If or two gases of molecular weights `M_(A)` and `M_(B)` at temperature `T_(A)` and `T_(B)`, `T_(A)M_(B)=T_(B)M_(A)`, then which of the following properties has the same magnitude for both the gases?
(a) Density
(b) Pressure
(c) `KE` per mole
(d) `u_(rms)`

Explanation

(`a`) Density of gas `(rho)=(PM)/(RT)`
Since `(M_(B))/(T_(B))=(M_(A))/(T_(A))`,
Therefore, at the same pressure `rho_(A)=rho_(B)`. But if pressure is different, then `rho_(A) != rho_(B)`.
(`b`) The pressure of the gases will be equal if their densities are equals, otherwise not [as in case (`a`)].
(`c`) `KE` per mole `=(3)/(2) RT`
Hence, it will be different for the two gases.
(`d`) `u_(rms)=sqrt((3RT)/(M))`
Since `(T_(A))/(M_(A))=(T_(B))/(M_(B))`, `u_(rms)` of `A=u_(rms)` of `B`