Let us consider Et = energy in the control volume at time’t, and
E t+ at= energy in the control volume at time’t +h.
If e in and e out correspond to specific energies, then at time ‘t, the total energy of the mass
of the control volume is
The first law as applied to flow system is
Now ` e + pv = ( u +1/2 v + gz) + pv
= ( u+ pu) + 1/2 v2 + gz
= h + 1/2 v2 + gz
Thus eqn. (5.4) becomes
In case of a number of streams we change min in to L m out and m OIII to Σ in out I in the above equation. Equation (5.5) is the mathematical statement of the first law of thermodynamics
for an OPEN SYSTEM.
The first law as applied to closed system is
dQ = dE +dw
dq / dt = de / dt + dw / dt
q = de / dt + w
In closed system m =constant
min = m out = 0, thus equation (5.5) reduces to equation (5.6).