An LPG (liquefied petroleum gas) cylinder weighs 14.8 kg when empty. When full it weighs 29.0 kg and shows a pressure of 2.5 atm. In the course of use at `27^(@)C`, the weight of the full cylinder reduces to 23.2 kg. Find out the volume of the gas in cubic metres used up at the normal usage conditions, and the final pressure inside the cylinder. Assume LPG to be n-butane with normal boiling point of `0^(@)C`.

Answer

`2.46 `m^(3)` , 1.48 atm

Explanation

Weight of butane gas in filled cylinder `= 29 - 14.8 kg`
`rArr` During the course of use, weight of cylinder reduces to 23.2 kg
`rArr` Weight of butane gas remaining now `= 23.2 - 14.8 = 8.4 kg`
Also, during use, V (cylinder) and T remains same.
Therefore, `(p_(1))/(p_(2)) = (n_(1))/(n_(2)) rArr p_(2) = ((n_(2))/(n_(1))) p_(1) = ((8.4)/(14.2)) xx 2.5 ` [Here, `(n_(2))/(n_(1)) = (w_(2))/(w_(1))`] = 1.48 atm
Also, pressure of gas outside the cylinder is 1.0 atm.
p V = n R T `rArr V = (nRT)/(p) = ((14.2 - 8.4) xx 10^(3))/(58) xx (0.082 xx 30)/(1) L = 2460 L = 2.46 m^(3)`
1.48 atm, `2.46 m^(3)`