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Mechanical Properties Of Fluids

Question

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Five molecules of an ideal gas have their speed 2km/s, 2.4km/s, 3km/s, 1.6 km/s and 2 km/s respectively. Find the r.m.s. velocity of gas molecules.

Solution

The r.m.s velocity of gas molecule is given by,
$v_{r} = \sqrt{\frac{{v_{1}}^{2} + {v_{2}}^{2} + {v_{3}}^{2} + {v_{4}}^{2} + {v_{5}}^{2}}{5}} = \sqrt{\frac{(2)^{2} + (2.4)^{2} + (3)^{2} + (1.6)^{2} + (2)^{2}}{5}} = 2.25 km / s$

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