Question

As the temperature is raised from ${20^ \circ }C$ to ${40^ \circ }C$, the average kinetic energy of neon atoms changes by a factor:
A. 2
B. $\sqrt {\dfrac{{313}}{{293}}} $
C. $\dfrac{{313}}{{293}}$
D. $\dfrac{1}{2}$

Answer 1

Hint:According to the kinetic molecular theory of gases, the average kinetic energy of gas particles is proportional to the absolute temperature of the gas. Average kinetic energy is expressed with the following equation where k represents the Boltzmann constant.
${E_k} = \dfrac{3}{2}kT$

Complete step by step answer:
-The kinetic molecular theory states that "the average kinetic energy of gas molecules is proportional to the absolute temperature of the gas". Not all molecules will have the same kinetic energy and the same speed. This means that as the temperature increases, the average speed of the molecules and the range of speeds will also increase.
-Thus, now as we know, the average kinetic energy of gas particles is proportional to the absolute temperature of the gas.
The equation for the average kinetic energy of the neon atom will be,
$K.E. = \dfrac{3}{2}RT$
According to the question, the temperature is raised from ${20^ \circ }C$ to ${40^ \circ }C$.
Using this formula, we get,
$
  \dfrac{{{K_{40}}}}{{{K_{20}}}} = \dfrac{{{T_{40}}}}{{{T_{20}}}} \\
   = \dfrac{{273 + 40}}{{273 + 20}} \\
   = \dfrac{{313}}{{293}} \\
  $
Thus, the average kinetic energy of neon atoms changes by a factor of $\dfrac{{313}}{{293}}$.

Hence, option C is the correct answer.

Note:
It is also important to know that although the average kinetic energy of all gases is the same at a specific temperature, the average velocity of the molecules is not the same because the heavier molecules tend to travel slower relative to the lighter ones.