Energy Balance
Open Systems

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.

Closed system balance:

combining the first two equations,

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.

ΔE_k = 0 if the system doesn't change velocity

ΔE_p = 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

W_s = 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.

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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