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At 27^(@)C, average translational kineti...

At `27^(@)C`, average translational kinetic energies of the molecules in 8g of `CH_(4),8g` of `O_(2)` and 8g of He are `overline(in_(1)),overline(in_(2))` and `overline(in_(3))` respectively and total kinetic energies of the molecules in these gases are `E_(1),E_(2) and E_(3)` respectively. which of the following is true-

A

`overline(in_(1))=overline(in_(2))=overline(in_(3))`

B

`overline(in_(3)) gt overline(in_(2)) gt overline(in_(1))`

C

`E_(1)=E_(2)=E_(3)`

D

`E_(2) lt E_(1) lt E_(3)`

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The correct Answer is:
A
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Knowledge Check

  • Two gases X (mol wt. M_(X) ) and Y (mo. At. 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 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-

    A
    `E_(X) gt E_(Y)`
    B
    `C_(X) gt C_(Y)`
    C
    `E_(X)=E_(Y)=(3)/(2)RT`
    D
    `E_(X)=E_(Y)=(3)/(2)k_(B)T`

  • If e_(1) and e_(2) are the respective eccentricities of the hyperbola 4x^(2) - 9y^(2) = 36 and the ellipse 2x^(2) + 9y^(2) = 36 , then which of the following relation is true?

    A
    `2e_(2)^(2)+e_(1)^(2)=3`
    B
    `2e_(1)^(2)+e_(2)^(2)=4`
    C
    `e_(1)^(2)+e_(2)^(2)=2`
    D
    `e_(1)^(2)-2e_(2)^(2)=1`

  • The kinetic energy of one mole of a gas is given by the expression K.E=(3PV)/2 and K.E.=3/2RT

    A
    `K.EpropP` at constant temperature
    B
    `K.EpropT` at constant pressure
    C
    `K.E. is` not `directly prop` to volume at constant temperature
    D
    `K.EpropV` at constant temperature
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