Pressure, Temperature and RMS Speed

Now consider our first kinetic theory problem. Imagine a gas, consisting of n moles being confined to a cubical box of volume V. ''What is the connection between the pressure p exerted by the gas on the walls and the speeds of the molecules?" Pressure is defined as Force divided by Area or  where . Using Newtonian Mechanics, shows that

where n is the number of moles, M is the mass of 1 mole of the gas (so that nM is the total mass of the gas), v_RMS is the average speed of the molecules and V is the volume of the gas. The above equation is derived purely from applying Newtonian mechanics to the individual molecules.  Now by comparing to the ideal gas law pV = nRT or we must have or

which shows that the temperature T is related to the speed of molecules!

As shown the speed of molecules at room temperature is very large; about 500 m/sec for air (about 1000 mph).