Conservation of Energy in Control Volume

The first law of thermodynamics states that the rate of change of total stored energy in a system equals the net rate of heat and work transferred into a system.

For a control volume that coincides with the system at a given moment, the net heat and work entering the system equal the net heat and work entering the control volume.

For this system and coincident control volume, the Reynolds Transport Theorem is applied.

The total rate of energy change within the control volume is determined by both the time rate of change in stored energy and the net energy flow through the boundary.

The energy flowing across the boundary includes contributions from heat and work, such as shaft work and pressure work.

Shaft work results from rotating components like turbines, while fluid stresses produce pressure work.

The general energy equation combines all elements: stored energy, heat, shaft work, and pressure work due to normal stresses.

This equation represents energy conservation in fluid systems, incorporating heat transfer, shaft work, and pressure forces at the control surface.