"Specific humidity" is the ratio of mass of water vapor in a volume of atmosphere to the total mass of that volume. We denote it q.
q = mass of water vapor / mass of air (1)This water is "dissolved" in the air. Now, if you've tried mixing salt or sugar in a glass of water, you know that given mass of water can hold only a certain amount of sugar or salt. If you add more, it just sits at the bottom. The same is true of air: if you try to add more water vapor to air than the "saturation specific humidity", denoted q_s, the rest falls out of the air as clouds or rain. The saturation specific humidity is given by the "Clausius-Claperyon relation":
q_s = (.622/p) exp(-.622 L/(R T)) (2)where p is the air pressure, T is the temperature, and L = 2500 J/g is the latent heat of vaporization of water, and R = 287 J/(kg K) is the ideal gas constant for dry air. Note that the saturation specific humidity increases very rapidly with temperature.
"Relative humidity" is the ratio of specific humidity to saturation specific humidity, that is, a measure of how close to saturation the air is. If specific humidity goes beyond 100%, clouds generally form as water vapor leaves the air solution and turns into liquid droplets. Usually, the specific humidity goes past 100% because the air cools down, which makes q_s smaller. Relative humidity is denoted U:
U = q / q_s (3)As for your second question, air density is more closely related to specific humidity than to relative humidity. A water molecule weighs only 0.622 as much as the average dry air molecule. (that's where the .622s in (2) came from.) Air is an "ideal gas": for a given pressure and temperature, the number of molecules per unit volume is always the same. Now, if dry air at a certain pressure and temperature has a density rho_d, moist air of specific humidity q has the same number of molecules per unit volume, but their average weight is 1+(0.622-1)q as much, so the density per unit volume of moist air is
rho_m = rho_d (1 - .378) q (4)