Locate the centroid of the shaded area between the two curves

Amass of 1.5 kg of air at 120 kpa and 24°c is contained in a gas-tight, frictionless piston-cylinder device. the air is now compressed to a final pressure of 720 kpa. during the process, heat is transferred from the air such that the temperature inside the cylinder remains constant. calculate the boundary work input during this process.

Two flowing streams of argon gas are adiabatically mixed to form a single flow/stream. one stream is 1.5 kg/s at 400 kpa and 200 c while the second stream is 2kg/s at 500 kpa and 100 ? . it is stated that the exit state of the mixed single flow of argon gas is 150 c and 300 kpa. assuming there is no work output or input during the mixing process, does this process violate either the first or the second law or both? explain and state all your assumptions.

Carbon dioxide gas expands isotherm a turbine from 1 mpa, 500 k at 200 kpa. assuming the ideal gas model and neglecting the kinetic and potential energies, determine the change in entropy, heat transfer and work for each kilogram of co2.