Question

For one mole of an ideal gas, increasing the temperature from $10^\circ C \, to\, 20^\circ C$________

• A. increases the rms velocity by $\sqrt {2}$ times.
• B. increases the average kinetic energy by two times.
• C. increases both the average kinetic energy and rms velocity, but not significantly
• D. increases the rms velocity by two times

Answer 1

Answer: (C)

increases both the average kinetic energy and rms velocity, but not significantly

Answer 2

Given, $T_{1} =273+10=283\, K$
$T_{2} =273+20=293\, K$

Average $KE =\frac{3}{2} K T$
$\frac{\left( KE _{1}\right)}{\left( KE _{2}\right)}=\frac{283}{293}=0.96$

Root mean square (rms) velocity,

$v_{ rms }=\sqrt{\frac{3 R T}{M}}$
$\frac{v_{( rms )_{1}}}{v_{( rms )_{2}}} =\sqrt{\frac{T_{1}}{T_{2}}}$
$=\sqrt{\frac{283}{293}}=0.98$

Thus, both average kinetic energy and root mean square velocity increase but not significantly when temperature is increased. from $10^{\circ} C$ to $20^{\circ} C$.