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The total kinetic energy of a sample of ...

The total kinetic energy of a sample of gas which contains N molecules at `-123^(@)C` is `E_(k)` joules. Another sample of gas at `27^(@)C` has total kinetic energy `2E_(k)` joules. The number of molecules in the second sample of gas is

A

`N//2`

B

`2N`

C

`N`

D

`N^(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
`E_(k) = (3)/(2) NR xx 150 = 225 NR`
`2E_(k) =(3)/(2) N_x R xx 300 = 450 N_x R`
`2 xx 225 NR = 450 N_x R implies N_x= N`
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Knowledge Check

  • Kinetic energy of a gram molecule of the gas is

    A
    `1/2`RT
    B
    `3/2`RT
    C
    RT
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    `5/2`RT

  • The most probable kinetic energy of a gas molecule

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    `(kT)/(2)`
    B
    `kT`
    C
    2kT
    D
    RT

  • Average kinetic energy of a gas molecule is

    A
    inverserly proportional to the square of its absolute temperature
    B
    directly proportional to square root of its absolute temperature
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    directly proportional to its absolute temperature
    D
    directly proportional to square of absolute temperature

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