Final answer:
The equation to verify the average speed of molecules in an ideal gas is related to the kinetic theory of gases, and it shows that the average speed depends on both temperature and the mass of the gas molecules.
Step-by-step explanation:
The question is related to the average speed of molecules in an ideal gas and how it depends on the temperature and the mass of the molecules. The equation provided, ˆv=√(8πkBT/m), can be derived from the kinetic theory of gases, where kB is the Boltzmann's constant, T is the absolute temperature in kelvins, and m is the mass of a gas molecule.
The equation for the average kinetic energy of a molecule is KEavg = (3/2)kBT. When we solve for the rms speed (vrms), we use the equation vrms = √(3kBT/m). This formula relates to the average speed of the gas molecules because in a collection of gas particles, the average speed will be proportional to the square root of temperature and inversely proportional to the square root of the particle mass.
Regarding the multiple choices provided, the answer is: a) The equation for the average speed can be confirmed considering the kinetic theory of gases equations, while b) the scaling transformation may or may not be applicable based on the context of the previous problem, c) the average speed is not independent of temperature as it directly depends on the square root of the temperature, and d) average speed does not depend on the specific heat of the gas but rather on the kinetic theory of gases as it's related to kinetic energy and not heat capacity.