### Thermodynamics

 Pressure    Pressure is a measure of the force exerted per unit area on the boundaries of a substance (orsystem). It is caused by the collisions of the molecules of the substance with the boundaries ofthe system. As molecules hit the walls, they exert forces that try to push the walls outward. Theforces resulting from all of these collisions cause the pressure exerted by a system on itssurroundings. Pressure is frequently measured in units of lbf/in2 (psi).Pressure Scales    When pressure is measured relative to a perfect vacuum, it is called absolute pressure (psia);when measured relative to atmospheric pressure (14.7 psi), it is called gauge pressure (psig). Thelatter pressure scale was developed because almost all pressure gauges register zero when opento the atmosphere. Therefore, pressure gauges measure the difference between the pressure ofthe fluid to which they are connected and that of the surrounding air.If the pressure is below that of the atmosphere, it is designated as a vacuum. A perfect vacuumwould correspond to absolute zero pressure. All values of absolute pressure are positive, becausea negative value would indicate tension, which is considered impossible in any fluid. Gaugepressures are positive if they are above atmospheric pressure and negative if they are belowatmospheric pressure Pabs = Patm + Pgauge Pabs = Patm - Pvac Patm is atmospheric pressure, which is also called the barometric pressure. Pgauge is the gaugepressure, and Pvac is vacuum. Once again, the following examples relating the various pressureswill be helpful in understanding the idea of gauge versus absolute pressures. Temperature and Pressure Scales SummaryThe following properties were defined as follows.    • Temperature is a measure of the molecular activity of a substance.    • Pressure is a measure of the force per unit area exerted on the boundaries of asubstance (or system).The relationship between the Fahrenheit, Celsius, Kelvin, and Rankine temperature scaleswas described.    • Absolute zero = -460 °F or -273 °C    • Freezing point of water = 32 °F or 0 °C    • Boiling point of water = 212 °F or 100 °CConversions between the different scales can be made using the following formulas.    • °F = 32 + (9/5)°C    • °C = (°F - 32)(5/9)    • °R = °F + 460    • °K = °C + 273Relationships between absolute pressure, gauge pressure, and vacuum can be shownusing the following formulas.    • Pabs = Patm + Pgauge    • Pabs = Patm - Pvac Converting between the different pressure units can be done using the followingconversions.    • 14.7 psia = 408 inches of water    • 14.7 psia = 29.9 inches of mercury    • 1 inch of mercury = 25.4 millimeters of mercury    • 1 millimeter of mercury = 103 microns of mercury Energy    Energy is defined as the capacity of a system to perform work or produce heat.Potential Energy    Potential energy (PE) is defined as the energy of position. Using English system units, Energy, Work, and Heat Summary• Heat is described as energy in transit. This transfer occurson a molecular level as a result of temperature differences.The unit of heat is the British thermal unit (Btu).    Latent heat = the amount of heat added or removed to produce only aphase change.    Sensible heat = the heat added or removed that causes a temperature change.• The following properties were defined:    Specific enthalpy (h) is defined as h = u +Pn, where u is the specific internal energy(Btu/lbm) of the system being studied, P is the pressure of the system (lbf/ft2), and n isthe specific volume (ft3/lbm) of the system.    Entropy is sometimes referred to as a measure of the inability to do work for agiven heat transferred.Rev. Thermodynamic Systems and SurroundingsThermodynamics involves the study of various systems. A system in thermodynamics is nothingmore than the collection of matter that is being studied. A system could be the water within oneside of a heat exchanger, the fluid inside a length of pipe, or the entire lubricating oil system fora diesel engine. Determining the boundary to solve a thermodynamic problem for a system willdepend on what information is known about the system and what question is asked about thesystem.Everything external to the system is called the thermodynamic surroundings, and the system isseparated from the surroundings by the system boundaries. These boundaries may either be fixedor movable. In many cases, a thermodynamic analysis must be made of a device, such as a heatexchanger, that involves a flow of mass into and/or out of the device. The procedure that isfollowed in such an analysis is to specify a control surface, such as the heat exchanger tubewalls. Mass, as well as heat and work (and momentum), may flow across the control surface. Types of Thermodynamic Systems    Systems in thermodynamics are classified as isolated, closed, or open based on the possibletransfer of mass and energy across the system boundaries. An isolated system is one that is notinfluenced in any way by the surroundings. This means that no energy in the form of heat orwork may cross the boundary of the system. In addition, no mass may cross the boundary of thesystem.    A thermodynamic system is defined as a quantity of matter of fixed mass and identity uponwhich attention is focused for study. A closed system has no transfer of mass with itssurroundings, but may have a transfer of energy (either heat or work) with its surroundings.    An open system is one that may have a transfer of both mass and energy with its surroundings.Thermodynamic Equilibrium    When a system is in equilibrium with regard to all possible changes in state, the system is inthermodynamic equilibrium. For example, if the gas that comprises a system is in thermalequilibrium, the temperature will be the same throughout the entire system.Control Volume    A control volume is a fixed region in space chosen for the thermodynamic study of mass andenergy balances for flowing systems. The boundary of the control volume may be a real orimaginary envelope. The control surface is the boundary of the control volume.Steady State    Steady state is that circumstance in which there is no accumulation of mass or energy within thecontrol volume, and the properties at any point within the system are independent of time. Thermodynamic Process    Whenever one or more of the properties of a system change, a change in the state of the systemoccurs. The path of the succession of states through which the system passes is called thethermodynamic process. One example of a thermodynamic process is increasing the temperatureof a fluid while maintaining a constant pressure. Another example is increasing the pressure ofa confined gas while maintaining a constant temperature. Thermodynamic processes will bediscussed in more detail in later chapters.Cyclic Process    When a system in a given initial state goes through a number of different changes in state (goingthrough various processes) and finally returns to its initial values, the system has undergone acyclic process or cycle. Therefore, at the conclusion of a cycle, all the properties have the samevalue they had at the beginning. Steam (water) that circulates through a closed cooling loopundergoes a cycle.Reversible Process    A reversible process for a system is defined as a process that, once having taken place, can bereversed, and in so doing leaves no change in either the system or surroundings. In other wordsthe system and surroundings are returned to their original condition before the process took place.In reality, there are no truly reversible processes; however, for analysis purposes, one usesreversible to make the analysis simpler, and to determine maximum theoretical efficiencies.Therefore, the reversible process is an appropriate starting point on which to base engineeringstudy and calculation.    Although the reversible process can be approximated, it can never be matched by real processes.One way to make real processes approximate reversible process is to carry out the process in aseries of small or infinitesimal steps. For example, heat transfer may be considered reversibleif it occurs due to a small temperature difference between the system and its surroundings. Forexample, transferring heat across a temperature difference of 0.00001 °F "appears" to be morereversible than for transferring heat across a temperature difference of 100 °F. Therefore, bycooling or heating the system in a number of infinitesamally small steps, we can approximate areversible process. Although not practical for real processes, this method is beneficial forthermodynamic studies since the rate at which processes occur is not important.Irreversible Process    An irreversible process is a process that cannot return both the system and the surroundings totheir original conditions. That is, the system and the surroundings would not return to their original conditions if the process was reversed. For example, an automobile engine does not giveback the fuel it took to drive up a hill as it coasts back down the hill.    There are many factors that make a process irreversible. Four of the most common causes ofirreversibility are friction, unrestrained expansion of a fluid, heat transfer through a finitetemperature difference, and mixing of two different substances. These factors are present in real,irreversible processes and prevent these processes from being reversible.Adiabatic Process    An adiabatic process is one in which there is no heat transfer into or out of the system. Thesystem can be considered to be perfectly insulated.Isentropic Process    An isentropic process is one in which the entropy of the fluid remains constant. This will be trueif the process the system goes through is reversible and adiabatic. An isentropic process can alsobe called a constant entropy process.Polytropic Process    When a gas undergoes a reversible process in which there is heat transfer, the process frequentlytakes place in such a manner that a plot of the Log P (pressure) vs. Log V (volume) is a straightline. Or stated in equation form PVn = a constant. This type of process is called a polytropicprocess. An example of a polytropic process is the expansion of the combustion gasses in thecylinder of a water-cooled reciprocating engine.Throttling Process    A throttling process is defined as a process in which there is no change in enthalpy from stateone to state two, h1 = h2; no work is done, W = 0; and the process is adiabatic, Q = 0. To betterunderstand the theory of the ideal throttling process let’s compare what we can observe with theabove theoretical assumptions.    An example of a throttling process is an ideal gas flowing through a valve in midposition. Fromexperience we can observe that: Pin > Pout, velin < velout (where P = pressure and vel = velocity).These observations confirm the theory that hin = hout. Remember h = u + Pv (v = specificvolume), so if pressure decreases then specific volume must increase if enthalpy is to remainconstant (assuming u is constant). Because mass flow is constant, the change in specific volumeis observed as an increase in gas velocity, and this is verified by our observations. The theory also states W = 0. Our observations again confirm this to be true as clearly no"work" has been done by the throttling process. Finally, the theory states that an ideal throttlingprocess is adiabatic. This cannot clearly be proven by observation since a "real" throttlingprocess is not ideal and will have some heat transfer. First Law of Thermodynamics Summary    • The First Law of Thermodynamics states that energy can neither becreated nor destroyed, only altered in form.    • In analyzing an open system using the First Law of Thermodynamics, theenergy into the system is equal to the energy leaving the system.    • If the fluid passes through various processes and then eventually returnsto the same state it began with, the system is said to have undergone acyclic process. The first law is used to analyze a cyclic process.    • The energy entering any component is equal to the energy leaving thatcomponent at steady state.    • The amount of energy transferred across a heat exchanger is dependentupon the temperature of the fluid entering the heat exchanger from bothsides and the flow rates of thse fluids.    • A T-s diagram can be used to represent thermodynamic processes. Second Law of Thermodynamics Summary    • Planck’s statement of the Second Law of Thermodynamics is:It is impossible to construct an engine that will work in acomplete cycle and produce no other effect except the raising ofa weight and the cooling of a heat reservoir.    • The Second Law of Thermodynamics demonstrates that the maximum possibleefficiency of a system is the Carnot efficiency written as:h = (TH - TC)/TH    • The maximum efficiency of a closed cycle can be determined by calculating theefficiency of a Carnot cycle operating between the same value of high and lowtemperatures.    • The efficiency of a component can be calculated by comparing the workproduced by the component to the work that would have been produced by anideal component operating isentropically between the same inlet and outletconditions.    • An isentropic expansion or compression process will be represented as a verticalline on a T-s or h-s diagram. A real expansion or compression process will looksimilar, but will be slanted slightly to the right.    • Efficiency will be decreased by:            Presence of friction            Heat losses            Cycle inefficiencies Compression Processes Summary    • The ideal gas law can be used to determine how the properties of pressure,temperature, and volume will be related during compression processes.Pv = R T    • A fluid may be considered incompressible if one of two conditions is true:The fluid is a liquid.The fluid is a gas with a velocity greater than one-third of the speed ofsound in the gas.    • The work for certain types of processes can be determined as follows:        Constant pressure process W1-2 = P(DV)        Constant volume process W1-2 = V(DP)   Heat Transfer Terminology Summary*    Heat is energy transferred as a result of a temperature difference. *    Temperature is a measure of the amount of molecular energy containedin a substance.*    Work is a transfer of energy resulting from a force acting through adistance.*    The Second Law of Thermodynamics implies that heat will not transferfrom a colder to a hotter body without some external source of energy.*    Conduction involves the transfer of heat by the interactions of atoms ormolecules of a material through which the heat is being transferred.*    Convection involves the transfer of heat by the mixing and motion ofmacroscopic portions of a fluid.*    Radiation, or radiant heat transfer, involves the transfer of heat byelectromagnetic radiation that arises due to the temperature of a body.*    Heat flux is the rate of heat transfer per unit area.*    Thermal conductivity is a measure of a substance’s ability to transfer heatthrough itself.*    Log mean temperature difference is the DT that most accurately represents theDT for a heat exchanger.*    The local heat transfer coefficient represents a measure of the ability to transferheat through a stagnant film layer.*    The overall heat transfer coefficient is the measure of the ability of a heatexchanger to transfer heat from one fluid to another.*    The bulk temperature is the temperature of the fluid that best represents themajority of the fluid which is not physically connected to the heat transfer site.   Radiant Heat Transfer Summary*    Black body radiation is the maximum amount of heat that can betransferred from an ideal object.*    Emissivity is a measure of the departure of a body from the ideal blackbody.*    Radiation configuration factor takes into account the emittance andrelative geometry of two objects.   Heat Exchangers Summary*    Heat exchangers remove heat from a high-temperature fluid byconvection and conduction.*    Counter-flow heat exchangers typically remove more heat thanparallel flow heat exchangers.*    Parallel flow heat exchangers have a large temperature difference atthe inlet and a small temperature difference at the outlet.*    Counter-flow heat exchangers have an even temperature differenceacross the heat transfer length.*    Regenerative heat exchangers improve system efficiency byreturning energy to the system. A non-regenerative heat exchangerrejects heat to the surroundings.*    The heat transfer rate for a heat exchanger can be calculated usingthe equation below.˙Q=Uo* Ao* DTlm   Boiling Heat Transfer Summary    • Nucleate boiling is the formation of small bubbles at a heat transfer surface. Thebubbles are swept into the coolant and collapse due to the coolant being asubcooled liquid. Heat transfer is more efficient than for convection.    • Bulk boiling occurs when the bubbles do not collapse due to the coolant beingat saturation conditions.    • Film boiling occurs when the heat transfer surface is blanketed with steambubbles and the heat transfer coefficient rapidly decreases.    • Departure from nucleate boiling (DNB) occurs at the transition from nucleate tofilm boiling.    • Critical heat flux (CHF) is the heat flux that causes DNB to occur.   Heat Generation Summary    • The power generation process in a nuclear core is directly proportional to thefission rate of the fuel and the thermal neutron flux present.    • The thermal power produced by a reactor is directly related to the mass flow rateof the reactor coolant and the temperature difference across the core.    • The nuclear enthalpy rise hot channel factor is the ratio of the total kW heatgeneration along a fuel rod with the highest total kW, to the total kW of theaverage fuel rod.    • The average linear power density in the core is the total thermal power dividedby the active length of the fuel rods.    • The nuclear heat flux hot channel factor is the ratio of the maximum heat fluxexpected at any area to the average heat flux for the core.    • The total heat output of a reactor core is called the heat generation rate.    • The heat generation rate divided by the volume of fuel will give the averagevolumetric thermal source strength.   Decay Heat Summary*    Decay heat is the amount of heat generated by decay of fissionproducts after shutdown of the facility.*    The amount of decay heat is dependent on the reactor’s powerhistory.*    Methods for removing decay heat usually fall into one of thefollowing categories.        - Closed loop systems, where coolant is circulated between thereactor and a heat exchanger in a closed loop. The heatexchanger transfers the decay heat to the fluid in the secondaryside of the heat exchanger.        - Once through systems, where coolant from a source is injectedinto the reactor core. The decay heat is transferred from the fuelassemblies into the coolant, then the coolant leaves the reactor andis either collected in a storage structure or released to theenvironment.*    The limits for decay heat are calculated to prevent damage to thereactor core
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