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 m_{in} 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

m_{in} = m _{out} = 0, thus equation (5.5) reduces to equation (5.6).