An LPG (liquefied petroleum gas) cylinder weighs 14.8 kg when empty. When full it weighs29.0 kg and shows a pressure of 2.5 atm. In the course of use at27^(@)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.

An LPG (liquefied petroleum gas) cylinder weighs 14.8 kg when empty. W

1.	An LPG (liquefied petroleum gas) cylinder weighs 14.8 kg when empty. When full it weighs29.0 kg and shows a pressure of 2.5 atm. In the course of use at27^(@)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» <P> SOLUTION :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)`