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4 June, 17:08

Kinetic energy is defined as ½ mv2, where m is the mass of the object, and v is the velocity (or speed). Two gas molecules have the same kinetic energy, but molecule X has four times the mass of molecule Y. What can you say about their speeds?

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  1. 4 June, 18:56
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    The velocity of molecule Y is 2 times the velocity of molecule X

    Explanation:

    Data provided in the question:

    Formula for kinetic energy = ½ mv²

    Let the mass of molecule X be 'm₁' and velocity 'v₁'

    and mass of mass of molecule Y be 'm₂' and velocity 'v₂'

    Thus,

    According to the question

    m₁ = 4m₂ ... (1)

    since the kinetic energy of both the molecules are equal

    Therefore,

    ½ m₁v₁² = ½ m₂v₂²

    or

    m₁v₁² = m₂v₂²

    from (1)

    4m₂v₁² = m₂v₂²

    or

    4v₁² = v₂²

    or

    2v₁ = v₂

    hence,

    The velocity of molecule Y is 2 times the velocity of molecule X
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