Question

By what factor does the average velocity of a gaseous molecule increase when the absolute temperature is doubled?
(A) $ 1.4 $
(B) $ 2 $
(C) $ 2.8 $
(D) $ 4.0 $

Answer 1

Hint: Let us get some idea about absolute temperature. Thermodynamic temperature is a measure of absolute temperature and one of thermodynamics' main parameters. The fundamental physical feature that imbues matter with a temperature, transferred kinetic energy due to atomic motion, begins with a thermodynamic temperature reading of zero.
The average velocity formula is given as:
 $ {v_{avg}} = \sqrt {\dfrac{{8RT}}{{\pi M}}\,} \,\,\,\,\,\,\,\,\,\,..1 $
 $ R = $ Gas constant
 $ T = $ Temperature of gas.

Complete answer:
Let us know about Gas molecules. A gas molecule is made up of a number of atoms that are bound together. These interatomic links are analogous to springs that connect atoms of different masses. The gas molecules gather energy and vibrate more furiously as they absorb the radiation.
The average velocity formula is given as:
 $ {v_{avg}} = \sqrt {\dfrac{{8RT}}{{\pi M}}\,} \,\,\,\,\,\,\,\,\,\,..1 $
 $ R = $ Gas constant
 $ T = $ Temperature of gas
So from the about equation we can see that:
 $ v \propto \sqrt T $.......(a)
So according to the problem, given that the absolute temperature is doubled means
 $ {v^'} \propto \sqrt {2T} $.........(b)
By using equation (a) and equation (b) :
 $ \dfrac{{v'}}{v} = \sqrt {\dfrac{{2T}}{T}} $
 $ \dfrac{{v'}}{v} = \sqrt 2 $
 $ \dfrac{{v'}}{v} = 1.4 $
So the correct option is (A).

Additional Information:
Because most gases are difficult to detect directly, they are defined using four physical attributes or macroscopic characteristics: pressure, volume, particle number (chemists classify particles by moles), and temperature. For a variety of gases in diverse circumstances, scientists like as Robert Boyle, Jacques Charles, John Dalton, Joseph Gay-Lussac, and Amedeo Avogadro regularly noticed these four features. Their extensive research eventually resulted in a mathematical link between these features, which is described by the ideal gas law.

Note:
Because gas particles are so far apart, their intermolecular interactions are weaker than those of liquids or solids. Electrostatic interactions between gas particles cause these intermolecular forces. Plasmas are gases that include permanently charged ions that repel like-charged sections of various gas particles while attracting oppositely charged regions of other gas particles.