The average translational energy and the r.m.s. speed of molecules in a sample of oxygen gas at 300 K are 6.21 times {10^{

Q: The average translational energy and the $r.m.s.$ speed of molecules in a sample of oxygen gas at $300 K$ are $6.21 \times {10^{ - 21}}\,J$ and $484\, m/s$ respectively. The corresponding values at $600 K$ are nearly (assuming ideal gas behaviour)

d $E \propto T$ $\therefore \frac{{{E_2}}}{{{E_1}}} = \frac{{{T_2}}}{{{T_1}}} = \frac{{600}}{{300}} = 2$ $\therefore \,\,{E_2} = 2{E_1}\,\,\,$ $\therefore \,\,\,{E_2} = 2 \times 6.21 \times {10^{ - 21}}\,\, = 12.42 \times {10^{ - 21}}\,J$ ${\upsilon _{rms}} \propto \sqrt T $ પરથી $\frac{{{{({\upsilon _{rms}})}_2}}}{{{{({\upsilon _{rms}})}_1}}} = \sqrt {\frac{{{T_2}}}{{{T_1}}}} = \,\sqrt {\frac{{600}}{{300}}} \, = \,\sqrt 2 \,\,$ $\therefore {({\upsilon _{rms}})_2}\, = \,\sqrt 2 {({\upsilon _{rms}})_1}$ $\therefore {({\upsilon _{rms}})_2}\,\, = \,\sqrt 2 \times 325\,\, = \,459.6\,m/s$

SECTION - A [PHYSICS MCQ]

GSEB - English Medium

The average translational energy and the $r.m.s.$ speed of molecules in a sample of oxygen gas at $300 K$ are $6.21 \times {10^{ - 21}}\,J$ and $484\, m/s$ respectively. The corresponding values at $600 K$ are nearly (assuming ideal gas behaviour)

A$12.42 \times {10^{-21}}\,J,\;968\,m/s$
B$8.78 \times {10^{-21}}J,\;684\,m/s$
C$6.21 \times {10^{-21}}\,J,\,968\,m/s$
D$12.42 \times {10^{-21}}\,J,\;684\,m/s$

IIT 1997, Medium

STD 11 Science
JEE
STD 11 - 12 . kinetic theory of gases
Physics

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