Open Systems
In thermodynamic open systems, matter may flow in and out of the system boundaries. The first law of thermodynamics for open systems states: The increase in the internal energy of a system is equal to the amount of energy added to the system by matter flowing in and by heating, minus the amount lost by matter flowing out and in the form of work done by the system. The first law for open systems is given by:
- dU = δQ + dUin − dUout − δW
where Uin is the average internal energy entering the system and Uout is the average internal energy leaving the system.
The region of space enclosed by open system boundaries is usually called a control volume, and it may or may not correspond to physical walls. If we choose the shape of the control volume such that all flow in or out occurs perpendicular to its surface, then the flow of matter into the system performs work as if it were a piston of fluid pushing mass into the system, and the system performs work on the flow of matter out as if it were driving a piston of fluid. There are then two types of work performed: flow work described above, which is performed on the fluid (this is also often called pV work), and shaft work, which may be performed on some mechanical device.
These two types of work are expressed in the equation:
- δW = d(poutVout) − d(pinVin) + δWshaft.
Substitution into the equation above for the control volume cv yields:
- dUcv = δQ + dUin + d(pinVin) − dUout − d(poutVout) − δWshaft.
The definition of enthalpy, H, permits us to use this thermodynamic potential to account for both internal energy and pV work in fluids for open systems:
- dUcv = δQ + dHin − dHout − δWshaft.
This expression is described by Fig.1. If we allow also the system boundary to move (e.g. due to moving pistons) we get a rather general form of the first law for open systems. In terms of time derivatives it reads
where Σ represent algebraic sums and the indices k refer to the various places where heat is supplied, matter flows into the system, and boundaries are moving. The terms represent enthalpy flows, which can be written as
with the mass flow and the molar flow at position k respectively. The term dVk/dt represents the rate of change of the system volume at position k that results in pV power done by the system. The parameter P represents all other forms of power done by the system such as shaft power, but it can also be e.g. electric power produced by an electrical power plant. Note that the previous expression holds true only if the kinetic energy flow rate is conserved between system inlet and outlet. Otherwise, it has to be included in the enthalpy balance. During steady-state operation of a device (see turbine, pump, and engine), the average dU/dt may be set equal to zero. This yields a useful expression for the average power generation for these devices in the absence of chemical reactions
where <..> indicate time averages. The technical importance of the enthalpy is directly related to its presence in the first law for open systems, as formulated above.
Read more about this topic: Enthalpy, Applications
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