Question

Which one of the following statements is not true about the effect of an increase in the temperature on the distribution of molecular speeds in a gas?
A. The area under the distribution curve remains same as under the low temperature
B. The distribution becomes broader
C. The fraction of the molecules increases with the speed
D. The most probable speed increases

Answer 1

According to the kinetic theory of gases, the speed distribution for a gas at a certain temperature can be described by the Maxwell-Boltzmann equation. There are 3 types of molecular speeds in a gas. They are :
1. Average velocity
2. Root mean square velocity
3. Most probable velocity

Complete step by step answer:
- It is impossible to measure the velocity of each gas molecule in 1 mole under normal conditions. So Maxwell distribution curve is used to find the velocity of gas molecules.
-From the distribution function, we can find three types of speeds: average speed, most probable speed and the root mean square speed.
- The relationship between different velocities can be given as
${{v}_{mp}}=\sqrt{\dfrac{2{{K}_{B}}T}{m}}$
${{v}_{avg}}=\sqrt{\dfrac{8{{K}_{B}}T}{m\Pi }}$
${{v}_{rms}}=\sqrt{\dfrac{3{{K}_{B}}T}{m}}$
-So we see that the option D is correct.

-As the temperature increases, the speed of the gas molecules also increase. This makes the distribution curve steeper. But it does not change the total area of the curve as the shift in the peak also occurs from left to right. So, option A is also correct.
-With the increase in the temperature, the speed increases and so the number of molecules also increases. This makes the distribution curve wider with the change in the temperature, keeping the total area constant. So option B is also correct.
-The fraction of the molecules decreases with the temperature because the speed increases but the total number of molecules remains the same. The energy of the gas molecules increases with the temperature and they are able to attain higher kinetic energy. So, the fraction of molecules decreases.
So, the correct answer is “Option C”.

Note: The width of the distribution function signifies the ranges of the velocities that can be achieved by the gas molecules. With the increase in temperature, the molecules will gain their kinetic energies and so the range of velocities will also increase and so will the collision.