Question

What is the temperature of N2 gas if the average speed (actually the root-mean-square speed) of the molecules is 750 m/s

Answer 1

The equation for calculating rms, or root mean speed, is √(v^2)= √(3RT/M). T equals temperature and M is molecular mass. R is the molar gas constant at 8.314472 J/K mol.

Upon deriving the equation for temperature, one would come up with T = (v^2)*M/ (3R).

Where M is the molar mass(here the mass of N2 = 28 g/mol i.e. 28 x10^-3 kg/mol.) ; R is gaseous constant(8.314 J / mol. K) ; v is the average velocity which is 750 m/s.

T = (750 m/s)² x 28 x10^-3 kg/mol / 3 (8.314 J/Mol)

= (562500 x 28 ) / 6235500

= 15750000/6235500 = 2.52585 K