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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.

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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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