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If the absolute temperature of a gas is raised to four times its original temperature, how will its root-mean-square velocity be affected keeping all other variables unchanged? |
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Answer» l Energy of a given MASS M of a GAS (mass of each molecule = m) is given by the formula : E = 1/2 M v² = 3/2 * R T M = mass of gas v = rms velocity = root mean square velocity R = universal gas constant T = ABSOLUTE temperature of the gas Energy of a molecule is given by : 1/2 m v² = 3/2 k_B T k_B = Boltzmann's constant m = mass of a molecule. THUS v = √(3 R T / M) = √(3 k_B T/m) For a given gas, the rms velocity depends only on the square root of the absolute temperature of the gas. v2/v1 = √(T2/T1) = √4 = 2 So rms velocity becomes doubled. |
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