Simplification of the General Energy Equation

Isolated System

In an isolated system neither mass nor energy is exchanges with the surroundings. Thus,

dm_in = 0

dm_out = 0

dQ = 0

dV_sys = 0

dW_s = 0

Thus, the general energy equation simplifies as follows:

This indicates that in an isolated system, energy is converted from one form to another but the total energy remains constant. Note that this is the statement of the first law of thermodynamics.

Closed System

For a closed system, mass cannot cross the boundary. Hence,

dm_in = dm_out = 0

Thus, the general energy equation simplifies as follows:

where the term dW includes the work associated with the displacement of the system boundaries, i.e., expansion or contraction, and shaft work. Integration of the above equation results in:

ΔU + ΔE_K + ΔE_P = Q + W

In most practical applications, both ΔE_K and ΔE_P are negligible. Thus, the equation simplifies as follows:

ΔU = Q + W

 

Steady-State Flow System

Under steady-state conditions, dm_sys/dt = 0, indicating that the total mass of the system does not change with respect to time.

dm_in = dm_out = dm

Since the boundaries of the system are fixed, dVsys = 0. Under these conditions, the general energy equation reduces to;