Question
The average velocity of an ideal gas molecule at $${27^ \circ }C$$ is $$0.3\,m/\sec .$$ The average velocity at $${927^ \circ }C$$ will be:
A.
$$0.6\,m/\sec $$
B.
$$0.3\,m/\sec $$
C.
$$0.9\,m/\sec $$
D.
$$3.0\,m/\sec $$
Answer :
$$0.6\,m/\sec $$
Solution :
$$\eqalign{
& {U_{av}} = \sqrt {\frac{{8RT}}{{\pi M}}} ;\,\,\,\left\{ {_{{T_2} = 927 + 273 = 1200\,K}^{{T_1} = 27 + 273 = 300K}} \right\} \cr
& \frac{{{U_{a{v_1}}}}}{{{U_{a{v_2}}}}} = \sqrt {\frac{{{T_1}}}{{{T_2}}}} \,or\frac{{0.3}}{{{U_{a{v_2}}}}} = \sqrt {\frac{{300}}{{1200}}} \,or\frac{{0.3}}{{{U_{a{v_2}}}}} = \sqrt {\frac{1}{4}} \cr
& or\,{U_{a{v_2}}} = 0.6\,\,m/\sec . \cr} $$