Power plants generate electrical power by using fuels like coal, oil or natural gas. A simple power plant consists of a boiler, turbine, condenser and a pump. Fuel, burned in the boiler and superheater, heats the water to generate steam. The steam is then heated to a superheated state in the superheater. This steam is used to rotate the turbine which powers the generator. Electrical energy is generated when the generator windings rotate in a strong magnetic field. After the steam leaves the turbine it is cooled to its liquid state in the condenser. The liquid is pressurized by the pump prior to going back to the boiler A simple power plant is described by a Rankine Cycle.
Rankine cycleSaturated or superheated steam enters the turbine at state 1, where it expands isentropically to the exit pressure at state 2. The steam is then condensed at constant pressure and temperature to a saturated liquid, state 3. The heat removed from the steam in the condenser is typically transferred to the cooling water. The saturated liquid then flows through the pump which increases the pressure to the boiler pressure (state 4), where ts1.gif (9k) the water is first heated to the saturation temperature, boiled and typically superheated to state 1. Then the whole cycle is repeated.
Typical Modificationsts
Rehaeat
When steam leaves the turbine, it is typically wet. The presense of water causes erosion of the turbine blades. To prevent this, steam is extracted from high pressure turbine (state 2), and then it is reheated in the boiler (state 2') and sent back to the low pressure turbine.Regeneration
Regeneration helps improve the Rankine cycle efficiency by preheating the feedwater into the boiler. Regeneration can be achieved by open feedwater heaters or closed feedwater heaters. In open feedwater heaters, a fraction of the steam exiting a high pressure turbine is mixed with the feedwater at the same pressure. In closed system, the steam bled from the turbine is not directly mixed with the feedwater, and therefore, the two streams can be at different pressures.
Energy is the capacity or capability to do work and energy is used when work are done.
The unit for energy is joule J, where
1 J = 1 Nm
which is the same unit as for work.
Energy forms
There can be several forms of energy, including
* mechanical energy
* heat or thermal energy
* electrical energy
* chemical energy
* nuclear energy
* light energy
Energy Efficiency
Energy efficiency is the ratio between useful energy output and input energy, and can be expressed as
μ = Eo / Ei (1)
where
μ = energy efficiency
Eo = useful energy output
Ei = energy input
It is common to state efficiency as a percentage by multiplying (1) with 100.
Example - Energy Efficiency
A lift moves a mass 10 m up with a force of 100 N. The input energy to the lift is 1500 J. The energy efficiency of the lift can be calculated as
μ = 100 (N) 10 (m) / 1500 (J)
= 0.67 or
= 67 %
Refrigeration is the withdrawl of heat from a substance or space so that temperature lower than that of the natural surroundings is achieved.
Refrigeration may be produced by
- thermoelectric means
- vapor compression systems
- expansion of compressed gases
- throttling or unrestrained expansion of gases.
Vapor compression systems are employed in most refrigeration systems. Here, cooling is accomplished by evaporation of a liquid refrigerant under reduced pressure and temperature. The fluid enters the compressors at state 1 where the temperature is elevated by mechanical compression (state 2). The vapor condenses at this pressure, and the resultant heat is dissipated to the surrounding. The high pressure liquid (state 3) then passes through an expansion valve through which the fluid pressure is lowered. The low-pressure fluid enters the evaporator at state 4 where it evaporates by absorbing heat from the refrigerated space, and reenters the compressor. The whole cycle is repeated.
The simplest model for IC engines is the air-standard model, which assumes that:
- The system is closed.
- Air is the working fluid and is modeled as an ideal gas throughout the cycle.
- Compression and expansion processes are isentropic.
- A reversible heat transfer process characterizes the combustion of fuel and air.
- Heat rejection takes place reversibly and at constant volume.
Spark Ignition Engines (Otto Cycle)
The spark-ignition engines are the most common type used in cars. Larger engines operate using a four-stroke cycle, while smaller engines operate on a two-stroke cycle. In a simple four-stroke cycle, a combustible mixture of air and fuel is drawn into a cylinder during the intake stroke, and the temperature and pressure of the mixture is raised during the compression stroke. At near the maximum compression, a spark initiates combustion of the mixture, raising its temperature and forcing expansion. The expanding gases do work on the piston during the power stroke and then the burnt gases are purged during the exhaust stroke. Typically 3000 or more such cycles are repeated in a minute.
The Otto cycle is an air-standard model of the actual cycle. In addition to the air-standard assumptions listed above, the combustion process is modelled as a reversible constant volume heat addition process. The four steps of the air-standard Otto cycle are outlined below:
- (1-2) Isentropic compression (Compression Stroke)
- (2-3) Constant-volume, reversible heat addition (Ignition)
- (3-4) Isentropic expansion (Power Stroke)
- (4-1) Reversible, constant-volume heat rejection (Exhaust)
Typical pv and Ts diagrams for an Otto cycle are shown below where steps (1-2) and (3-4) are isentropic, and (2-3) and (4-1) are isochoric.
The Specific Heat Capacity is the amount of heat required to change a unit mass of a substance by one degree in temperature. The heat supplied to a unit mass can be expressed as
dQ = m c dt (1)
where
dQ = heat supplied (kJ, Btu)
m = mass (kg, lb)
c = Specific Heat Capacity (kJ/kgoC, Btu/lboF)
dt = temperature change (oC, oF)
Expressing Specific Heat Capacity using (1)
c = dQ / m dt (1b)
Converting between Common Units
* 1 Btu/lbmoF = 4186.8 J/kg K = 1 kcal/kgoC
Specific Heat Capacity Gases
There are two definitions of Specific Heat Capacity for vapors and gases:
cp = (δh/δT)p - Specific Heat Capacity at constant pressure (kJ/kgoC)
cv = ( δh/ δT)v - Specific Heat Capacity at constant volume (kJ/kgoC)
Gas Constant
The gas constant can be expressed as
R = cp - cv (2)
where
R = Gas Constant
Ratio of Specific Heat
The Ratio of Specific Heat Capacities is expressed
k = cp / cv (3)
he energy transfer of a substance can be expressed as
Q = m cp dt (1)
where
Q = quantity of energy transferred (kJ)
m = mass of substance (kg)
cp = specific heat capacity of the substance (kJ/kgoC)
dt = temperature difference (rise or fall) in the substance (oC)
The First Law of Thermodynamics forms the
* basis for quantitative analysis of chemical reactions
The Second Law of Thermodynamics is used to
* identify the directions of chemical reactions
The Third Law of Thermodynamics states that
* the entropy of any pure substance in thermodynamic equilibrium approaches zero as the temperature approaches zero (Kelvin), or conversely
* the temperature (Kelvin) of any pure substance in thermodynamic equilibrium approaches zero when the entropy approaches zero
The Third Law of Thermodynamics can mathematically be expressed as
lim ST→0 = 0 (1)
where
S = entropy (J/K)
T = absolute temperature (K)
At a temperature of absolute zero there is no thermal energy or heat. At a temperature of zero Kelvin the atoms in a pure crystalline substance are aligned perfectly and do not move. There is no entropy of mixing since the substance is pure.
The temperature of absolute zero is the reference point for determination entropy. The absolute entropy of a substance can be calculated from measured thermodynamic properties by integrating the differential equations of state from absolute zero. For a gas this requires integrating through solid, liquid and gaseous phases.
Kelvin & Planc
"No (heat) engine whose working fluid undergoes a cycle can absorb heat from a single reservoir, deliver an equivalent amount of work, and deliver no other effect"
Clausius
"No machine whose working fluid undergoes a cycle can absorb heat from one system, reject heat to another system and produce no other effect"
Both statements of the second law place constraints on the first law by identifying that energy goes downhill.
The second law is concerned with entropy (S), which is a measure of disorder at the microscopic level. Entropy is produced by all processes and associated with the entropy production is the loss of ability to do work. The second law says that the entropy of the universe increases. An increase in overall disorder is therefore spontaneous. If the volume and energy of a system are constant, then every change to the system increases the entropy. If volume or energy change, then the entropy of the system actually decrease. However, the entropy of the universe does not decrease.
For energy to be available there must be a region with high energy level and a region with low energy level. Useful work must be derived from the energy that would flows from the high level to the low level.
* 100% of the energy can not be transformed to work
* Entropy can be produced but never destroyed
Efficiency of a heat machine
The efficiency of a heat machine working between two energy levels is defined in terms of absolute temperature:
η = ( Th - Tc ) / Th = 1 - Tc / Th(1)
where
η = efficiency
Th = temperature high level (K)
Tc = temperature low level (K)
As a consequence, to attain maximum efficiency the Tc would have to be as cold as possible. For 100% efficiency the Tc would have to equal 0 K. This is practically impossible, so the efficiency is always less than 1 (less than 100%).
Change in entropy > 0, irreversible process
Change in entropy = 0, reversible process
Change in entropy < 0, impossible process
Entropy is used to define the unavailable energy in a system. Entropy defines the relative ability of one system to act to an other. As things moves toward a lower energy level, where one is less able to act upon the surroundings, the entropy is said to increase.
* For the universe as a whole the entropy is increasing!
Entropy definition
Entropy is defined as :
S = H / T (2)
where
S = entrophy (kJ/kg K)
H = enthalpy (kJ/kg)
T = absolute temperature (K)
A change in the entropy of a system is caused by a change in its heat content, where the change of entropy is equal to the heat change divided by the average absolute temperature (Ta):
dS = dH / Ta (3)
The sum of (H / T) values for each step in the Carnot cycle equals 0. This only happens because for every positive H there is a countering negative H, overall.
Carnot Heat Cycle
In a heat engine, a gas is reversibly heated and then cooled. A model of the cycle is as follows: State 1 --(isothermal expansion) --> State 2 --(adiabatic expansion) --> State 3 --(isothermal compression) --> State 4 --(adiabatic compression) --> State 1
State 1 to State 2: Isothermal Expansion
Isothermal expansion occurs at a high temperature Th, dT = 0 and dE1 = 0. Since dE = H + w, w1 = - H1. For ideal gases, dE is dependent on temperature only.
State 2 to State 3: Adiabatic Expansion
The gas is cooled from the high temperature, Th, to the low temperature, Tc. dE2 = w2 and H2 = 0 (adiabatic).
State 3 to State 4: Isothermal Compression
This is the reverse of the process between states 1 and 2. The gas is compressed at Tc. dT = 0 and dE3 = 0. w3 = - H3
State 4 to State 1: Adiabatic Compression
This is the reverse of the process between states 2 and 3. dE4 = w4 and H4 = 0 (adiabatic).
The processes in the Carnot cycle can be graphed as the pressure vs. the volume. The area enclosed in the curve is then the work for the Carnot cycle because w = - integral (P dV). Since this is a cycle, dE overall equals 0. Therefore,
-w = H = H1 + H2 + H3 + H4
If you decrease Tc, then the quantity -w gets larger in magnitude.
if -w > 0 then H > 0 and the system, the heat engine, does work on the surroundings.
The laws of thermodynamics were determined empirically (by experiment). They are generalizations of repeated scientific experiments. The second law is a generalization of experiments dealing with entropy--it is that the dS of the system plus the dS of the surroundings is equal to or greater then 0.
* Entropy is not conserved like energy!
Example - Entropy Heating Water
A process raises 1 kg of water from 0 to 100oC (273 to 373 K) under atmospheric conditions.
Specific enthalpy at 0oC (hf) = 0 kJ/kg (from steam tables) (Specific - per unit mass)
Specific enthalpy of water at 100oC (hf) = 419 kJ/kg (from steam tables)
Change in specific entropy:
dS = dH / Ta
= (419 - 0) / ((273 + 373)/2)
= 1.297 kJ/kgK
Example - Entropy Evaporation Water to Steam
A process changes 1 kg of water at 100oC (373 K) to saturated steam at 100oC (373 K) under atmospheric conditions.
Specific enthalpy of steam at 100oC (373 K) before evaporating = 0 kJ/kg (from steam tables)
Specific enthalpy of steam at 100oC (373 K) after evaporating = 2 258 kJ/kg (from steam tables)
Change in specific entropy:
dS = dH / Ta
= (2 258 - 0) / ((373 + 373)/2)
= 6.054 kJ/kgK
The total change in specific entropy from water at 0oC to saturated steam at 100oC is the sum of the change in specific entropy for the water, plus the change of specific entropy for the steam.
Example - Entropy Superheated Steam
A process superheats 1 kg of saturated steam at atmospheric pressure to 150oC (423 K).
Specific total enthalpy of steam at 100oC (373 K) = 2 675 kJ/kg (from steam tables)
Specific total enthalpy of superheated steam at 150oC (373 K) = 2 777 kJ/kg (from steam tables)
Change in specific entropy:
dS = dH / Ta
= (2 777 - 2 675) / ((423 + 373)/2)
= 0.256 kJ/kgK
* Entropy table for superheated steam
The energy transfer between different systems can be expressed as:
E1 = E2 (1)
where
E1 = initial energy
E2 = final energy
The internal energy encompasses:
* The kinetic energy associated with the motions of the atoms
* The potential energy stored in the chemical bonds of the molecules
* The gravitational energy of the system
The first law is the starting point for the science of thermodynamics and for engineering analysis.
Based on the types of exchange that can take place we will define three types of systems:
* isolated systems: no exchange of matter or energy
* closed systems: no exchange of matter but some exchange of energy
* open systems: exchange of both matter and energy
The first law makes use of the key concepts of internal energy, heat, and system work. It is used extensively in the discussion of heat engines.
Internal Energy - Internal energy is defined as the energy associated with the random, disordered motion of molecules. It is separated in scale from the macroscopic ordered energy associated with moving objects; it refers to the invisible microscopic energy on the atomic and molecular scale. For example, a room temperature glass of water sitting on a table has no apparent energy, either potential or kinetic . But on the microscopic scale it is a seething mass of high speed molecules. If the water were tossed across the room, this microscopic energy would not necessarily be changed when we superimpose an ordered large scale motion on the water as a whole.
Heat - Heat may be defined as energy in transit from a high temperature object to a lower temperature object. An object does not possess "heat"; the appropriate term for the microscopic energy in an object is internal energy. The internal energy may be increased by transferring energy to the object from a higher temperature (hotter) object - this is called heating.
Work - When work is done by a thermodynamic system, it is usually a gas that is doing the work. The work done by a gas at constant pressure is W = p dV, where W id work, p is pressure and dV is change in volume.
For non-constant pressure, the work can be visualized as the area under the pressure-volume curve which represents the process taking place.
Heat Engines -Refrigerators, Heat pumps, Carnot cycle, Otto cycle
The change in internal energy of a system is equal to the head added to the system minus the work done by the system:
dE = Q - W (2)
where
dE = change in internal energy
Q = heat added to the system
W = work done by the system
1st law does not provide the information of direction of processes and does not determine the final equilibrium state. Intuitively, we know that energy flows from high temperature to low temperature. Thus, the 2nd law is needed to determine the direction of processes.
Enthalpy is the "thermodynamic potential" useful in the chemical thermodynamics of reactions and non-cyclic processes. Enthalpy is defined by
H = U + PV (3)
where
H = enthalpy
U = internal energy
P = pressure
V = volume
Enthalpy is then a precisely measurable state variable, since it is defined in terms of three other precisely definable state variables.
Entropy is used to define the unavailable energy in a system. Entropy defines the relative ability of one system to act to an other. As things moves toward a lower energy level, where one is less able to act upon the surroundings, the entropy is said to increase. Entropy is connected to the Second Law of Thermodynamics.
For the universe as a whole the entropy is increasing.
Compression Ignition engines are mostly used in marine applications, power generation and heavier transportation vehicles. Here, in a typical four-stroke cycle, air is drawn into the cylinder in the intake stroke and then compressed during the Compression Stroke. At near maximum compression, finely atomized diesel fuel is sprayed into the hot air, initiating auto-ignition of the mixture. During the subsequent power stroke, the expanding hot mixture does work on the piston, then the burnt gases are purged during the exhaust stroke.
The Diesel Cycle is an air-standard model of the actual cycle described above. The Diesel Cycle differs from the Otto Cycle only in the modeling of the combustion process: In a Diesel Cycle, it is assumed to occur as a reversible constant pressure heat addition process, while in an Otto Cycle, the volume is assumed constant. The four steps of the air-standard Diesel Cycle are outlined below:
- (1-2) Isentropic Compression (Compression Stroke)
- (2-3) Reversible, constant pressure heat addition (Ignition)
- (3-4) Isentropic expansion to initial volume (Power Stroke)
- (4-1) Reversible constant-volume heat rejection (Exhaust)
The gas turbine is used in a wide range of applications. Common uses include power generation plants and military and commercial aircraft. In Jet Engine applications, the power output of the turbine is used to provide thrust for the aircraft.
In a simple gas turbine cycle, low pressure air is drawn into a compressor (state 1) where it is compressed to a higher pressure (state 2). Fuel is added to the compressed air and the mixture is burnt in a combustion chamber. The resulting hot products enter the turbine (state 3) and expand to state 4. Most of the work produced in the turbine is used to run the compressor and the rest is used to run auxiliary equipment and produce power.
Air standard models provide useful quantitative results for gas turbine cycles. In these models the following assumptions hold true.
- The working substance is air and treated as an ideal gas throughout the cycle
- The combustion process is modeled as a constant pressure heat addition
- The exhaust is modeled as a constant pressure heat rejection process
Brayton Cycle
The Brayton cycle depicts the air-standard model of a gas turbine power cycle.
The four steps of the cycle are:
- (1-2) Isentropic Compression
- (2-3) Reversible Constant Pressure Heat Addition
- (3-4) Isentropic Expansion
- (4-1) Reversible Constant Pressure Heat Rejection
Temperature (sometimes called thermodynamic temperature) is a measure of the average kinetic energy of a systems particles. Temperature is the degree of "hotness" ( or "coldness"), a measure of the heat intensity.
When two objects of different temperature are in contact, the warmer object becomes colder while the colder object becomes warmer. It means that heat flows from the warmer object to the colder one.
Degree Celsius (oC) and Degree Fahrenheit (oF)
Thermometer helps us determine how cold or how hot a substance is. Temperatures in science (and in most of the world) are measured and reported in degrees Celsius (oC). In the US, it is common to report temperature in degrees Fahrenheit (oF). On both the Celsius and Fahrenheit scales the temperature at which ice melts (water freezes) and the temperature at which water boils, are used as reference points.
- On the Celsius scale, the freezing point of water is defined as 0 oC, and the boiling point of water is defined as 100 oC.
- On the Fahrenheit scale, the water freezes at 32 oF and the water boils at 212 oF.
Thus the following formulas can be used to convert temperature between the two scales:
tF = 1.8 tC + 32 = 9/5 tC + 32 (1)
tC = 0.56(tF -32) =5/9(tF - 32) (2)
where
tC = temperature in oC
tF = temperature in o
Example - A patient with SARS (Severe Acute Respiratory Syndrome) has a temperature of 106 oF. What does this read on a Celsius thermometer?tC = 5/9 (106-32)= 41.1 oC
Degree Kelvin - K
Another scale (common in science) is Kelvin, or the Absolute Temperature Scale. On the Kelvin scale the coldest temperature possible, -273 oC, has a value of 0 Kelvin (0 K) and is called the absolute zero. Units on the Kelvin scale are called Kelvins (K) and no degree symbol is used.
Because there are no lower temperatures the Kelvin scale do not have negative numbers.
A Kelvin equal in size to a Celsius unit: 1 K= 1 oC.
To calculate a Kelvin temperature, add 273 to the Celsius temperature:
tK = tC + 273.16 (3)
Example - What is normal body temperature of 37 oC on the Kelvin scale?
tK = tC + 273.16 = 37 + 273.16 = 310.16 K
Degree Rankine - R
In the English system the absolute temperature is in degrees Rankine (R), not in Fahrenheit:
tR = tF + 459.69 (4)
Density
Density is defined as an objects mass per unit volume. Mass is a property.
- Mass and Weight - the Difference! - What is weight and what is mass? An explanation of the difference between weight and mass.
ρ = m / V = 1 / vg (1)
where
ρ = density (kg/m3)
m = mass (kg)
V = volume (m3)
vg = specific volume (m3/kg)
The SI units for density are kg/m3. The imperial (BG) units are lb/ft3 (slugs/ft3). While people often use pounds per cubic foot as a measure of density in the U.S., pounds are really a measure of force, not mass. Slugs are the correct measure of mass. You can multiply slugs by 32.2 for a rough value in pounds.
- Unit converter for other units
property constant at a given temperature and density can help to identify a substance.
- Densities and material properties for common materials
Relative density of a substance is the ratio of the substance to the density of water, i.e.
Example - Use the Density to Identify the Material:
An unknown liquid substance has a mass of 18.5 g and occupies a volume of 23.4 ml. (milliliter).
The density can be calculated as
ρ = [18.5 (g) / 1000 (g/kg)] / [23.4 (ml) / 1000 (ml/l) 1000 (l/m3) ]
= 18.5 10-3 (kg) / 23.4 10-6 (m3)
= 790 kg/m3
If we look up densities of some common substances, we can find that ethyl alcohol, or ethanol, has a density of 790 kg/m3. Our unknown liquid may likely be ethyl alcohol!
Example - Use Density to Calculate the Mass of a Volume
The density of titanium is 4507 kg/m3 . Calculate the mass of 0.17 m3 titanium!
m = 0.17 (m3) 4507 (kg/m3)
= 766.2 kg
Specific Weight
Specific Weight is defined as weight per unit volume. Weight is a force.
* Mass and Weight - the difference! - What is weight and what is mass? An explanation of the difference between weight and mass.
Specific Weight can be expressed as
γ = ρ g (2)
where
γ = specific weight (N/m3)
ρ = density (kg/m3)
g = acceleration of gravity (m/s2)
The SI-units of specific weight are N/m3. The imperial units are lb/ft3. The local acceleration g is under normal conditions 9.807 m/s2 in SI-units and 32.174 ft/s2 in imperial units.
Example - Specific Weight Water
Specific weight for water at 39 oF (4 oC) is 62.4 lb/ft3 (9.81 kN/m3) in imperial units. Specific weight in SI units can be calculates like
γ = 1000 kg/m3 9.81 m/s2
= 9810 N/m3
= 9.81 kN/m3