Two gases X (Mol. Wt `M_(X)` ) and (Mol. Wt. `M_(y), M_(y)gtM_(X)`) are at the same temperature T in two different containers. Their root mean square velocities are `C_(x)` and `C_(Y)` respectively. If the average kinetic energies per molecule of two gases X and Y are `E_(X()` and `E_(Y)` respectively, then which of the following relations (s) is (are) true?
A
`E_(X)gtE_(Y)`
B
`C_(X)gtC_(Y)`
C
`E_(X)=E_(Y)=3/2RT`
D
`E_(X)=E_(Y)=3/2k_(B)T`
Text Solution
Verified by Experts
Average kinetic energy per molecule of gas `E_(k)` `=3/2k_(B)T` where `k_(B)=` Boltzmann constant `impliesbar_(k)=3/2(RT)/(N_(A))" "( :. k_(B)=R/(N_(A)))` `C_(X)=sqrt((3RT)/(M_(x)),C_(Y)=sqrt((3RT)/(M_(Y)))` `(C_(X))/(C_(Y))=sqrt((3RT)/(M_(X))xx(M_(Y))/(3RT))=sqrt((M_(Y))/(M_(X)))gt1 " "[............M_(Y)gtM_(X)]` `:.C_(X)gtC_(Y)`
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