A gas is compressed in a piston–cylinder assembly from 푝-= 2 bar to 푝.= 8 bar, 푉.= 0.02 푚:in a process during which the relation between pressure and volume isdefined as푝푉-.;=constant. The mass of the gas is 0.2 kg. The specific internal energy of the gas increases by 50 kJ/kg during the process. Kinetic and potential energy changes are negligible. For the gas as the system, determine the work, in kJ, and the heat transfer, in kJ.

Consider a double atwood machine constructed as follows: a mass 4m is suspended from a string that passes over a massless pulley on frictionless bearings. the other end of this string supports a second similar pulley, over which passes a second string supporting a mass of 3m at one end and m at the other. using two suitable generalized coordinates, set up the lagrangian and use the lagrange equations to find the acceleration of the mass 4m when the system is released. explain why the top pulley rotates even though it carries equal weights on each side.