A gas-gun has a cylindrical bore made in an insulating material. Length of the bore is L. A small bullet having mass m just fits inside the bore and can move frictionlessly inside it. Initially n moles of helium gas is filled in the bore to a length `L_(0)`. The bullet does not allow the gas to leak and the bullet itself is kept at rest by a stopper S. The gas is at temperature `T_(0)`. The gun fires if the stopper S is removed suddenly. Neglect atmospheric pressure in your calculations [Think that the gun is in space].
(a) Calculate the speed with which the bullet is ejected from the gun.
(b) Find the maximum possible speed that can be imparted to the bullet by using n moles of helium at temperature `T_(0)`.

Answer

(a) `u = sqrt((3nRT_(0))/(m)[1-((L_(0))/(L))^(2//3)])`
(b) `u_(max) = sqrt((3nRT_(0))/(m))`