If for two gases of molecular weights `M_(A)` and `M_(B)` at temperature `T_(A)` and `T_(B)`, respectively, `T_(A)M_(B)=T_(B)M_(A)`, then which property has the same magnitude for both the gases?

Options

A. `Pv` if mass of gases taken are same
B. Pressure
C. `KE` per mole
D. `V_(rms)`

Explanation

Hint: When `(T_(A))/(M_(A))=(T_(B))/(M_(B))` or `T_(A)M_(B)=T_(B)M_(A)`
`(PV)_(A)=nRT` or `(W_(A))/(M_(A))RT_(A)`
and `(PV)_(B)=(W_(B))/(M_(B))RT_(B)`
`:. ` When `W_(A)=W_(B)`
`(PV)_(A)=(PV)_(B)`
`mu_(rms)=sqrt((3RT)/(M))`
`mu_(A)=sqrt((3RT_(B))/(M_(A)))`
`mu_(B)=sqrt((3RT_(B))/(M_(B)))`
`:. mu_(A)=mu_(B)` `((T_(A))/(M_(A))=(T_(B))/(M_(B)))`