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Equation for Conservation of Energy

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).