`1 g` mole of oxygen at `27^@ C` and `1 ` atmosphere pressure is enclosed in a vessel.
(a) Assuming the molecules to be moving with `v_(r m s)`, find the number of collisions per second which the molecules make with one square metre area of the vessel wall.
(b) The vessel is next thermally insulated and moves with a constant speed `v_(0)`. It is then suddenly stoppes. The process results in a rise of temperature of the gas by `1^@ C`. Calculate the speed `v_0.[k = 1.38 xx 10^-23 J//K` and `N_(A) = 6.02 xx 10^23 //mol]`.

Answer

`1.965`

Explanation

`v_("m s") = sqrt((3RT)/M) = sqrt((3xx8.31 xx300)/(32 xx10^(-3))) = 483.4 m//s`
Given, `p0 = 1.01 xx10^5 N//m^2 = ` Force per unit area.
Let molecules of oxygen strike the wall per second per `m^2` and recoil with same speed. Change in momentum is
` (3nmv_("m s"))`.
`:." "n =(p_0)/("2m v"_("m s"))= (1.02xx10^5)/(2[32/(6.02xx10^(26))](483.4))`
`=1.965 xx10^(27)//s`