Respuesta :
Answer:
It increases but less than double
Explanation:
As the temperature of a gas increase, the average kinetic energy of the gas increases. The kinetic energy of a gas is the thermal energy that the gas contains.
We know, the kinetic energy of an ideal gas is given by :
[tex]$V_{avg} = \sqrt{\frac{8R}{\pi M}}$[/tex]
where, R = gas constant
T = absolute temperature
M = molecular mass of the gas
From the above law, we get
[tex]$V_{avg} \propto \sqrt{T}$[/tex]
Thus, if we increase the temperature then the average kinetic energy of the ideal gas increases.
In the context, if the temperature of the ideal gas increases from 100°C to 200°C, then
[tex]$\frac{(V_{avg)_2}}{(V_{avg)_1}} =\sqrt{\frac{T_2}{T_1}}$[/tex]
[tex]$\frac{(V_{avg)_2}}{(V_{avg)_1}} =\sqrt{\frac{473.15}{373.15}}$[/tex]
[tex]$\frac{(V_{avg)_2}}{(V_{avg)_1}} =\sqrt{1.26}$[/tex]
[tex]$\frac{(V_{avg)_2}}{(V_{avg)_1}} =1.12$[/tex]
[tex]$(V_{avg})_2 = 1.12\ (V_{avg})_1$[/tex]
Therefore, [tex]$(V_{avg})_2 > (V_{avg})_1$[/tex]
Thus the average kinetic energy of the molecule increases but it increases 1.12 times which is less than the double.
Thus, the answer is " It increases but less that double".
