A) increases the average kinetic energy by two times
B) increases the rms velocity by \[\sqrt{2}\] times
C) increases the rms velocity by two times
D) increases both the average kinetic energy and rms velocity, but not significantly
Correct Answer: D
Solution :
Given, \[{{T}_{1}}=273+10=283\,K\] \[{{T}_{2}}=273+20=293\,K\] Average \[KE=\frac{3}{2}KT\] \[\frac{(K{{E}_{1}})}{(K{{E}_{2}})}=\frac{283}{293}=0.96\] Root mean square (rms) velocity, \[{{v}_{rms}}=\sqrt{\frac{3RT}{M}}\]m \[\frac{{{v}_{{{(rms)}_{1}}}}}{{{v}_{{{(rms)}_{2}}}}}=\sqrt{\frac{{{T}_{1}}}{{{T}_{2}}}}\] \[=\sqrt{\frac{283}{293}}=0.98\] Thus, both average kinetic energy and root mean square velocity increase but not significantly when temperature is increased from \[{{10}^{o}}C\] to \[{{20}^{o}}C\].
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