Page 234 - The Mechatronics Handbook

Laws of Thermodynamics

The first steps in a thermodynamic analysis are definition of the system and identification of the relevant
interactions with the surroundings. Attention then turns to the pertinent physical laws and relationships
that allow the behavior of the system to be described in terms of an engineering model, which is a
simplified representation of system behavior that is sufficiently faithful for the purpose of the analysis,
even if features exhibited by the actual system are ignored.
Thermodynamic analyses of control volumes and closed systems typically use, directly or indirectly,
one or more of three basic laws. The laws, which are independent of the particular substance or substances
under consideration, are

• the conservation of mass principle,
• the conservation of energy principle,
• the second law of thermodynamics.
The second law may be expressed in terms of entropy or exergy.
The laws of thermodynamics must be supplemented by appropriate thermodynamic property data.
For some applications a momentum equation expressing Newton’s second law of motion also is required.
Data for transport properties, heat transfer coefficients, and friction factors often are needed for a compre-
hensive engineering analysis. Principles of engineering economics and pertinent economic data also can
play prominent roles.

12.2 Extensive Property Balances

The laws of thermodynamics can be expressed in terms of extensive property balances for mass, energy,
entropy, and exergy. Engineering applications are generally analyzed on a control volume basis. Accord-
ingly, the control volume formulations of the mass energy, entropy, and exergy balances are featured
here. They are provided in the form of overall balances assuming one-dimensional flow. Equations of
change for mass, energy, and entropy in the form of differential equations are also available in the literature
(Bird et al., 1960).

Mass Balance

For applications in which inward and outward flows occur, each through one or more ports, the extensive
property balance expressing the conservation of mass principle takes the form
dm ∑ m ˙ ∑
-------- = i – m ˙ (12.5)
dt e
i e
where dm/dt represents the time rate of change of mass contained within the control volume, m ˙ i denotes
the mass flow rate at an inlet port, and m ˙ e denotes the mass flow rate at an exit port.
The volumetric flow rate through a portion of the control surface with area dA is the product of the
velocity component normal to the area, v n , times the area: v n dA. The mass flow rate through dA is ρ(v n dA),
where ρ denotes density. The mass rate of flow through a port of area A is then found by integration
over the area
∫
m ˙ = ρv n A
d
A
For one-dimensional flow the intensive properties are uniform with position over area A, and the last
equation becomes
vA
m ˙ = ρvA = ------ (12.6)
v

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