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At what temperature do the molecules of nitrogen gas have an rms speed of 35 ?

  • physics -

    For the given rms speed of 35 (m/s)
    You can determine the temperature from the relation:
    (rms speed)² = 3RT/molar mass, or
    Temperature, T = (rms speed)²*(molar mass)/(3R)
    R=gas constant, 8.31 J/°K-mol
    T=temperature in °K
    molar mass = kg/mol

    T=(35² m²/s²)*(0.028 kg/mol)/(3*8.31 kg-m²/°K-mol-s²)
    =35²*0.028/(3*8.31) °K
    =1.38 °K

    I do not know if the equation still holds at such low temperatures.

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