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Consider two diatomic ideal gases A &B a...

Consider two diatomic ideal gases A &B at some temperature T. Molecules of A rigid and have mass 2m. Molecules of B have vibrational modes in addition and have mass m.The ratio of the specific heats `( C_(v) ^(4) ` & ` C_(v) ^(B))` of gas A &B,if both the molecules have planar structure is `:`

A

`( 5)/(7)`

B

`( 5)/(6)`

C

`( 6)/(7)`

D

`(3)/( 4)`

Text Solution

Verified by Experts

`C_(v) = ( f R)/(2)` (where the degree of the freedom and R is the universal gas constant )
For A, diatomic molecules, f = 5
For B, diatomic molecule, with vibration, f = 7
`C_(v) ^(A) = (5 xxR )/( 2) = ( 5R)/( 2) `, `C_(v) ^(B) = ( 7 xxR )/( 2) = ( 7R )/( 2) rArr (C_(v)^(A))/( C_(v)^(B)) = ( 5)/( 7)`
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Consider, two ideal diatomic gases A and B at some temperature T. Molecules of the gas A are rigid, and have a mass m. Molecules of the gas B have an additional vibrations mode, and have a mass m/4 . The ratio of the specific heats ( C_(V)^(A) and C_(V)^(B) ) of gas A and B, respectively is:

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Knowledge Check

  • For polyatomic molecules having f vibrational modes, the ratio of two specific heats, (C_(P))/(C_(V)) is …………… .

    A
    `(1+f)/(2+f)`
    B
    `(2+f)/(3+f)`
    C
    `(4+f)/(3+f)`
    D
    `(5+f)/(4+f)`

  • For polyatomic molecules having 'f' vibrational modes, the ratio of two specific heats, C_(P)/C_(V) is

    A
    `(1+f)/(2+f)`
    B
    `(2+f)/(3+f)`
    C
    `(4+f)/(3+f)`
    D
    `(5+f)/(4+f)`

  • For polyatomic molecules having 'f' vibrational modes, the ratio of two specific heat, (C_(P))/(C_(V)) is

    A
    `(1+f)/(2+f)`
    B
    `(2+f)/(3+f)`
    C
    `(4+f)/(3+f)`
    D
    `(5+f)/(4+f)`

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