Solving the incompressible Navier-Stokes equations numerically is a unique challenge because of the absence of direct link between pressure and density. As a workaround, the pressure equation must be derived from the velocity field and corrected in each iteration to ensure divergence free condition is satisfied.

Marker-and-cell (MAC) algorithm is the most common algorithm used to numerically solve in compressible Navier-Stokes equations. What is the main characteristic of this algorithm?

1kg of water contained in a piston-cylinder assembly undergoes two processes in series from an initial state where the pressure is 3.0 bar and the temperature is 150°c process 1-2: the water is compressed isothermally to a volume of 0.25 m^3 with 120 kj of work being done to the system. process 2-3: the water is heated at constant volume to a final pressure of 10 bar. a. find the change in internal energy for the system. b. calculate the amount of heat transferred, in kj. c. sketch both processes on a t-v diagram. (196.33 kj/kg, 76.33 kj)