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The pressure exerted by an ideal gas is ...

The pressure exerted by an ideal gas is `P = (1)/(3) (M)/(V)C^(2)`, where the symbols have their usual meaning. Using standard gas equation, PV = RT, we find that `C^(2) = (3 RT)/(M) or C^(2) oo T`. Average kinetic energy of translation of one mole of gas ` =(1)/(2) MC^(2) = (3 RT)/(2)` with the help of the passage given above, choose the most appropriate alternative for each of the following quetions :
Average thermal energy of a helium atom at room temperature `(27^(@)C)` is Given, Boltzmann constant `k = 1.38 xx 10^(-23) JK^(-1)` :

A

`2.61 xx 10^(21) J`

B

`6.21 xx 10^(21) J`

C

`6.21 xx 10^(-21) J`

D

`6.21 xx 10^(-23) J`

Text Solution

Verified by Experts

The correct Answer is:
C
Here, `T = 27^(@)C = 27+273 = 300K`
`k=1.38 xx 10^(23)jK^(-1)`
Average thermal energy of helium atom
`=3/2 kT = 3/2 xx 91.38 xx 10^(-23) xx 300`
`=6.21 xxx 10^(-21)J`.
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Knowledge Check

  • The pressure exerted by an ideal gas is P = (1)/(3) (M)/(V)C^(2) , where the symbols have their usual meaning. Using standard gas equation, PV = RT, we find that C^(2) = (3 RT)/(M) or C^(2) oo T . Average kinetic energy of translation of one mole of gas =(1)/(2) MC^(2) = (3 RT)/(2) with the help of the passage given above, choose the most appropriate alternative for each of the following quetions : Average thermal energy of a helium atom at 600 K would be

    A
    `6.21 xx 10^(-21) J`
    B
    `1.24 xx 10^(-20) J`
    C
    `1.24 xx 10^(-21) J`
    D
    `1.24 xx 10^(21) J`

  • The pressure exerted by an ideal gas is P = (1)/(3) (M)/(V)C^(2) , where the symbols have their usual meaning. Using standard gas equation, PV = RT, we find that C^(2) = (3 RT)/(M) or C^(2) oo T . Average kinetic energy of translation of one mole of gas =(1)/(2) MC^(2) = (3 RT)/(2) with the help of the passage given above, choose the most appropriate alternative for each of the following quetions : Average thermal energy of one mole of helium at this temperature is (Given gas constant for 1 gram mole =8.31 J "mole"^(-1) K^(-1) .

    A
    `3.74 xx 10^(3) J`
    B
    `3.74 xx 10^(-3) J`
    C
    `3.47 xx 10^(6) J`
    D
    `3.47 xx 10^(-6) J`

  • The pressure exerted by an ideal gas is P = (1)/(3) (M)/(V)C^(2) , where the symbols have their usual meaning. Using standard gas equation, PV = RT, we find that C^(2) = (3 RT)/(M) or C^(2) oo T . Average kinetic energy of translation of one mole of gas =(1)/(2) MC^(2) = (3 RT)/(2) with the help of the passage given above, choose the most appropriate alternative for each of the following quetions : At waht temperature, pressure remaining unchanged, will the rms velocity of a gas be half its value at 0^(@)C ?

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