The design, operation, and performance of electricity-generating power plants are based on thermodynamic principles
THE FIRST LAW OF THERMODYNAMICS
The first law of thermodynamics is the law of conservation of energy. It states that energy can be neither created nor destroyed. The energy of a system undergoing change (process) can vary by exchange with the surroundings. However, energy can be converted from one form to another within that system.
A system is a specified region, not necessarily of constant volume or fixed boundaries, where transfer and conversions of energy and mass are taking place. An open system is one where energy and mass cross the boundaries of the system. A steady-state open system, also called the steady-state, steady-flow (SSSF) system, is a system where mass and energy flows across its boundaries do not vary with time, and the mass within the system remains
constant.
An SSSF system is shown in Fig. 1.
The first-law equation for that system is
PE1 + KE1 + IE1+ FE1 +𝞓Q = PE2+ KE2 + IE2+ FE2 +𝞓Wsf (1)
where
PE = potential energy [= 𝘮𝘻𝘨/gc, where m = mass of quantity of fluid entering and leaving the system, z = elevation of station 1 or 2 above a datum,
g = gravitational acceleration, and gc = gravitational conversion factor
(32.2 𝗅𝖻𝓂 , ft/(lb𝒇 . S²) or 1.0 kg . m/(N . S²)].
KE = kinetic energy (= 𝑚Vs²/2gc), where Vs = velocity of the mass.
IE = internal energy (= U) . The internal energy is a sole function of temperature for perfect gases and a strong function of temperature and weak function of pressure for nonperfect gases, vapors, and liquids. It is a measure of the internal (molecular) activity and interaction of the fluid.
FE = flow energy (=PV = P𝑚𝑣) . The flow energy or flow work is the work done by the flowing fluid to push a mass m into or out of the system.
𝞓Q = net heat added [= 𝗤𝛢 - |𝗤𝒓|,
where 𝗤𝛢 = heat added
and 𝗤𝒓 = heat rejected across system boundaries; 𝞓Q=mc𝗇 (T2 -T1),
where c𝗇 = specific heat that depends upon the process taking place between 1 and 2. Values of c𝗇 vary with the process table 1
𝞓Wsf = net steady-flow mechanical work done by the system [= W𝒃𝒚 - |W𝒐𝒏|,
where W𝒃𝒚= work done by system (positive)
and W𝒐𝒏= work done on system (negative)] .
𝞓Wsf = - ₁⎰² V. 𝑑𝑝 (2)
A relationship between P and V is required. The most general relationship is given by
where n is called the polytropic exponent. It varies between zero and infinity. Its value for
certain processes is given in Table 1.
ENTHALPY
Enthalpy is defined as H=U + PV or h = u + P𝒗 and the first law becomes
Some Common Thermodynamic Symbols
cp = specific heat at constant pressure, Btu/(lbm .°F) [J/(kg. K)]
cv =specific heat at constant volume, Btu/(lbm. °F) [J/(kg .K)]
h =specific enthalpy, Btu/lbm (J/kg)
H =total enthalpy, Btu (J)
J =energy conversion factor =778.16 ft . lbf/Btu (1.0 N m/J)
M =molecular mass, lbm/lb . mol or kg/kg . mol
n = polytropic exponent, dimensionless
P = absolute pressure (gauge pressure barometric pressure), lbf/ft²; unit may be lbf/in² (commonly
written psia, or Pa)
Q =heat transferred to or from system, Btu or J, or Btu/cycle or J/cycle
R =gas constant, lbf ft/(lbm . °R) or J/(kg . K) =R/M
R= universal gas constant =1.545.33, lbf . ft/(lb . mol . °R) or 8.31434 10³J/(kg . mol . K)
s =specific entropy, Btu/(lbm . °R) or J/(kg . K)
S =total entropy, Btu/°R or J/kg
t =temperature, °F or °C
T =temperature on absolute scale, °R or K
u =specific internal energy, Btu/lbm or J/kg
U =total internal energy, Btu or J
v = specific volume, ft3/lbm or m3/kg
V = total volume, ft3 or m3
W =work done by or on system, lbf . ft or J, or Btu/cycle or J/cycle
x =quality of a two-phase mixture mass of vapor divided by total mass, dimensionless
k =ratio of specific heats, cp/cv, dimensionless
𝜂 = efficiency, as dimensionless fraction or percent
f refers to saturated liquid
g refers to saturated vapor
fg refers to change in property because of change from saturated liquid to saturated vapor
Enthalpies and internal energies are properties of the fluid. This means that each would
have a single value at any given state of the fluid. The specific heat at constant volume is
The specific heat at constant pressure is
Cp - Cv = R
where R is the gas constant.
where cv and cp are constants. They are independent of temperature for monatomic gases
such as He. They increase with temperature for diatomic gases such as air and more so for
triatomic gases such as CO2 and so forth. Therefore, for constant specific heats or for small
changes in temperature
CLOSED SYSTEM
In the open system, mass crosses the boundaries. In the closed system, only energy crosses
the boundaries. The first law for the closed system becomes
(change with time, before and after the process has taken place)
𝞓Wnf is called the no-flow work. It is given by
THE CYCLE
To convert energy from heat to work on a continuous basis, one needs to operate a cycle.
A cycle is a series of processes that begins and ends at the same state and can be repeated
indefinitely. Figure .2 illustrates an ideal diesel cycle.
Process 1 to 2. Ideal and adiabatic (no heat exchanged) compression
Process 2 to 3. Heat adidtion at constant pressure
Process 3 to 4. Ideal and adiabatic expansion process
Process 4 to 1. Constant-volume heat rejection
The first law becomes
VAPOR-LIQUID PHASE EQUILIBRIUM IN A PURE SUBSTANCE
Consider a piston-cylinder arrangement containing 1 kg of water (refer to Fig. .3). Suppose
the initial pressure and temperature inside the cylinder are 0.1 MPa and 20°C. As heat is transferred
to the water, the temperature increases while the pressure remains constant. When the
temperature reaches 99.6°C, additional heat transfer results in a change of phase, as indicated
in Fig..3 (b). Some of the liquid becomes vapor. However, during this process, both temperature
and pressure remain constant, but the specific volume increases considerably. When
all the liquid has vaporized, additional heat transfer results in increase in both temperature
and specific volume of the vapor.
The saturation temperature is the temperature at which vaporization occurs at a given pressure. This pressure is called the saturation pressure for the given temperature. For example, for water at 0.1 MPa, the saturation temperature is 99.6°C. For a pure substance, there is a relationship between the saturation temperature and the saturation pressure. Figure 4 illustrates this relationship. The curve is called the vapor-pressure curve.
If a substance exists as liquid at the saturation temperature and pressure, it is called saturated liquid. If the temperature of the liquid is lower than the saturation temperature for the existing pressure, it is called subcooled liquid (or compressed liquid, implying that the pressure is greater than the saturation pressure for the given temperature). When a substance exists as part liquid and part vapor at the saturation temperature and pressure, its quality (x) is defined as the ratio of the vapor mass to the total mass. If the substance exists as vapor at the saturation temperature, it is called saturated vapor. When the vapor is at a temperature greater than the saturation temperature (for the existing pressure), it is called superheated vapor. The temperature of a superheated vapor may increase while the pressure remains constant
Figure 5 illustrates a temperature-volume diagram for water showing liquid and vapor phases. Note that when the pressure is 1 MPa, vaporization (saturation temperature) begins at 179.9°C. Point G is the saturated-vapor state, and line GH represents the constant-pressure process in which the steam is superheated. A constant pressure of 10 MPa is represented by line IJKL. The saturation temperature is 311.1°C. Line NJFB represents the saturated-liquid line, and line NKGC represents the saturated-vapor line.
At a pressure 22.09 MPa, represented by line MNO, we find, however, that there is no constant-temperature vaporization process. Instead, there is one point, N, where the curve has a zero slope. This point is called the critical point. At this point, the saturated-liquid and
saturated-vapor states are identical.
The temperature, pressure, and specific volume at the critical point are called the critical
temperature, critical pressure, and critical volume. The critical-point data for some
substances are presented in Table 2
THE SECOND LAW OF THERMODYNAMICS
The second law puts a limitation on the conversion of heat to work. Work can always be
converted to heat; however, heat cannot always be converted to work. The portion of heat that cannot be converted to work is called unavailable energy. It must be rejected as low-grade heat after work is generated.
The second law states that the thermal efficiency of converting heat to work, in a power plant, must be less than 100 percent. The Carnot cycle represents an ideal heat engine that gives the maximum-value of that efficiency between any two temperature limits. In a steam or gas power plant, heat is received from a high-temperature reservoir (a reservoir is a source of heat or heat sink large enough that it does not undergo a change in temperature when heat is added or subtracted from it), such as steam generators or combustors.
Heat is also rejected in a steam or gas power plant to a low-temperature reservoir, such as condensers or the environment. The work produced in the steam or gas power plant is the difference between the heat received from the high-temperature reservoir and the heat rejected to the low-temperature reservoir.
THE CONCEPT OF REVERSIBILITY
Sadi Carnot introduced the concept of reversibility and laid the foundations of the second law. A reversible process, also called an ideal process, can reverse itself exactly by following the same path it took in the first place. Thus, it restores to the system or the surroundings the same heat and work previously exchanged. In reality, there are no ideal (reversible) processes. Real processes are irreversible.
However, the degree of irreversibility varies between processes. There are many sources of irreversibility in nature. The most important ones are friction, heat transfer, throttling, and mixing. Mechanical friction is one in which mechanical work is dissipated into a heating effect. One example would be a shaft rotating in a bearing. It is not possible to add the same heat to the bearing to cause rotation of the shaft.
An example of fluid friction is when the fluid expands through the turbine, undergoing internal friction. This friction results in the dissipation of part of its energy into heating itself at the expense of useful work. The fluid then does less work and exhausts at a higher temperature. The more irreversible the process, the more heating effect and the less the work.
Heat transfer in any form cannot reverse itself. Heat transfer causes a loss of availability because no work is done between the high- and low-temperature bodies.
EXTERNAL AND INTERNAL IRREVERSIBILITIES
External irreversibilities are those that occur across the boundaries of the system. The primary source of external irreversibility in power systems is heat transfer both at the highand low-temperature ends.
Internal irreversibilities are those that occur within the boundaries of the system. The primary source of internal irreversibilities in power systems is fluid friction in rotary machines, such as turbines, compressors, and pumps.
THE CONCEPT OF ENTROPY
Entropy is a property (e.g., pressure, temperature, and enthalpy). Entropy is given by the
equation
THE CARNOT CYCLE
Sadi Carnot introduced the principles of the second law of thermodynamics, the concepts of reversibility and cycle. He also proved that the thermal efficiency of a reversible cycle is determined by the temperatures of the heat source and heat sink.
The Carnot cycle is shown in Fig. 6 on the P-V and T-S diagrams. It is composed of four processes:
1. Process 1-2. Reversible adiabatic compression
2. Process 2-3. Reversible constant-temperature heat addition
3. Process 3-4. Reversible adiabatic expansion
4. Process 4-1. Reversible constant-temperature heat rejection
Heat addition :
Heat rejection:
Net work:
Thermal efficiency:
Thus, the thermal efficiency of the Carnot cycle 𝜂c is given by
The thermal efficiency of the Carnot cycle is dependent on the heat source and heat sink temperatures. It is independent of the working fluid. Since the Carnot cycle is reversible, it produces the maximum amount of work between
two given temperature limits, TH and TL. Therefore, a reversible cycle operating between given temperature limits has the highest possible thermal efficiency of all cycles operating between these same temperature limits. The Carnot cycle efficiency is to be considered an upper efficiency limit that cannot be exceeded in reality.
thanks for your visit