Answer to Question #176245 in Physics for Hetty

Question #176245

A helium atom has a mass of 6.7 × 10^-27 kg. If a sample of gas has a root mean square speed of 500 m s^-1, calculate the temperature of the gas.


1
Expert's answer
2021-04-01T18:42:03-0400

We can find the root mean square speed as follows:


vrms=3RTM.v_{rms}=\sqrt{\dfrac{3RT}{M}}.

From this formula we can find the temperature of the gas:


T=vrms2M3R,T=\dfrac{v_{rms}^2M}{3R},T=(500 ms)24103 kgmol38.314 JKmol=40.1 K.T=\dfrac{(500\ \dfrac{m}{s})^2\cdot4\cdot10^{-3}\ \dfrac{kg}{mol}}{3\cdot8.314\ \dfrac{J}{K\cdot mol}}=40.1\ K.

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