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Two gases X (Mol. Wt M(X) ) and (Mol. W...

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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Knowledge Check

  • Two gases X (mol. wt. M_(X)) and Y (mol. wt. M_(Y) , M_(Y) gt M_(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 relation (s) is (are) true ?

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  • E_(0) and E_(n) respectively represent the average kinetic energy of a molecule of oxygen and hydrogen. If the two gases are at the same temperature, which of the following statements is true?

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