Question
Five gas molecules chosen at random are found to have speeds of 500, 600, 700, 800 and $$900\,m/s$$
A.
the root mean square speed and the average speed are the same.
B.
the root mean square speed is $$14\,m/s$$ higher than the average speed.
C.
the root mean square speed is $$14\,m/s$$ lower than the average speed.
D.
the root mean square speed is $$\sqrt {14} \,m/s$$ higher than the average speed.
Answer :
the root mean square speed is $$14\,m/s$$ higher than the average speed.
Solution :
$${v_{av}} = \left[ {\frac{{500 + 600 + 700 + 800 + 900}}{5}} \right] = 700\,m/s\,\,{\text{and}}\,\,{v_{rms}} = \sqrt {\frac{{{{500}^2} + {{600}^2} + {{700}^2} + {{800}^2} + {{900}^2}}}{5}} = 714\,m/s$$
Thus $${v_{rms}}$$ is greater than average speed by $$14\,m/s.$$