Energy Balance
Open Systems

Upon studying this section, you should be familiar with the following:

Energy Balance for Open Systems

Explanation:

Energy balances on open systems are actually very similar to energy balances for closed systems. However, since there is the work from flow in all cases, we like to rewrite the equation so that this is taken into account.

Derivation:

Closed system balance:

ΔU + ΔEk + ΔEp = Q + W
with
W = Ws (moving parts) + Wflow
and,
ΔH = ΔU + Wflow
combining these three equations completes the derivation, giving us an energy balance for open systems from the definition of enthalpy and the closed system energy balance.

combining the first two equations,

ΔU + ΔEk + ΔEp = Q - Ws - Wflow
Inserting the enthalpy equation gives
ΔH + ΔEk + ΔEp = Q - Ws
this is our energy balance equation for open systems.

Open System Energy Balance Equation:

ΔH + ΔEk + ΔEp = Q - Ws

ΔH = 0 if there are no temperature changes, phase changes, or chemical reactions. Also, ΔU = 0 for small pressure changes pf a few atm for most systems.

ΔEk = 0 if the system doesn't change velocity

ΔEp = 0 if the system doesn't move vertically

Q = 0 if the system doesn't exchange heat with the surroundings, that is, if the system is adiabatic or insulated

Ws = 0 if there are no moving parts, no electrical currents, or radiation exchanged between the system and the surroundings.

Example 1:

Two streams of water are mixed to form the feed to a boiler.
inlet stream 1: 120 kg/min of liquid water at 30 °C and a specific enthalpy of 125.7 kJ/kg. inlet stream 2: 175 kg/min of liquid water at 65 °C and a specific enthalpy of 271.9 kJ/kg. outlet stream 3: water vapor at 17 bar and 204 °C with a specific enthalpy of 2793 kJ/kg, in a 6-cm diameter pipe. Neglect the inlet kinetic energies, that is, set them equal to zero. If you need the specific volume of the vapor, you may consider it to be an ideal vapor if you like; or, you can use the steam tables in the back of the book. For either way, the volume is found using the given pressure and temperature.

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Note: Often, even for the simplest energy balances on open systems, we will need to calculate ΔH for changes in temperature and pressure(unlike in the previous example, where the enthalpys were simply given). In this book, obtaining ΔH from changes in temperature and pressure are given in chapter 8. So, even though the equations have already been given here, we will continue these problems in that section.



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