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Write the kinetic gas equation and expre...

Write the kinetic gas equation and express it as `P = (2)/(3) E`, where E is the kinetic energy per unit volume.

Text Solution

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For one mole of ideal gas the kinetic gas equation is
`PV=(1)/(3)m u^(2)=(1)/(2)xx(2)/(3)m u^(2)=(2)/(3)xx(1)/(2)m u^(2)`
or `P=(2)/(3)((1)/(2)(m u^(2))/(V))=(2)/(3)E`
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Knowledge Check

  • Kinetic energy per unit volume of a gas is

    A
    `(3P)/2`
    B
    `(2P)/3`
    C
    `P/2`
    D
    `P/3`

  • Relation between pressure (P) and average kinetic energy per unit volume of gas (E ) is

    A
    `P = (2)/(3) E`
    B
    `P = (1)/(3) E`
    C
    `P = (1)/(2) E`
    D
    `P = 3E`

  • The pressure exerted in terms of total kinetic energy per unit volume (E) is

    A
    `3/2`E
    B
    E
    C
    `2/3`E
    D
    `sqrt3`E

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    Assuming the expression for the pressure exerted by an ideal gas, prove that the kinetic energy per mole of the gas =(3)/(2) RT. Hencce prove that the kinetic energy per molecule of the gas =(3)/(2)k_(B)T .

    Assuming the expression for the pressure p exerted by an ideal gas, prove that the kinetic energy per unit volume of a gas is (3)/(2) p.

    Kinetic theory of gases is a generalization offered by Maxwell. Boltzmann, Clausius, etc. to explain the behaviour of ideal gases. This theory assumes that ideal gas molecules neither attract nor repel each other. Average kinetic energy of gas molecules is directly proportional to the absolute temperature. A gas equation called kinetic gas equation was derived on the basis of kinetic theory PV = (1)/(3) mv^(2) The average kinetic energy per molecule of an ideal gas is equal to :

    If P is the pressure of gas then translational kinetic energy per unit volume of the gas is

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