The ideal gas equation is pV = 1/3 Nm < c² >.
a. State the meaning of the symbols N, m and < c² >.
b. A cylinder of helium-4 contains gas with volume 4.1 × 10⁴ cm³ at a pressure of 6.0 × 10⁵ Pa and a temperature of 22 °C. You may assume helium acts as an ideal gas and that a molecule of helium-4 contains 4 nucleons, each of mass 1.66 × 10⁻²⁷ kg.
Determine:
i. The amount of gas in mol
ii. The number of molecules present in the gas
iii. The root-mean-square speed of the molecules.