Q. For one mole of an ideal gas, increasing the temperature from $10℃\ to\ 20℃$
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
Explanation
(d)
Given $T_{1} = 273 + 10 = 283\ K$
$\ \ \ \ \ \ \ \ \ \ \ \ T_{2} = 273 + 20 = 293\ K$
Average KE $= \frac{3}{2}kT$
$\frac{KE_{1}}{KE_{2}} = \frac{283}{293} = 0.96$
Root mean square (rms) velocity,
$\ \ \ \ \ v_{rms} = \sqrt{\frac{3RT}{M}}$
$\frac{v_{(rms)_{1}}}{v_{(rms)_{2}}} = \sqrt{\frac{T_{1}}{T_{2}}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \sqrt{\frac{283}{293}} = 0.98$
Thus both average kinetic energy and root mean square velocity increase but not significantly when temperature is increased from $10℃\ to\ 20℃.$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.