A family is using Liquefied petroleum gas (LPG) of weight `14.2 kg` for conumption.(Full weight `29.5 kg` includes the empty cylinders tare weight of `15.3 kg`). If it is use with constant rate then it lasts for 24 days. Then the new cylinder is replaced
Q (i) Find the equation relating the quantity of gas in the cylinder to the days.

A gas in equilibrium has uniform density and pressure throughout its volume. This is strictly true only if there are no external influences. A gas column under gravity, for example, does not have uniform density (and pressure). As you might expect, its density decreases with height. The precise dependence is given by the so-called law of atmospheres n_(2)= n_(1) "exp"[-mg(h_(2)-h_(1))//k_(B)T] where n_(2), n_(1) refer to number density at heights h_(2) and h_(1) respectively. Use this relation to derive the equation for sedimentation equilibrium of a suspension in a liquid column: n_(2)= n_(1)"exp"[ -mgN_(A)(rho-rho')(h_(2)-h_(1))//rhoRT)] where rho is the density of the suspended particle, and rho' , that of surrounding medium. [ N_(A) is Avogadro's number, and R the universal gas constant.] [Hint : Use Archimedes principle to find the apparent weight of the suspended particle.]