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The pressure exerted by an ideal gas is ...

The pressure exerted by an ideal gas is p=`1/3 M/Vc^2` where the symbols have their usual meanings. Using standard gas equation, pV=nRT we find that `c^2=(3RT)/M` or `C^2 prop T`. Average kinetic energy of translation of 1 mol of gas=`1/2 Mc^2=(3RT)/2`
Average thermal energy of a helium atom at room temperature `(27^@C)` is (given Boltzmann constant `k=1.38 times 10^-23 J.K^-1`)

A

`2.16 times 10^21 J`

B

`6.21 times 10^21 J`

C

`6.21 times 10^-21 J`

D

`6.21 times 10^-23 J`

Text Solution

Verified by Experts

The correct Answer is:
C
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Calculate the translational kinetic energy and net kinetic energy of an oxygen molecule at 27^@C , where Avogadro number , N=6.023 times 10^23 and Boltzmann constant k= 1.38 times 10^-23 J.K^-1

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Knowledge Check

  • The pressure exerted by an ideal gas is p= 1/3 M/Vc^2 where the symbols have their usual meanings. Using standard gas equation, pV=nRT we find that c^2=(3RT)/M or C^2 prop T . Average kinetic energy of translation of 1 mol of gas= 1/2 Mc^2=(3RT)/2 Average thermal energy of 1 mol of helium at 27^0 C temperature is (given constant for 1 mol= 8.31 J.mol^-1.K^-1 )

    A
    `3.74 times 10^3J`
    B
    `3.74 times 10^-3 J`
    C
    `3.74 times 10^6 J`
    D
    `3.74 times 10^-6 J`

  • The pressure exerted by an ideal gas is p= 1/3 M/Vc^2 where the symbols have their usual meanings. Using standard gas equation, pV=nRT we find that c^2=(3RT)/M or C^2 prop T . Average kinetic energy of translation of 1 mol of gas= 1/2 Mc^2=(3RT)/2 At what temperature, when pressure remain unchanged , will the rms speed of a gas be half its value at 0^@C ?

    A
    `204.75 K`
    B
    `204.75^@C`
    C
    `-204.75K`
    D
    `-204.75^@C`

  • The pressure exerted by an ideal gas is p= 1/3 M/Vc^2 where the symbols have their usual meanings. Using standard gas equation, pV=nRT we find that c^2=(3RT)/M or C^2 prop T . Average kinetic energy of translation of 1 mol of gas= 1/2 Mc^2=(3RT)/2 At what temperature when pressure remains unchanged, will the rms speed of hydrogen be double its value at STP?

    A
    819 K
    B
    `819^@C`
    C
    1000 K
    D
    `1000^@C`

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    Find out the temperature at which the average translational kinetic energy of a gas molecule will be equal to the energy gained by an electron on acceleration across a potential difference of 5V, Boltzmann constant, k=1.38 times 2.^-23 J.K^-1 1 ev=1.6 times 10^-19 J .

    Calculate the molecular kinetic energy of 1 g helium gas at 127^@C Molecular weight of helium=4 and R=8.3 times 10^7 erg. Mol^-1.K^-1 .

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