present per unit volume`=E," "therefore P=2//3E" "` (proved)