Question

A vertical cylinder contains N atoms of an ideal gas and is closed off by a piston having mass m and area a. The acceleration due to gravity is g. The gas has a heat capacity Cy which is independent of temperature. (Note that the preceding sentence contains the words "heat capacity" and does not contain the words "specific heat.") Neglect the heat capacity of the cylinder and piston, ignore friction, and the entire system is thermally insulated. The piston is initially clamped such that the gas has a volume Vi and a temperature T. The piston is released, and after some oscillations it comes to rest at a position corresponding to a larger volume of gas (a) Does the temperature of the gas increase, decrease, or stay the same? (b) Does the entropy of the gas increase, decrease or stay the same? (c) Calculate the final temperature of the gas in terms of the parameters given in the problem statement

Answer 1

vertical cylinder Contains Natoms of an ideal gas, and is closed off by a piston having mass m. and area a. The piston is witially clamped such that stre gas has volune vi and temporetone To Afler pistons relased The volune of the Cyliser increases @ In this expansion The work is done by the system & on the environment by consuming its internal energy. Thus its temporetne mie decrease. 6 In This process the volume of the gas increases. Thus The govs has a more random states them previous. Thus entrophy of the Syslem méreases. Now The com expasion is adiabatic Thus. TV 2 TE V final temporetme. If - Ti (ve