To which one of the following is the average speed of molecules of a gas directly proportional ?

According to the Kinetic Theory of Gases, the average speed (v_avg) of gas molecules is derived from the Maxwell-Boltzmann distribution. The formula for average speed is v_avg = ∑(8RT/̀M), where R is the gas constant, T is the absolute temperature, and M is the molar mass. This relationship demonstrates that the average speed is directly proportional to the square root of the absolute temperature (T). While context [c1] mentions the Gas Law relating pressure and temperature, and [c2] notes that the speed of sound in an ideal gas depends on temperature, the specific molecular speed relationship is a fundamental principle of thermal physics. As temperature increases, the kinetic energy of the molecules increases, leading to a higher average speed proportional to ∑T. Therefore, the average speed of molecules is directly proportional to the square root of the absolute temperature.

Sources

1. [1] Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 22: Vertical Distribution of Temperature > 22.3. Adiabatic Lapse Rate (ALR) > p. 296
2. [2] Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 20: Earths Atmosphere > 20.2. Structure of The Earth's Atmosphere > p. 274