Industrial Plant Design

THE FIRST LAW OF THERMODYNAMICS The first law of thermodynamics is the law of conservation of energy, which states that energy can neither be created nor destroyed. The energy of a system undergoing change (processed) can be increased or decreased by exchange with the surroundings and converted from one to another within that system. A system is a specified region, not necessarily of constant volume or fixed boundaries, where transfers conversions of energy and mass are to be studied. An open system is one where energy and mass cross the boundaries of that system. Internal energy is a sole function of temperature for perfect gases and strong function of temperature and weak function of pressure for non perfect gases, vapor, and liquids. Flow energy, or flow work, is the work done by the flowing fluid to push the quantity represented by mass into, and out of the system. The Enthalpy The sums U + PV and u + Pv appear together very frequently in thermodynamics. The combination, therefore, has been given the name enthalpy and the symbol H and h, where h = specific enthalpy = H/m. thus H = U + PV h = u + Pv and THE CYLE Process – begins at one state of the working fluid and ends at another. Cycle – is a processes that begins and ends at the same state and thus can indefinitely, or as long as needed. PROPERTY RELATIONSHIPS Perfect (or Ideal) Gases – is one which, at any state, obeys the equation of state for perfect gases. PV = mRT Pv = RT pV = nRoT where: R = specific gas constant. Different gases have different values of R; for air ft .lb

R = 53.3 lbm ° Rf ' 286.8 kgJ− K

m

n = number of moles = M , where M is molecular mass of the gas = 28.97 for air Ro = universal gas constant = RM, the same for all perfect gases ft .lb

= 1545.33 lb.mol .f° R J = 8314.34 kg .mol .K

T = absolute temperature in degrees Rankine or Kelvin Vapor Quality of x – is the ratio of mass of vapor to mass of vapor and liquid in a two phase mixture. Thus the specific enthalpy of a two phase mixture is given by h = hf + xhfg where hf is the enthalpy of the saturated liquid and hfg is the difference between the enthalpy of the saturated vapor, hg, and hf; that is, hfg = hg - hf, all obtain at the pressure of the system. For specific volume and entropy as v = vf + xvfg and s = sf + xsfg Subcooled Liquid Subcooled liquid – is one at a temperature below the saturation temperature at the given pressure. Compressed liquid – is synonyms with subcooled liquid. THE SECOND LAW OF THERMODYNAMICS Reversible process, also called an ideal process, is one can reverse itself exactly by following the same path it undertook in the first place thus restore to the system or the surroundings the same heat and work previously exchanged. Mechanical friction is one in which mechanical work is dissipated into a heating effect, such as in the case of shaft rotating in a bearing. Fluid friction is similar to mechanical. A fluid expanding behind a piston or through a turbine undergoes internal friction, resulting in the dissipation of part of its energy into heating itself at the expense of useful work. Heat transfer in any of its forms, conduction, convection, or radiation, occurs from a higher temperature to a lower temperature. Heat transfer causes a loss of availability because no work is done between the high and lowtemperature.

Throttling is an uncontrolled expansion process of a liquid from a high pressure region to a low-pressure region. External irreversibilities are those that occur across the boundaries of the system. The primary source of external irreversibility in power system is heat transfer, both at the high-temperature end, the heat source, and the lowtemperature end, the heat sink. Internal irreversibilities are those that occur within the boundaries of the system. The primary source of internal irreversibility in power system is fluid friction in rotary machine such as turbine, compressors, and pumps and in pipes and valves. THE CONCEPT OF ENTROPY Entropy, first introduced by Clausius in 1865, is a property, as are pressure, temperature, internal energy, and enthalpy. It is given the symbol S and has the units Btu per degree Rankine (Btu/oR) or the units joule per Kelvin (J/K). Specific entropy s has the units Btu/(lbm.oR) or J/(kg.K). entropy is the property that remains constant in an adiabatic reversible process. THE CARNOT CYCLE Sadi Carnot laid the foundation of the second law of thermodynamics, introduced the concepts of reversibility and cycles, and introduced the principle that the temperature of the heat source and heat sink determined the thermal efficiency of a reversible cycle.η Carnot cycle on the P-V and T-S diagram 1. 2. 3. 4.

1-2: reversible adiabatic compression 2-3: reversible constant-temperature heat addition 3-4: reversible adiabatic expansion 4-1: reversible heat rejection

The thermal efficiency of the Carnot cycle nc can now be easily obtained, noting that the change in entropy during heat addition and rejection are equal in magnitude. Thus QA =

TH S3 − S 2

QR =

TL S1 − S 4

QR = TL ( S 4 − S1 ) = TL ( S 3 − S 2 )

where TH and TL are the heat source and heat sink absolute temperature, respectively. Hence TH = T2. Similarly TL = T1. For all power cycles the net work and the thermal efficiency are defined by ∆Wnet =Q A − QR

and ∆Wnet QA Thus, the thermal efficiency of the Carnot cycle ηc is given by

ηth =

ηc =

TH − TL TL

THE IDEAL RANKINE CYCLE Schematic flow diagram of a Rankine Cycle PV & TS diagram of a Rankine Cycle Processes: 1-2 or 1’-2’: adiabatic reversible expansion through the turbine. The exhaust vapor at 2 or 2’ is usually in the two-phase region. 2-3 or 2’-3: constant temperature and being a two-phase mixture process, constant pressure heat rejection in the condenser. 3-4 adiabatic reversible compression by the pump of saturated liquid at the condenser pressure, 3, to subcooled liquid at the steam generator pressure, 4. Line 3-4 is vertical on both the P-V and T-S diagrams because the liquid is essentially in compressible and the pump is adiabatic reversible. 4-1 or 4-4’ constant pressure heat addition in the steam generator. Line 4-B-11’ is a constant pressure line on both diagrams. The portion 4-B represents bringing the subcolled liquid, 4, to saturated liquid at B. the section 4-B represents in the steam generator is called an economizer. The portion B-1 represents heating the saturated liquid to saturated vapor at constant pressure and temperature (being a two-phase mixture), and section B-1 in the steam generator is called the boiler or evaporator. Portion 1-1’, in the superheat cycle,

represents heating the saturated vapor at 1-1’. Section 1-1’ in the steam generator is called a super-heater.

Heat added qA = h1 – h4

Btu lb

or kgJ

Turbine work wT = h1 – h4

B tu lb

or kJg

Heat rejected q R = h2 − h3

Btu lb

or kgJ

Pump work W p = h4 −h3

B tu lb

or kJg

Net work ΔWnet = ( h1 − h2 ) − ( h4 − h3 )

B tu lb

or kgJ

ΔW net qa ( h − h ) − ( h4 − h3 ) = 1 2 h1 − h4

Thermal efficiency ηth =

REHEAT An additional improvement in cycle efficiency with gaseous primary fluids as in fossil-fueled and gas-cooled powerplants achieved by the use of reheat.