Combined cycle power plant

 combined cycle power plant is more efficient than a conventional power plant because it uses a higher proportion of the energy that the fuel produces when it burns.

In a combined cycle power plant (CCPP), or combined cycle gas turbine (CCGT) plant, a gas turbine generates electricity and the waste heat is used to make steam to generate additional electricity via a steam turbine; this last step enhances the efficiency of electricity generation. Most new gas power plants in North America and Europe are of these types.

The Integrated Gasification Combined Cycle, or IGCC, is a process that turns coal into gas known as synthesis gas (syngas) before it is burnt. The impurities in the syngas, like CO₂, can also be removed before it is burnt.

The syngas is often used to power a gas turbine generator for electricity whose waste heat is passed to a steam turbine system. If CO₂ is removed before burning (pre-combustion) it can be stored in deep geological formations..

Steam Turbine

Steam turbines are devices which convert the energy stored in steam into rotational mechanical 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 steam may be wet, dry saturated or superheated.

Consider the steam turbine shown in the cycle above. The output power of 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 specific enthalpy of the steam at inlet respective outlet of the turbine.

The efficiency of the steam turbines are often described by the isentropic efficiency for expansion 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 fraction of the steam at the outlet of the turbine should not be less than 0.9.

Heat Engine

Heat engine is defined as a device that converts heat energy into mechanical energy or more exactly a system which operates continuously and only heatand work may pass across its boundaries. 
The operation of a heat engine can best be represented by a thermodynamic cycle. Some examples are: Otto, Diesel, Brayton, Stirling and Rankine cycles.

Forward Heat Engine

LTER= Low Temperature Energy Reservoir
HTER= High Temperature Energy Reservoir 

A forward heat engine has a positive work output such as Rankine or Brayton cycle. Applying the first law of thermodynamics to the cycle gives:

Q1 - Q2 - W = 0 

The second law of thermodynamics states that the thermal efficiency of the cycle, , has an upper limit (the thermal efficiency of the Carnot cycle), i.e.

It can be shown that:

Q1 > W

which means that it is impossible to convert the whole heat input to work and

Q2 > 0 

which means that a minimum of heat supply to the cold reservoir is necessary.

Reverse Heat Engine

LTER= Low Temperature Energy Reservoir
HTER= High Temperature Energy Reservoir 

A reverse heat engine has a positive work input such as heat pump and refrigerator. Applying the first law of thermodynamics to the cycle gives:

- Q1 + Q2 + W = 0 

In case of a reverse heat engine the second law of thermodynamics is as follows: It is impossible to transfer heat from a cooler body to a hotter body without any work input i.e.

W > 0 

which means that the coefficient of performance for a heat pump is greater than unity.

Fundamentals of Thermodynamics

• Introduction, laws of thermodynamics, notation. 
•  Work and processes. 
•  First and second laws. 
•  Gibbsian equations, chemical potential. 
•  Mathematical methods, Legendre transforms. 
•  Partial derivative game. 
•  Process evaluation. Residual functions. 
•  Residual functions and example problems. 
•  Introduction to statistical mechanics and quantum mechanics. 
•  Quantum mechanics I. 
•  Quantum mechanics II. 
• Check out this link for a description of the rotational energy of a molecule. 
•  Statistics and ensembles. 
•  Ensembles and partition functions. 
•  Semi-classical partition function. 
•  Properties of ideal gases. 
•  Properties of ideal gases, examples. 
•  Chemical equilibria: ideal and real fluids. 
•  Pair potentials and nonideal behavior. Van der Waals partition functions for mixture, local compositions, activity coefficient models. 
•  Conformal solution theory. 
•  Conformal solution theory, pure fluids and mixtures. 
•  Ideal solutions and partial molar quantities. 
•  Partial molar properties and fugacity. 
•  Local composition models. 
• Applet for plotting radial distribution functions. 
• Molecular simulation code written as a Java Applet. 
•  Mixture thermodynamics calculations. 
•  Local compositions. 

Relation between PVT

Gas Laws:
Relationship between Pressure (P), Volume (V), Temperature (T) and quantity; Moles (n)

Boyle’s Law (PV = constant)

This is an inverse relationship:  As volume decreases, pressure increases.

Charles’ Law: (V/T = constant)

This is an inverse relationship:  As volume decreases, pressure increases.
Charles’ Law: (V/T = constant)

This is a direct relationship.  As Temperature decreases, Volume decreases.

Avogadro’s Law: (V/n = constant)
This is a direct relationship.  As the number of moles decreases, the volume decreases

Summary:

Combined Gas Law:
PV/nT = constant (T in Kelvins)
P1V1/n1T1 = P2V2/n2T2
Ideal gas Law:
PV = nRT
R = .0821L atm/mol K
Gay-Lussac’s/Avogadro’s Law of Combining Volumes

Equal volumes of any gases at the same temperature and pressure contain the same number of moles of
gas.
The coefficients of a balanced equation can be used to calculate relative volumes.
Standard Molar Volume: At standard temperature and pressure (STP = 1atm and 273.15K) 1 mole of any
ideal gas has a volume of 22.4L
Variations on the ideal gas law equation:
PV = mRT/M (m = sample mass, M = molar mass of the gas)
d = MP/RT (d = density of the gas in g/L)
Examples:
1.  Calculate:
a.  The new pressure in a closed container if a 5.0L volume of gas at 2.5atm has its volume increased to
7.5L.
b.  The new volume of gas (at constant T and P) if 2.0mol of He in a 3.0L container has another 3.0mol of
He placed into the container.
Answers:
a.  (5.0L)(2.5atm) = (7.5L)(P2)
P2 = 1.7atm
b. 3.0L/2.0mol = V2/5.0mol
V2 = 7.5L
2.  When a rigid hollow sphere containing 680 L of helium gas is heated from 300.K to 600.K, the
pressure of the gas increases to 18atm.  How many moles of helium does the sphere contain?
Answer:
n = PV/RT = (18atm)(680L)/(.0821)(600.K)
n = 248.48 = 250moles
3.  A child has a lung capacity of 2.2 L.  How many grams of air do her lungs hold at a pressure of 1.0
atm and a normal body temperature of 37
o
C?  Assume a “formula mass” of 29g/mol for air.
Answer:
m = MPV/RT = (29g/mol)(1.0atm)(2.2L)/(.0821Latm/molK)(310.15K) = 2.5g
4.  A gas with a volume of 300.mL at 150.
o
C is heated until its volume is 600.mL.  What is the new
temperature of the gas if the pressure is unaltered?
Answer:
300mL/423.15K = 600mL/T2
T2 = 846K = 573
o
C5.  Calculate the number of liters occupied, at STP.
 a.  0.350 mol O2
 b.  63.5g He
Answers:
a. 0.350mol (22.4L/mol) = 7.84L
b. (63.5g)(1mol/4.003g)(22.4L/1mol) = 355L
6.  Determine the molar mass of a gas for which a 2.5g sample of that gas occupies a volume of 3.0L at
STP.
Answer:
M =(2.5g)(.0821)(273.15K)/(3.0L)(1atm) =18.7g/mol
or
(2.5g)/(3.0L/22.4L/mol) = 18.7g/mol
7.  Find the density of fluorine gas (g/L) at 700torr and 50
o
C.
Answer:
d = MP/RT
= (38.00g/mol)(700/760) / (.0821)(50+273.15) = 1.32g/L
8.  For the equation
Ag2S(s)
 + H2(g) → Ag(s)
  +  H2S(g)
How many Liters of H2S can be produced from 15.0g of Ag2S and 1.00L of H2(g)
 if the reaction occurs at
STP?
Answer:
Ag2S(s)
 + H2(g) → 2Ag(s)
  +  H2S(g)
mol Ag2S = 15.0g (1mol/247.8g) = .0605mol
mol H2 = (1.00L)(1mol / 22.4L) = .0446mol
Hydrogen gas limits
 0446mol H2 (1mol H2S / 1mol H2) = .0446mol H2S.
V = .0446mol (22.4L/mol) = 1.0L
(Note that the last two steps aren’t really necessary because of the 1:1 mole ratio between H2S and H2.)

Diesel Cycle

Diesel Cycle

The Diesel cycle is an ideal air standard cycle which consists of four processes:

• 1 to 2: Isentropic compression
• 2 to 3: Reversible constant pressure heating
• 3 to 4: Isentropic expansion
• 4 to 1: Reversible constant volume cooling

By defining the compression ratio, r, as:

and cut-off ratio, , as:

The thermal efficiency of an Diesel cycle with a perfect gas as working fluid is:

where,
n=  = a constant depending on specific heat capacity

Heat balance

An application of the first law of thermodynamics to a process in which any work terms are negligible.

For a closed system, one that always consists of the same material, the first law is Q + W = ΔE, where Q is the heat supplied to the system, W is the work done on the system, and ΔE is the increase in energy of the material forming the system. It is convenient to treat ΔE as the sum of changes in mechanical energy, such as kinetic energy and potential energy in a gravitational field, and of internal energy ΔU that depends on changes in the thermodynamic state of the material. Because the rates at which any changes occur are usually of interest, heat balances are often written in terms of heat flow rates (heat per unit time), sometimes denoted by a dot over the symbol, , so that for a process with negligible work, kinetic energy and potential energy terms, , the rate of change of internal energy with time.

Often it is more convenient to apply the first law or a heat balance to an open system, a fixed region or control volume across the boundaries of which materials may travel and inside which they may accumulate, such as a building, an aircraft engine, or a section of a chemical process plant. Then the first law is expressed by the equation below, where is the rate of doing shaft work

on the system; is the mass flow rate of any stream entering or leaving the control volume; h is the enthalpy per unit mass; c is the velocity; gz is the gravitational potential for each stream at the point of crossing the boundary of the control volume; and E is the energy of all material inside the control volume. When conditions inside the control volume do not change with time, although they need not be spatially uniform, dE/dt = 0, and the balance equation is known as the steady-flow energy equation.

Enthalpy is a thermodynamic property defined by h = u + pv, where u is the specific internal energy (enthalpy per unit mass), p the pressure, and v the specific volume. It is used, along with shaft work, because the derivation of the first-law equation for a control volume from the more fundamental equation for a closed system involves work terms pv that are not available for use outside the control volume. Changes in enthalpy occur because of changes in temperature, pressure, physical state (for example, from liquid to vapor), and changes in chemical state

Differnace Between Thermal and internal energy.

According to many sources, internal energy is the kinetic and potential energies of molecules of a substance – combined. Some sources also say that thermal energy is that definition.

However, I don’t think that thermal energy is kinetic and potential energy combined. I know that heat transfer occurs between a region with higher temperature and a region with lower temperature, but it isn’t necessarily the case with tworegions of different internal energies. So that seems to imply to me that temperature is a measurement of thermal energy – so in that sense thermal energy is merely the average kinetic energy of molecules and as such, doesn’t include the potential energy. Is that right?

EFFECT OF THERMAL HISTORY ON CRYSTALLIZATION

Experimental 
Two  samples  of LLDPE with  different structural parameters  studied  in  this
paper are  listed in Table  1.
Specimens were prepared by cutting the granular resins into slices of mass ap-
proximately  5.5  mg.  A  Perkin-Elmer  model  DSC-2C  differential  scanning
calorimeter  was  used  to  measure  the  enthalpies  of  fusion  and  crystallization.
Three reference materials, indium, phenyl ether and o-terphenyl were used for in-
strument calibration. The  temperature range  of scanning was 213  K  (-60~  to
443 K  (170~  high purity nitrogen was used as purging gas. Unless indicated the
scanning rates  (both heating and cooling) were  10 deg.min -1.
1.  For  the  observation  of  structural  differences between  these  two LLDPE
resins,  identical  thermal  treatment  were  applied  to  all  specimens  in  order  to
eliminate the  thermal history caused by processing and storage conditions. Each
specimen was  heated up  to 443 K  and held at  this  temperature  for  10 min, then
cooled down  to 213  K  and held isothermally for  10 minutes. The DSC measure-
ment was made during reheating to 443 K.
2.  To observe  the  effect of heating rate on  the melting behaviour, specimens
were isothermally conditioned at 443 K for 10 min cooled to 213 K, then reheated
up  to  443  K  at  four  separate  heating  rates  (20,  10,  5  and  1 deg.min-t).  A DSC
measurement was made during reheating.
3. To observe  the effect of cooling rate on  the crystallization behaviour,  the
specimens  were  isothermally conditioned at  443  K  for  10 min  then  cooled  to
213  K  at  three cooling rates  (20,  10 and  1 deg.min-~). Finally, the  samples were
reheated up to 443 K and DSC measurement recorded during this reheating cycle.
4.  To  observe  the  annealing  effect  on  the  melting  behaviour,  the  melt
specimens were  cooled  to  four given  annealing  temperatures of 398  K,  393  K,
383 K and 373 K, and held at these temperatures for  10 and  120 minutes respec-
tively. The annealed specimens were cooled to 213 K  and reheated up  to 443  K
finally, DSC measurements being made for the final heating process.

Results  and  discussion
The  results  of the effects of thermal history are  shown  in Fig.  1.
Comparing  the peak  shape of the  two LLDPE samples as received  in Fig.  1,  it
can  be  seen  that more  comonomer content  in LLDPE  leads  to a broader peak  and
lower peak  temperature.  The  amount of comonomer  in Dowlex  2045  is  less  than
that in  Stamylex  1048,  i.e.  the degree of linearity for Dowlex 2045  is higher than
that  for Stamylex  1048.  This  is  in  accord with  the  structural parameters  listed  in
Table  1.  The  melting  temperatures  of  both  LLDPE  samples  measured  after
eliminating thermal history were a  little higher than those measured before. These
indicate  that  the  crystalline  integrity  of both  LLDPE  increased  during  the  new
thermal  history. The  changes  of peak  shape  illustrate  that  the  size distribution  of
crystailites  also  changed.  The  changes  of  fusion  enthalphy, AHf,  for  Stamylex
1048  were  slightly higher  than  those  for Dowlex  2045  before  and  after  elimina-
tion  of  the  thermal  history effect. These  reflected the  small difference  in  crystal-
linity between  these  two samples. The effect of heating rate on melting behaviour
is  shown  in  Fig.  2.  It  can  be  seen  that  the  lower  the  heating  rate,  the  better  the
peak  resolution, and  consequently  the clearer  the  shoulder peak. This may be  in-
terpreted  that  the  slower  heating  rates  enable  a  semicrystalline polymer  to  have
more  time  for crystal  growth prior  to  final melting. Curve  'a'  in Fig. 2  illustrates
 ~

Compensating for ideality factor and series resistance differences between thermal-sense diodes

Abstract: When using an external thermal diode to measure temperature, the accuracy of the temperature measurement depends on the characteristics of the external diode. Two critical parameters that affect measurement accuracy are ideality factor and series resistance. This application note explains the effects of these parameters on remote temperature-sensor measurements and discusses how to determine compensation factors for their effects.

The most common approach to measuring temperature with a "remote-diode" temperature sensor is to force two different currents through the diode¹, typically with a current ratio of about 10:1. The diode's voltage is measured at each current level and the temperature is calculated based on the equation:

Where:
I_H is the larger diode bias current.
I_L is the smaller diode bias current.
V_H is the diode voltage while IH is flowing.
V_L is the diode voltage while IL is flowing.
n is the ideality factor of the diode (nominally 1, but varies with processing).
k is Boltzmann's constant (1.38 × 10^-23joules/K).
T is the temperature in K.
q is the charge of an electron (1.60 × 10^-19C)

If = 10, this can be simplified to:

V_H - V_L = 1.986 × 10^-4 × πT

Ideality factor correction

Note that the accuracy of the temperature reading depends on the value of n. If the remote diode sensor is designed to produce correct readings with a diode that has a specific value of n, then changing to a diode with a different ideality factor will change the apparent measured temperature.

Correcting for differences in ideality factor is done as follows. Assume that a remote diode sensor designed for a nominal ideality factor, n_NOMINAL, is used to measure the temperature of a diode with a different ideality factor, n_ACTUAL. The measured temperature, T_MEASURED, can be corrected using:

Where T is the temperature in K.

Most remote diode temperature sensors for CPUs are designed to produce accurate temperature data when used with an ideality factor of 1.008. Some newer CPU thermal-sense diodes have lower ideality factors. To use a CPU optimized for an ideality factor of 1.008 with a CPU that has an ideality factor of 1.0021, the data can be corrected (assuming no series resistance) as follows:

For an actual temperature of 85°C (358.15K), the measured temperature will be 82.91°C (356.06K), an error of -2.09°. Note that the error is proportional to absolute temperature. At 125°C, the error increases to -2.32°.

Series resistance correction

Series resistance in one of the diodes contributes additional errors. For the nominal diode currents of 10µA and 100µA used in Maxim's remote temperature sensors, the change in the measured voltage will be:

R_S(100µA - 10µA) = 90µA × R_S

Since 1°C corresponds to 198.6µV, series resistance contributes a temperature offset of:

Assume that the diode being measured has a series resistance of 3.86Ω. The series resistance contributes an offset of:

3.86Ω × 0.453°C/Ω = 1.75°C

If the diode has an ideality factor of 1.0021 and series resistance of 3.86Ω, the total offset can be calculated as follows. Combining the correction for series resistance with the correction for ideality factor, we have:

1.75°C - 2.09°C = -0.34°C

This is for a diode temperature of 85°C. Thus, in this case the effect of the series resistance and the ideality factor partially cancel each other.

Note that if the diode bias current is different, the effect of series resistance will change proportionally. For example, some remote temperature sensors have diode bias currents two or more times larger than those of Maxim's remote sensors. The resulting temperature errors can be on the order of two or more degrees larger than those observed with Maxim's sensors.

Some temperature sensors include automatic series resistance cancellation within their remote-diode sensing circuitry. When this function is enabled, these sensors bias the external diodes with three or four different current levels and use the resulting voltage measurements to eliminate the effect of series resistance from the temperature calculation. The MAX6654 and MAX6690 temperature sensors have a single remote channel with optional series resistance cancellation. Several multichannel remote sensors, including the MAX6602, MAX6689, MAX6697, MAX6698, and MAX6699, have series resistance cancellation on one of the remote channels. The MAX6581, with seven remote channels, includes series resistance cancellation on all remote channels.



¹This diode is not a two-lead rectifier or signal diode like a 1N4001. Such diodes will not work with remote-diode temperature sensors. Instead, the diode is really a bipolar transistor connected as a diode. If the transistor is a discrete unit, its base and collector should be connected together. If the transistor is a substrate PNP, the collector will be grounded and the base and emitter serve as the cathode and anode. When "diode" is used in this document, it refers to the diode-connected transistors described above.