chapter 2 thermodynamic definitions

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MAE 501 course notes Spring 2011 Copyrighted by R. D. Gould

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ADVANCED ENGR THERMODYNAMICS

II. THERMODYNAMICS DEFINITIONS

1. System:

A collection of matter in a three-dimensional region of space bounded by anarbitrary surface. You MUST define this BEFORE working your problem!

a.) Closed System:

No mass crosses a closed system boundary, however, energy may

Constraint: impermeable to mass

i.) Closed System with Rigid Boundary (internal constraint):

Rigid boundary: Constant volume (dV = 0)

Example: Steel tank

ii.) Closed System with Moving Boundary:

Boundary moves: (Volume of the system is not constant)

Examples: Balloon with tied knot, piston-cylinder device


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b.) Open System (or Control Volume, C.V.):

Mass is permitted to cross system boundaries

i.) Open System with Rigid Boundary: Constant volume (rigid) control volume

Examples: Water nozzle, rigid tank with valve opened,

turbines, compressors, heat exchangers,

ii.) Open System with Moving Boundary: Volume of the C.V. is not constant)

Example: Untie knot of balloon W

2. Surroundings (or environment):

Everything external to the system. Q

Tsurr system

bdry


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3. Boundary:

A zero volume (no mass, not wall) surface, usually located at the interface

between two materials (or commonly between the system and surroundings)

The properties on a boundary are shared by both the system and the

surroundings (i.e continuous function).

Consider the boundaries of the control volumes and systems below

(a) (b)

(c) (d) (e)


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Distinction between wall and boundary (Bejan, pp. 1-3):

Bejan Fig. 1.1 Bejan Fig. 1.2


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4. Isolated system:

A system not influenced by its surroundings.

No heat or work (ENERGY) crosses an isolated system boundary!

5. Property : Any measurable characteristic of a system.

Properties are point functions and thus do not depend on how the system

arrived at its condition.

a.) Extensive Property: (Depends upon the size of the system): add

1. Volume partition

2. Mass

3. Total energy, total enthalpy, total entropy,

4. All mass dependent properties

5. 1st and 2nd laws use extensive properties! (1) (2)b.) Intensive Property: (Independent of system size):

1. Temperature

2. Pressure

3. Specific volume (v V/m)

4. Any specific extensive property (per unit mass or mole)


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6. Walls and constraints:

Permit or prevent redistribution of extensive properties.

In an closed composite system the internal constraints are impermeable walls

Extensiveproperty

Non-permitted

or restrictive

Permitted or

nonrestrictive

Observation ifpermitted

V, volume Rigid wall Moving wall Boundary work

N, moles Impermeable Permeable wall Mass transfer

E, energy Adiabatic Diathermal Heat transfer

Adiabatic: Zero heat transfer regardless of magnitude of temperature gradient

normal to the boundary.

Diathermal: Temperature gradient normal to the boundary is zero even in the

presence of heat transfer.

Recall Fouriers law for heat conduction: qn = kAn T/ n


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7. State:

A description of the condition of the substance defined by specifying its

properties (p, T, v, u, h, s, ).

8. State Postulate: The number of independent intensive thermodynamic properties required to

fully describe a specified pure substance is equal to the number of reversible

work modes plus one. For simple systems (1 work mode) only 2 properties are

needed to fully describe the state of a pure substance. Wbdry

Development of the State Postulate

1st law (closed system): Qnet,in,1-2 - Wnet,out,1-2 = E = E2 E1Q

The 1st law says that we can change the energy of a system by transferring

energy as work and/or heat. If we have a compressible substance we can increase its energy through PdV

work. Volume is the independently variable property of the work mode (i.e.

Wbdry,out = PdV)


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In addition, we can hold the volume fixed and change the system energy by

heat transfer, for which temperature may be the most appropriate

independently variable property. This gives us one more free variable.

Therefore, for each of the independent ways of varying the energy of a

substance there is one independently variable thermodynamic property.

Thus: The number of independent intensive thermodynamic properties

required to fully describe a specified pure substance is equal to the

number of reversible work modes plus one.

The state of a pure simple compressible substance is completely defined by

two independent, intensive properties (i.e. u = u(T,v)).

If, in addition, potential energy is active in your problem, you have one

additional work mode and will need to specify an additional variable, i.e.

E(T,v,z).


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Callens Postulate I: Equilibrium states of simple systems are completely characterized

by internal energy U, volume V and the number of moles N1, N2,

.., Nr of each chemical component. (Callen, p. 13)

9. Simple Compressible Substance (SCS) or Simple System:

Any substance for which the only important reversible work mode is volume

change (i.e. boundary or PdV work).

Not subject to the influence of gravitational, electrical, and magnetic fields and

inertial forces.

Sufficiently large that surface effects can be neglected.

Homogeneous and isotropic definite chemical composition.

The state of a single component, simple compressible substance is completely

defined by two independent, intensive properties (i.e. u = u(T,v)).

10. Phase of a Substance:

Defined as a quantity of matter which is homogeneous in chemical

composition and in physical structure.

All substances can exist in solid, liquid and gaseous phases.


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11. Equilibrium:

A system is in a state of equilibrium if a change of state cannot occur while the

system is not subject to interactions with the surroundings.

Thermodynamic properties are defined only when a system is in equilibrium!

a.) Thermal Equilibrium:

Temperature is uniform throughout the system (no temperature

gradient).

b.) Mechanical Equilibrium:

There are no unbalanced forces within the system.

Pressure is uniform throughout the system (no pressure gradient).

c.) Chemical Equilibrium:

There is no tendency for a net chemical reaction to take place when

chemical species are allowed to interact.

Chemical composition is uniform throughout the system.

d.) Phase Equilibrium:

There is no tendency for phase transformation (i.e. melting) when the

two phases are brought in contact


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e.) Thermodynamic Equilibrium:

There is no flow of macroscopic energy or matter within a system in

thermodynamic equilibrium, though the molecules are free to flow.

The atoms/molecules have relaxed to a stable state.

If all the conditions for mechanical, thermal, chemical and phaseequilibrium are satisfied, this system is in a state of thermodynamic

equilibrium.

12. Process:

The change of a system from one equilibrium state to another.

A complete description of a process requires specification of end states and itspath.

a.) Isothermal Process (constant temperature) Wout P

b.) Isobaric Process (constant pressure)

c.) Isochoric Process (constant volume)

d.) Isentropic Process (constant entropy)

Qin

system boundary V


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13. Quasistatic (Quasiequilibrium) Process:

A series of state changes where the substance within the system is

infinitesimally close to a state of equilibrium at all times.

A quasistatic process may be considered practically as a series of equilibrium

states and its path can be represented graphically as a continuous line on a statediagram.

The expressions for boundary work (i.e. W = PdV) and heat transfer (i.e. Q

= TdS) are valid only for quasistatic processes.

From an atomic/molecular point of view, how quickly one can undergo a

process, while meeting the quasistatic requirement, is a matter of how quicklythe atom/molecules communicate the change amongst one another and relax to

an equilibrium state.


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14. Reversible Process:

If at the conclusion of the process, the initial states of the system and

surroundings can be restored without leaving any net change at all elsewhere,

the process is reversible.

A reversible process must be a quasistatic process. Reversible processes cannot involve such phenomena as solid or fluid friction,

electric resistance, inelastic deformation, and hysteresis in magnetization or

polarization.

Some debate on definitions

Old interpretation: quasistatic implies reversibleNew interpretation: reversible process is more restrictive

If complete equilibrium is reached at each step along the path, then quasistatic

is also reversible.

If for example, the thermal diffusion time scale is different from the viscous

mixing time scale, this process may be quasistatic in terms of mixing, but maynot reversible.

15. Cycle:

A process whose initial and final states are identical


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Solution Flowchart

chapter 2 thermodynamic definitions

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