Question

Air molecules in a warm room (27°C = 300 K) typically have speeds of about 500 m/s (1,100 mph). Why is it that we are unaware of these fast-moving particles continuously colliding with our bodies? Because the air molecules are everywhere around us they constantly collide with our bodies from all directions. The effect of these collisions tend to cancel out. The mass of an air molecule is so miniscule that its momentum and kinetic energy are too small to be evident in the collision with a human body. The density of the warm air is so low that the air molecules tend to miss our bodies. The size of an air molecule is extremely small, so its momentum and kinetic energy are not efficiently transferred to our bodies when the collisions with a human body occur.

Answer 1

We are unaware of fast-moving air molecules at room temperature because their kinetic energy is too small to be felt and collisions from all directions cancel out, resulting in no perceivable force. Moreover, their mean free path is small, limiting momentum transfer to our bodies. However, their collective rapid motion facilitates the transmission of sound.

Step-by-step explanation:

The reason we are unaware of the fast-moving air molecules continuously colliding with our bodies, despite their high speeds at around 500 m/s in a warm room at 27°C (300 K), has to do with a few factors. Firstly, although air molecules, like nitrogen, have a large rms (root-mean-square) velocity, their kinetic energy is very small compared to the energies associated with macroscopic objects. This small energy does not translate to an appreciable force or sensation when these molecules impact our skin. Secondly, these collisions occur from all directions and tend to cancel each other out, resulting in no macroscopic movement of air or noticeable sensation. Lastly, even though these air molecules have a high speed, their mean free path is quite small, meaning they frequently collide with each other and don't travel far before another collision, impeding any significant momentum transfer to larger objects like the human body.

The high rms speed of molecules is noticed when we consider the speed of sound, which is around 340 m/s at room temperature. The faster the molecules move, the quicker they can transfer sound vibrations through the air. Hence, while individual molecules are imperceptible to us, their collective movement is critical for phenomena such as sound propagation.