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Question

A gas bulb of 1 L capacity contains 20×1021 molecules of nitrogen exerting a pressure of 7.57×103Nm2.

Calculate the root mean square (rms) speed and the temperature of the gas molecules. If the ratio of the most probable speed to root mean square speed is 0.82, calculate the most probable speed for these molecules at this temperature.

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Solution

P=7.57×103Nm2

Mass=2×10216.023×1023×28×103kg

Volume=1L=103m3

Density=MassVolume=2×10216.023×1023×28×103103

=0.09297kgm3

Vrms=3Pd=3×7.57×1030.09297=494.23ms1

VmostprobableVrms=0.82 (given)

Vmostprobable=0.82×Vrms

=0.82×494.23

=405.269405ms1

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