Exergy or Availability

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Exergy or Availability

Exergy of a system is defined as the theoretical maximum amount ofworkthat can be

obtained from the system at a prescribed state (P, T, h, s, u, v) when operating with areservoir at the constant pressure and temperature P0 and T0. The specific exergy of a

non-flow system is:

and for a steady flow system:

where,u= Specific internal energy,h= Specific enthalpy,v= Specific volume,s= Specific entropy,

C= Velocity,Z= Height of the system measured from a fixed datum,g= Gravity constant.

Forced Convection

Forced convection studies the heat transferbetween a moving fluid and a solid surface.

There are various types of forced convection, such as flow in a tube or across a flat plateand so on. In general there are no mathematical solution available to all types of forced

convection problems. These problems are usually analyzed by equations based on

empirical values and generalized by dimensional analysis. The analysis can be formulated

by the following equation:Nu=f(Pr,Re,Ma)

where,

Nu= Nusselt number

Pr= Prandtl number

Re= Reynolds number

Ma= Mach number

In cases when the flow speed is low, the influence of the Mach number can be neglected

and we obtain:Nu=f(Pr,Re)

Fourier's Law of Conduction

Fourier's law is an empirical law based on observation. It states that the rate ofheat flow,dQ/dt, through a homogenous solid is directly proportional to the area, A, of the section

at right angles to the direction of heat flow, and to the temperature difference along the

path of heat flow, dT/dx i.e.
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The proportionality ratio, , is called thermal conductivity of the material.

Free Convection

Natural convection or free convection is caused by fluid motion due to density

differences. In most practical cases, the free convection may be neglected when there is afluid flow i.e. forced convection. A dimensional analysis of the heat transferby free

convection results in:Nu=f(Pr,Gr)

where,

Nu= Nusselt number

Pr= Prandtl numberGr= Grashof number

Free or Unresisted Expansion

Consider two vessels A and B which are connected to each other by a pipe and a valve.

Vessel A is initially filled with a fluid at a certain pressure and B is completely

evacuated. By opening the valve, the fluid in the vessel A will expand until it fills bothvessels. This process is known as free or unresisted expansion. It is anirreversible

process because it needs external work to be done to restore the fluid to its initial

condition. Consider a system, consisting of both vessels which is perfectly thermally

insulated. Apply the first law of thermodynamics to the system, i.e.
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Q + W = U2 - U1

where indices 1 and 2 represent initial and final states.

Q = 0, because the thermal insulation will not allow any heat transfer between the system

and the surroundings. W=0 because the boundaries of the system are not moved. Theresult will then be:

U2=U1

The free expansion process is adiabaticbut irreversible. If the working fluid is aperfect

gas, then U2=U1 is equivalent to T2=T1.

Fuel

Fuels are chemical substances which may be burned in oxygen to generateheat. They

mainly consist of carbon and hydrogen and sometimes a small amount of sulfur orminerals. There are solid, liquid and gaseous fuels. Coal and Coke are examples of solidfuels. Petroleum oils are usually a mixture of several liquid fuels. Gaseous fuels may be a

mixture of gases such as methane (CH4), ethane (C2H6) and so on. The components

before the combustion process are called reactants. The combustion process producesnew components which are called products. E.g. combustion of 1 kmol of carbon with 1

kmol of pure oxygen will produce 1 kmol carbon dioxide:

C+O2-->CO2

Here, C and O2 are reactants and CO2 is the product. Related Topics:

Ignition Temperature

Air-Fuel Ratio

Stoichiometric Combustion

Excess Air

Heating Value

Gas Turbine

Gas turbines use hot gases generated directly from the combustion of fossil fuels. The hot

gas expands through the blades on the turbine rotor causing them to move. The gas

turbine process is:
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3-4 irreversible but approximately adiabatic expansion of combustion gases

The work output of the turbine is:

where

m=mass flow of hot gases

h3=enthalpy of hot gases at inlet

h4=enthalpy of exhaust gases

The isentropic efficiency of the turbine is:

Heating Value

Heating Value is defined as the amount ofenergy released when afuel is burned

completely in a steady-flow process and the products are returned to the state of the

reactants. The heating value is dependent on the phase of water/steam in the combustionproducts. If H2O is in liquid form, heating value is called HHV (higher Heating Value).

When H2O is in vapor form, heating value is called LHV (Lower Heating Value).

Humidifiers
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Humidifiers are used in air conditioningsystems to increase the humidity of the air.

There are several types of humidifiers:

Adiabatic Humidification Process

Adiabatic Humidifier with Recirculation of Spray Water

Adiabatic Humidifiers without Recirculation of Spray Water Spray Water with Recirculation and Heating or Cooling

Steam humidifiers are also used in air conditioning system. The two basic types are:

Direct steam injection

Pan steam humidifier

Humidity Ratio or Relative Humidity

Humidity ratio or relative humidity is the ratio of the actual mass of water vapor in the airto the mass of water vapor that would saturate the air at the same temperature

Hygrometer or Psychrometer

Hygrometers are devices for measuring the wet-bulb temperature of the air. The

temperature reading is affected by air movement over the instrument. There are two types

of measuring instrument, sling and screen hygrometer. The sling hygrometer is the moreaccurate one, therefore it is preferred by air conditioning engineers.

Sling hygrometer measures the wet-bulb temperature in a moving air stream,

preferably above 2 m/s. The instrument has two thermometers. One of these

thermometers is covered with muslin sleeve which is kept moist with distilled andclean water. This thermometer will measure the wet-bulb temperature and the

other one dry-bulb temperature. A sling wet-bulb temperature may also be

obtained by an Assman hygrometer. In the Assman hygrometer, the wet-bulb

thermometer is installed in a duct where the air is flowing at reasonable velocity.
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Screen hygrometer measures the wet-bulb temperature in still air. Thermometers

are installed in a Stevenson screen as used by meteorologists.

Ignition Temperature

Each fuel should be brought above its Ignition Temperature for starting the combustion

process. An appropriate air-fuel ratio is also necessary. The minimum ignition

temperature at atmospheric pressure for some substances are:

carbon 400 C

gasoline 260 C

hydrogen 580 C

carbon monoxide 610 C

methane 630 C

Intensity of Radiation

The intensity of radiation is defined as the rate of emitted energy from unit surface area

through unit solid angle. The radiation from a surface has different intensities in different

directions. The intensity of radiation along a normal to the surface is known as intensityof normal radiation, In. By using Lambert's cosine law andStefan-Boltzmann law for a

surface at absolute temperature, T and emissivity, , we obtain:

Internal Energy

Internal energy of a system, is the energy content of the systemdue to its thermodynamic

properties such aspressure and temperature. The change of internal energy of a systemdepends only on the initial and final states of the system and not in any way by the path

or manner of the change. This concept is used to definethe first law of thermodynamics.
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Specific Internal Energy

Specific internal energy is defined as the internal energy of the system per unit mass of

the system and naturally has the same dimension as [energy/mass] orenthalpy.

Isentropic Process

An isentroic process is one during which theentropyofworking fluid remains constant.

Isobaric Process

An isobaric process is one during which thepressureofworking fluid remains constant.

Isometric Process

An isometric process is one during which the volume ofworking fluid remains constant.

Isothermal Process

An isothermal process is one during which the temperatureofworking fluid remainsconstant.

Joule's Law

Joule's law state that the internal energy of aperfect gas is a function of the temperatureonly, i.e.

u=f(t)

Lambert's Cosine Law

Lambert's cosine law states that the intensity of radiation along a direction which has

angle with the normal to the surface is:
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where In is the intensity of radiationin normal direction.

Latent Heat

Latent Heat is defined as the heat which flows to or from a material without a change totemperature. The heat will only change the structure or phase of the material. e.g. melting

or boiling of pure materials.

Liquids and Vapors

If a pure liquid is heated at a constantpressure there is a fixed temperatureat which

bubbles of vapor form in the liquid; this phenomenon is known as boiling. The states ofsubstance at this condition represents a point on the properties diagram, known as boiling

point; e.g. point 1. A slight addition of heat to the liquid at this state changes some of it

into vapor.

Saturated liquid line, SLL, is formed by connecting a series of boiling points. Boilingtemperature known also as saturation temperature, T, for a pure liquid is only a function

of pressure, P, i.e.T2 = T1 = f(P)

Vaporization continues by further heat supply to the system until no liquid is left. This

state is known as dry saturated vapor, e.g. point 2. If the system is slightly cooled at this

state, then droplets of liquid will begin to form. Connecting a series of points at dry

saturated vapor builds a line, known as saturated vapor line, SVL. The state of substancebetween saturated liquid and dry vapor is called wet vapor. Further heating of a dry

saturated vapor at constant pressure causes a rise of vapor temperature and it becomes

superheated. The state of substance is completely defined by its pressure and temperatureif it is in liquid or superheated vapor phase i.e.

h = f1(P,T) = Specific enthalpyv = f2(P,T) = Specific volumes = f3(p,T) = Specific entropy
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These properties for different substances are either tabulated or can be calculated by

certain equations, e.g. IFC formulation for water and steam properties. The state of wetvapor can not be defined by just pressure and temperature until one other property is

given. The condition or quality of wet vapor is often defined by its dryness or wetness

fraction.dryness fraction, x = the mass of dry vapor in 1 kg of the mixture,and,

wetness fraction, 1 - x = the mass of liquid in 1 kg of the mixture.

For wet vapor with the dryness fraction, x,h = (1-x) hf + x hgv = (1-x) vf + x vgs = (1-x) sf + x sg

where f and g indicate the property of the substance at saturated liquid and dry saturated

vapor states respectively. The heat supplied to the liquid for the complete phase change is

called the specific enthalpy of vaporization.hg - hf = hfg

Mass

The SI unit of mass is kg (kilogram). Other units are:

1 g= 0.001 kg

1 t (metric ton)= 1 ton= 1000 kg 1 lbm (pound mass)= 0.453 kg

1 slug= 14.594 kg

1 U.K.ton (long ton)= 1016.05 kg

1 U.S.ton (short ton)= 907.185kg

Mass Flow

Mass flow rate is the amount ofmass which enters or leaves a system per unittime. TheSI unit for mass flow rate is kg/s. Other units are:

1 kg/h= 1/3600 kg/s

1 t/h= 1/3.6 kg/s

1 lbm/s= 0.453 kg/s
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Molar Mass

Molar mass is defined as the mass per number ofmoles, e.g. molar mass of oxygen (O2)

is 32 kg/kmol. The SI unit used for molar mass is kg/kmol. Other units are:

1 g/mol= 1 kg/kmol

1 lbm/kmol= 0.453 kg/kmol

Mole

Mole is defined by 1971 General Conference of Weights and Measures. The amount ofmass of a system, also known as mole, is the quantity which contains as many elementary

entities (atoms, ions or molecules) as there are atoms in 0.012 kg of carbon-12. The unitfor mole in SI system is mol. Another unit is:

1 kmol=1000 mol

Newton's Law of Cooling

At contact surfaces between a fluid and a solid wall, there is always a thin layer of fluid

through which the heat is transferred by conduction. Whenever there is an appreciablemovement of the fluid, conduction heat transfer in fluid may be neglected compared withconvection heat transfer. The heat transferfrom the solid surface to the fluid can be

described by Newton's law of cooling. It states that the heat transfer, dQ/dt, from a solid

surface of area A, at a temperature Tw, to a fluid of temperature T, is:
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where is the heat transfer coefficient.

Pan Steam Humidifier

A Pan Steam Humidifier uses a heating element inside a water tank. The tank is mounted

at the bottom of the air duct. The air flowing over the water surface will cause someevaporative cooling which results in drop of air dry-bulb temperature

Percentage Saturation

Percentage saturation is defined as the ratio of the specific humidity of air to the specific

humidity of saturated air at the same temperature.

Perfect Gas or Ideal Gas

Experimental information about gases at low pressures i.e. Charles's law, Boyle's law and

Avogadro's principle may be combined to one equation:P V=n R T

known as perfect gas equation. Where,

P= absolute pressure,

T= absolute temperature,

V=volume of the gas,

n= number ofmoles,

and R is a constant, known as gas constant.R=8314.51 J/(kmol.K)

The surface of possible states, (P,V,T), of a fixed amount of a perfect gas is shown infigure below.
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Any gas that obeys the above mentioned equation under all conditions is called a perfect

gas (or ideal gas). A real gas (or an actual gas), behaves like a perfect gas only at lowpressures. Some properties of actual gases such as specific heat at constant pressure and

specific enthalpy are dependent on temperature but the variation due to pressure isnegligible. There are empirical relations that calculate gas properties. The following

polynom is a good approximation for the specific enthalpy of gases:

where a1 to a6 are constants depending only on the type of the gas. It should be noted

that this formulation will agree with Joule's law and we obtain a set of

thermodynamically consistent equations. The above equation can be used directly for

calculation of specific heat capacity of the gas:

By using the relationship:

The specific entropy of the gas, s, will be:

where a7 is a constant and P0 is a reference pressure

Polytropic Process


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Many processes can be approximated by the law:

where,

P= Pressure,

v= Volume,n= an index depending on the process type.

Polytropic processes are internallyreversible. Some examples are vapors andperfect

gases in many non-flow processes, such as:

n=0, results in P=constant i.e. isobaric process.

n=infinity, results in v=constant i.e. isometric process.

n=1, results in P v=constant, which is an isothermal process for a perfect gas.

n= , which is a reversible adiabatic process for a perfect gas.

Some polytropic processes are shown in figure below:

The initial state ofworking fluidis shown by point 0 on the P-V diagram. The polytropic

state changes are:

0 to 1= constant pressure heating,

0 to 2= constant volume heating,

0 to 3= reversible adiabatic compression,

0 to 4= isothermal compression,

0 to 5= constant pressure cooling,

0 to 6= constant volume cooling,

0 to 7= reversible adiabatic expansion,

0 to 8= isothermal expansion.

Power

Power is defined as work(orenergy transfer) per unittime:P = dW / dt
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The SI unit of power is watt (w).

1 w= 1 J/s

Other units are:

1 kw= 1E3 w

1 Mw= 1E6 w

1 kpm/s= 9.80665 w

1 cal/s= 4.1868 w

1 kcal/h= 1.163 w

1 erg/s=1E-7 w

1 hp (horse power)= 745.7 w

1 ft.lbf/s= 1.35582 w

1 Btu/h= 0.293071 w

Psychrometric Chart

The psychrometric chart is a useful design tool for air conditioning engineers. The chart

presents a number of properties of moist air:

dry-bulb temperature

sling wet-bulb temperature

moisture content specific enthalpy

specific volume

percentage saturation
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Psychrometry or Hygrometry

Psychrometry or hygrometry is the study of how the properties of moist air can change as

a result ofair conditioning processes

Rankine Cycle

Rankine cycle is aheat engine with vapor power cycle. The common working fluid is

water. The cycle consists of four processes:

1 to 2: Isentropic expansion (Steam turbine)

2 to 3: Isobaric heat rejection (Condenser)

3 to 4: Isentropic compression (Pump) 4 to 1: Isobaric heat supply (Boiler)

Work output of the cycle (Steam turbine), W1 and work input to the cycle (Pump), W2are:

W1 = m (h1-h2)W2 = m (h4-h3)
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where m is the mass flow of the cycle. Heat supplied to the cycle (boiler), Q1 and heat

rejected from the cycle (condenser), Q2 are:Q1 = m (h1-h4)Q2 = m (h2-h3)

The net work output of the cycle is:W = W1 - W2

The thermal efficiencyof a Rankine cycle is:

The efficiency of the Rankine cycle is not as high as Carnot cycle but the cycle has lesspractical difficulties and more economic.

Specific Humidity or Moisture Content of Air

Specific humidity or moisture content of air is the ratio of the mass of water to the massofdry airin a given volume of moist air.

State of Working Fluid

Working fluid is the matter contained within boundaries of a system. Matter can be insolid, liquid, vapor or gaseous phase. The working fluid in applied thermodynamic

problems is either approximated by aperfect gas or a substance which exists as liquid and

vapor. The state of the working fluid is defined by certain characteristics known as

properties. Some of the properties which are important in thermodynamic problems are:

Pressure(P)

Temperature(T)

Specific enthalpy(h)

Specific entropy(s)

Specific volume(v)

Specific internal energy(u)
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The thermodynamic properties for a pure substance can be related by the generalrelationship, f(P,v,T)=0, which represents a surface in the (P,v,T) space. The

thermodynamic laws do not give any information about the nature of this relationship for

the substances in the liquid and vapor phases. These properties may only be related bysetting up measurements. The measured data can be described by equations obtained e.g.

by curve fitting. In this case the equations should be thermodynamically consistent.

The state of any pure working fluid can be defined completely by just knowing twoindependent properties of the fluid. This makes it possible to plot state changes on 2D

diagrams such as:

pressure-volume (P-V) diagram,

temperature-entropy (T-s) diagram,

enthalpy-entropy (h-s) diagram.

Steady-Flow System
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Applying the first law of thermodynamics to a steady-flow system, defined by control

volume shown above, gives:

known as steady-flow energy equation. Where,

dQ/dt= Supplied heat to the system per unit time,

dW/dt= Input work to the system per unit time,

m= Mass flow rate,

h=h2-h1,

h= Specific enthalpy,

C /2= Difference in kinetic energy between outlet and inlet,

Z= Height measured from some reference datum,1, 2 = refer to inlet and outlet, respectively.

Steam Turbine

Steam turbines are devices which convert the energy stored in steam into rotationalmechanical energy. These machines are widely used for the generation of electricity in a

number of different cycles, such as:

Rankine cycle

Reheat cycle

Regenerative cycle

Combined cycle

The steam turbine may consists of several stages. Each stage can be described by

analyzing the expansion of steam from a higher pressure to a lower pressure. The steammay be wet, dry saturated or superheated.
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Consider the steam turbine shown in the cycle above. The outputpowerof the turbine at

steady flow condition is:P = m (h1-h2)

where m is the mass flow of the steam through the turbine and h1 and h2 are specificenthalpy of the steam at inlet respective outlet of the turbine.

The efficiency of the steam turbines are often described by the isentropic efficiencyforexpansion process. The presence of water droplets in the steam will reduce the efficiency

of the turbine and cause physical erosion of the blades. Therefore the dryness fractionof

the steam at the outlet of the turbine should not be less than 0.9.

Stefan-Boltzmann Law

The Stefan-Boltzmann law states that theemissive power, P, from ablack body isdirectly proportional to the forth power of its absolute temperature i.e.

P = T

where is the Stefan-Boltzmann constant
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= 5.67E-8 W/(m K )

The emitted power, P, for a non-black body with emissivity, , is:

P= T

Stoichiometric Combustion

Stoichiometric or Theoretical Combustion is the ideal combustion process during which a

fuel is burned completely. A complete combustion is a process which burns all the carbon(C) to (CO2), all hydrogen (H) to (H2O) and all sulfur (S) to (SO2). If there are unburned

components in the exhaust gas such as C, H2, CO the combustion process is uncompleted

The First Law of Thermodynamics

Conservation of Energy

The principle of the conservation ofenergy states that energy can neither be created nor

destroyed. If a system undergoes a process by heat and work transfer, then the net heat

supplied, Q, plus the net work input, W, is equal to the change ofintrinsic energy of the

working fluid, i.e.

where U1 and U2 are intrinsic energy of the system at initial and final states,

respectively. The special case of the equation applied to asteady-flow system is knownas steady-flow energy equation. Applying this general principle to a thermodynamic

cycle, when the system undergoes a complete cycle, i.e. U1 = U2, results in:

where:

Q= The algebraic sum of the heat supplied to (+) or rejected from (-) the system.

W= The algebraic sum of the work done by surroundings on the system (+) or by

the system on surroundings (-).

Applying the rule to the power plant shown in figure below,
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gives:

Q = Qin - Qout

W = Win - Wout

Qin + Win - Qout - Wout = 0

where,

Qin = Heat supplied to the system through boiler,

Win = Feed-pump work,

Qout = Heat rejected from the system by condenser,

Wout = Turbine work.

The Second Law of Thermodynamics

The second law of thermodynamics states that no heat engine can be more efficient than areversibleheat engine working between two fixed temperature limits (Carnot cycle) i.e.

the maximum thermal efficiency is equal to the thermal efficiency of the Carnot cycle:

or in other wordsIf the heat input to a heat engine is Q, then the work output of theengine, Wwill be restricted to an upper limitWmax i.e.

It should be noted that real cycles are far less efficient than the Carnot cycle due to

mechanical friction and other irreversibility

The Zeroth Law of Thermodynamics

This law states that if objectA is in thermal equilibrium with objectB, and objectB is inthermal equilibrium with objectC, then objectCis also in thermal equilibrium with

objectA. This law allows us to build thermometers. For example the length of a mercury
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column (object B) may be used as a measure to compare the temperatures of the two

other objects.

Thermal Conductivity

The thermal conductivity of a substance is defined as the heat flow per unit area per unit

time when the temperaturedecreases by one degree in unit distance. TheSI unit ofthermal conductivity is W/(m.K). Other units are:1 kW/(m.K)= 1000 W/(m.K)

Thermal Efficiency

LTER= Low Temperature Energy Reservoir

HTER= High Temperature Energy Reservoir

The thermal efficiency of a cycle (or more precisely a forward heat engine) is defined asthe ratio of net work output, W, to the heat supplied at high temperature, Q1, i.e.
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Thermal Radiation

Thermal radiation is the energy radiated from hot surfaces as electromagnetic waves. It

does not require medium for its propagation. Heat transferby radiation occur betweensolid surfaces, although radiation from gases is also possible. Solids radiate over a wide

range of wavelengths, while some gases emit and absorb radiation on certain wavelengthsonly.

When thermal radiation strikes a body, it can be absorbed by the body, reflected from the

body, or transmitted through the body. The fraction of the incident radiation which is

absorbed by the body is calledabsorptivity (symbol ). Other fractions of incident

radiation which are reflected and transmitted are called reflectivity (symbol ) and

transmissivity (symbol ), respectively. The sum of these fractions should be unity i.e.

Thermodynamic Cycle

Thermodynamic cycle is defined as a process in which a working fluid undergoes a seriesof state changes and finally returns to its initial state. A cycle plotted on any diagram of

properties forms a closed curve.

A reversible cycle consists only of reversible processes. The area enclosed by the curveplotted for a reversible cycle on a p-v diagram represents the net work of the cycle.
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The workis done on the system, if the state changes happen in an anticlockwise

manner.

The work is done by the system, if the state changes happen in a clockwisemanner.

Thermodynamically Consistent Set of Equations

There are differential relations between properties ofworking fluid. By using the so-

called thermodynamic potentials i.e. specific free energy (Helmholtz function f) andspecific free enthalpy (Gibbs function g), which are related by the following equation:

g = f + P v

we can write:

where,

P= PressureT= Temperature

v= Specific volume

h=Specific enthalpy

s=Specific entropy

Any set of equations which satisfy the above mentioned relations is called a

thermodynamically consistent set of equations. These equations can be based on

experimentally obtained data.

Turbine

Turbines are devices that convert mechanical energy stored in a fluid into rotational

mechanical energy. These machines are widely used for the generation of electricity. The

most important types of turbines are: steam turbines,gas turbines, water turbines andwind turbines.
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Throttling

A fluid can be throttled by several means. Examples are: a partly open valve, an orifice or

any other sudden reduction in the cross-section of the flow. The enthalpy remains almost

constant and pressure reduces in this process. Throttling is anirreversibleprocess due toeddying of the fluid.

Consider a perfectly thermally insulated pipe which fluid flows steadily through an

orifice. Applying the first law of thermodynamics to the steady flow system defined bythe control volume between sections 1-1 and 2-2, gives:

dQ/dt+dW/dt=m [ h + C /2 + g Z]

dQ / dt = 0 because the system is thermally insulated. dW / dt is also zero. If velocities

at sections 1-1 and 2-2 are small or approximately equal and the height difference

between these two sections, Z, is negligible, then we can write:

h=h2-h1=0

where h1 and h2 represent the enthalpy of the working fluidat sections 1-1 and 2-2

respectively.
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