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ક્લોરિન વાયુના એક નમૂનામાં $300\, K$ તાપમાને સરેરાશ ગતિઊર્જા (અણુદીઠ) = $6.21 \times 10^{-21}$ અને $\nu_{rms}$ $325 m/s$ છે, તો $600\, K$ તાપમાને આ રાશિઓનાં મૂલ્યો કેટલાં હશે?
$12.42 \times 10^{-21}\, J, \,650 m/s$
$6.21 \times 10^{-21}\, J, \,650 m/s$
$12.42 \times 10^{-21} J,\, 325 m/s$
$12.42 \times 10^{-21} J,\, 459.6 m/s$
Solution
ગતિઉર્જા $ \propto $તાપમાન
$\therefore \frac{{{E_2}}}{{{E_1}}} = \frac{{{T_2}}}{{{T_1}}} = \frac{{600}}{{300}} = 2\,\,\,\,\therefore \,\,{E_2} = 2{E_1}\,\,\,$
$\therefore \,\,\,{E_2} = 2 \times 6.21 \times {10^{ – 21}}\,\, = 12.42 \times {10^{ – 21}}\,J\,\,\,\,\,$
${\upsilon _{rms}} \propto \sqrt T $ પરથી $\frac{{{{({\upsilon _{rms}})}_2}}}{{{{({\upsilon _{rms}})}_1}}}\,\,\, = \sqrt {\frac{{{T_2}}}{{{T_1}}}} = \,\sqrt {\frac{{600}}{{300}}} \, = \,\sqrt 2 \,\,$
$\therefore {({\upsilon _{rms}})_2}\, = \,\sqrt 2 {({\upsilon _{rms}})_1}\,\,\,\,\,\therefore {({\upsilon _{rms}})_2}\,\, = \,\sqrt 2 \times 325\,\, = \,459.6\,m/s$
