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18 January, 08:46

By what factor must the absolute temperature of a gas be increased to increase the rms speed of its molecules by a factor of 3?

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  1. 18 January, 09:51
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    The temperature of the molecule will be increased by a factor of 9

    Explanation:

    The relationship between the temperature and the rms speed of a gas is given by

    Vrms=√ (3RT/MM)

    Where R = Universal gas constant

    T = Absolute temperature of the gas in kelvin

    MM = Molar mass of the gas

    Since from the question, only the rms speed and the temperature are said to change, the term 3R/MM can be represented by a constant k. The relationship then becomes Vrms=√kT

    At the intitial speed, temperature = T1

    Vrms=√ (kT1) (1)

    When the speed is increased by a factor of 3, the relationship becomes

    (3V) rms=√ (kT2) (2)

    Dividing equation (2) by equation (1)

    (3V) rms/Vrms = √ (kT2) / √ (kT1)

    3=√ (T2/T1)

    T2/T1 = 9

    The temperature of the molecule will be increased by a factor of 9
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