Thermodynamic Properties - Memorial University of …€¦ · · 2010-09-17A pure substance can...

Faculty of Engineering and Applied Science Memorial University of Newfoundland

St. John’s, Newfoundland, Canada

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Thermodynamic Properties



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Thermodynamic Properties •  In thermodynamics we are interested in the

interactions of work and heat with matter and its properties. We consider to types of properties: –  physical properties: require the specification of an

external frame of reference, e.g. velocity, kinetic energy, potential energy

–  thermodynamic properties: do not require an external frame of reference, e.g. temperature, pressure, volume, etc.



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Thermodynamic Properties •  Phase and Pure Substances

–  phase refers to the homogeneity of physical structure and composition of matter, i.e. solid, liquid or gas (vapor)

–  pure substances are uniform and invariable in chemical structure. A pure substance can exist in more than one phase.

•  In thermodynamics, we refer to the vapor state to indicate that the substance can be condensed into the liquid phase.



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Thermodynamic Properties •  Recall that we consider both extensive and

intensive properties. In the case of many thermodynamic properties and physical properties, we frequently define them per unit mass (intensive): – extensive property:

–  intensive property:

€

Ysys = Yii=1

n

∑

€

y =Ym

Upper Case

Lower Case



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Thermodynamic Properties •  Energy and its Forms

–  macroscopic energy: is related to the gross characteristic of a substance on a scale that is large compared with the mean free path of its molecules, e.g. kinetic energy and potential energy are only related to mass

–  microscopic energy: is related to energy possessed by the individual molecules and interaction between molecules, e.g. energy related to the temperature of a substance

•  Total Energy is defined as the sum of all contributions of micro and macroscopic energy

€

E = Emicroscopic + Emacroscopic



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Thermodynamic Properties •  Energy forms considered in thermodynamic

analysis consist mainly of: –  Kinetic Energy:

–  Potential Energy:

–  Internal Energy: the sum of all molecular scale microscopic energies is defined as internal energy. Since internal energy is in part a measure of of the kinetic energy of molecules, it increases as the temperature of the substance increases.

€

EK .E . =12mV 2 or eK .E . =

V 2

2

€

EP .E . = mgz or eP .E . = gz



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Thermodynamic Properties •  Internal energy is given the symbol U

(extensive) and u (intensive) = U/m •  The total energy of a particular mass of matter

is then:

or

€

E = EK .E . + EP .E . +U =12mV 2 +mgz +U

€

e =Em

= eK .E . + eP .E . + u =V 2

2+ gz + u



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Thermodynamic Properties •  Enthalpy: In the analysis of open systems we

find the combination of properties U + pV or u + pv, occurs frequently.

•  This combination is called Enthalpy, and is given its own symbol, h, and is also tabulated with internal energy:

•  Since it is determined from other properties, it too is a property.

€

H =U + pVh = u + pv



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Thermodynamic Properties •  Fixing the State:

– To establish the thermodynamic state we frequently require two independent properties, e.g. T, p, u, v, etc.

•  The state postulate dictates that: the number of independent intensive thermodynamic properties required to completely and uniquely specify the state of a homogenous substance is one more than the number of relevant reversible modes of work. PdV work is usually the only significant mode of work! As such we refer to these substances as simple compressible.



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p-v-T Behaviour •  We can plot data according to a general p-v-T

plot. There are three common plots for substances: – T-v diagrams

– p-v diagrams

– p-T diagrams

•  On the general p-v-T diagram we also have solid, liquid, vapor and liquid-vapor regions.

•  The thermodynamic state is fixed when any two of p, v, or T are given.



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p-v-T Behaviour

(a) Substance that expands on freezing.

(b) Substance that contracts on freezing.



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p-v-T Behaviour •  p-v-T plot construction:



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p-v-T Behaviour •  p-v-T plot construction:



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T-v Diagrams •  Compressed Liquid States

– The region to the left of the “dome” is called the compressed liquid state

•  Liquid-Vapor (Mixture) States – The region within the “dome” is the two

phase or mixture state •  Superheated Vapor States

– The region to the right of the “dome” is the superheated vapor state

Two Phase Region •  In the “dome” region two properties are

not enough to establish state.



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Mixture Quality •  Mixtures (Liquid-Vapor Region)

•  x = 0 (liquid only, a) •  0 < x < 1 (mixture, b) •  x = 1 (vapor only, c)

€

x =mvapor

mliquid +mvapor



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Property Data •  Data are given in the form of Tables in your

text. You also have a copy available in PDF format. – Tables A2-A6 for water – Tables A7-A9 for Refrigerant 22 – Tables A16-A18 for Refrigerant 134a – Tables A13-A15 for Ammonia – Tables A16-A18 for Propane

•  Samples for water follow.



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p-v-T Behaviour (Tables)



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Example •  Water is at 150 C and 5 bar. Locate this

state on a T-v diagram and determine whether it is: compressed liquid, two phase, or superheated?

p-v-T Behaviour Vapor dome for water:



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Using Saturation Tables •  Given a pressure p1 and its corresponding

saturation temperature Tsat, then if T1 > Tsat the state is superheated

•  If the saturation pressure corresponding to a temperature T1 is psat, then if p1 < psat the state is superheated

•  Finally if any of the properties v, u, or h are greater than the values for saturated vapor (v1 > vg, u1 > ug, h1 > hg) at Tsat or psat, then the state is superheated.



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Using Saturation Tables •  If Tsat the saturation temperature corresponding to

p1 then state 1 is in a compressed liquid (or sub-cooled) state, if T1 < Tsat but greater than the solidification temperature.

•  If psat the saturation pressure corresponding to T1 then state 1 is in a compressed liquid (or sub-cooled) state if p1 > psat.

•  Finally if any of the properties v, u, or h are less than the values for saturated liquid (v1 < vf, u1 < uf, h1 < hf) at Tsat or psat, then the state is compressed liquid.

• 



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Using Saturation Tables •  In the vapor dome region temperature and

pressure are not independent properties and are not sufficient to specify the state. As a result:

•  Therefore, given a value for v, u, or h, the state is liquid-vapor if these fall between the saturated liquid or saturated vapor limits. €

v f < v1 < vguf < u1 < ugh f < h1 < hg



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Using Saturation Tables •  In this region the property can be evaluated by

summing the extensive properties for each phase:

•  But these can be written in terms of the intensive properties for each phase:

•  In terms of mixture quality we can obtain: €

Y =Yf +Yg

€

Y = mf y f +mgyg

€

Y = m(1− x)y f +mxyg



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Using Saturation Tables •  We may also write this as:

•  Finally, in terms of the intensive property we wish to evaluate, we obtain:

where y = v, u, or h.

€

Y = m(y f + xy fg )

€

y fg = yg − y f

€

y = y f + xy fgy = (1− x)y f + xyg



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Property Interpolation •  Frequently data fall between lines in the

tables. We use linear interpolation to evaluate the properties:

€

slope =0.2275 − 0.2060240 − 200

=v − 0.2060215 − 200

€

v = 0.2060 +215 − 200240 − 200⎛

⎝ ⎜

⎞

⎠ ⎟ ⋅ (0.2275 − 0.2060)€

v = v1 +T −T1T2 −T1

⎛

⎝ ⎜

⎞

⎠ ⎟ ⋅ (v2 − v1)

€

v = 0.2141⋅ m3

kg



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Example •  Determine the pressure, specific volume, and

internal energy of water at 25 C and a quality of 70%.



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Example •  2 kg of water at 200 C and 300 kPa are

contained in a weighted piston assembly. As a result of heating at constant pressure, the temperature of the water increases to 400 C. Determine the change in volume, the change in internal energy, and the change in enthalpy for this process.



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Example •  A BBQ propane tank contains 6 kg of propane.

The tank has a volume of 18 L. During a warm summer’s day the temperature of the tank and its contents is approximately 32 C, while at night it is approximately 16 C. –  What is the pressure, quality, and internal energy in

the tank at 16 C and 32 C? –  How much does the pressure in the tank change? –  How much heat is transferred to the propane? –  How much liquid propane is vaporized/condensed? –  What is the volume of liquid propane at each state?



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Example •  A closed system holds a mixture of 1 kg of

liquid water and 1 kg of vapor in equilibrium at 700 kPa. –  Determine the initial temperature. –  If heat is transferred to the system until the

temperature reaches 350 C, determine the change in volume if pressure is maintained constant.

Thermodynamic Properties - Memorial University of …€¦ · · 2010-09-17A pure substance can...

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