Thermodynamics Learning summary

1. ThermodynamicsLearning summary By the end of this chapter you should have learnt about: • Air conditioning • Gas mixtures • Combustion • Reciprocating compressors • Heat transfer • Heat exchangers • Vapour power cycles • Reciprocating internal combustion engines. An Introduction to Mechanical Engineering: Part Two

2. 2.2 Air conditioning – key points By the end of this section you should have learnt that: • atmospheric air is a mixture of dry air and water vapour • air condition defines the temperature and humidity of atmospheric air • the law of partial pressures and partial internal energy determines what proportion of a gaspressure or internal energy is due to each individual gas component An Introduction to Mechanical Engineering: Part Two

3. 2.2 Air conditioning – key points • there are two measures of humidity: specific (or absolute) humidity – the mass of water vapour perunit mass of dry air; and relative humidity – the ratio of the partial pressure of water vapour in theair, ps, to the maximum partial pressure of the water vapour at that temperature, pg, which is thewater saturation pressure • gases may be quantified in moles, which is a specific number of molecules (the Avogadro number 6.02331026 per kmol) An Introduction to Mechanical Engineering: Part Two

4. 2.2 Air conditioning – key points • dew point is the temperature at which atmospheric air becomes 100 per cent saturated with watervapour (i.e. ps= pg), such that if the temperature is further reduced, water condenses out of theatmosphere • the psychrometric chart is the key tool of air condition monitoring together with the wet and drybulb thermometers, and the terms psychrometry and hygrometry are introduced to describe thestudy of atmospheric air An Introduction to Mechanical Engineering: Part Two

5. 2.2 Air conditioning – key points • the principles of operation of an air-conditioning unit require enthalpy balances to determine theheat power required by heating and cooling in the unit to produce a particular condition • the heat pump is the generic refrigeration unit that is required to produce cooling in the airconditioning unit, and that can also be used to provide heating energy from a cold source An Introduction to Mechanical Engineering: Part Two

6. 2.2 Air conditioning – key points • the p–h diagram is used to plot heat pump processes, since it quickly yields enthalpy changesbetween points, which represent the heat and work transfers required to produce the changes of state • the coefficient of performance is introduced as the measure of heat pump effectiveness. An Introduction to Mechanical Engineering: Part Two

7. 2.3 Gas mixtures – key points By the end of this section you should have learnt that: • gas mixtures have several gases intimately mixed, which can be quantified in proportion by massor by volume • the Gibbs–Dalton law of partial pressures leads to proportion analysis by mass, or gravimetricanalysis • Amagat’s law of partial volumes leads to analysis by volume proportions An Introduction to Mechanical Engineering: Part Two

8. 2.3 Gas mixtures – key points • combining the two with the gas law leads to a useful relationship between partial volumes,molar proportions and partial pressures of the gases,which can be used to makeconversions between gravimetric and volumetric analysis. An Introduction to Mechanical Engineering: Part Two

9. 2.4 Combustion – key points By the end of this section you should have learnt that: • combustion involves mixing a fuel (hydrocarbon) and an oxidizer, in order to produce heat whileconverting the chemicals involved in the reaction into reaction products • some hydrocarbon fuels only have hydrogen and carbon composition, andproduce the ultimate product gases carbon dioxide and water vapour An Introduction to Mechanical Engineering: Part Two

10. 2.4 Combustion – key points • molecular reaction equations can be balanced by counting the atoms of all molecules on thereacting side of the equation, and matching the number of atoms of all molecules on the productside of the equation • a stoichiometric combustion reaction is ideal: every carbon atom combines with exactly onediatomic oxygen molecule to produce a carbon dioxide molecule, and every hydrogen atomcombines with one other hydrogen atom and one oxygen atom to produce water vapour An Introduction to Mechanical Engineering: Part Two

11. 2.4 Combustion – key points • when there is either too much or too little oxygen, incomplete products of reaction appearincluding carbon monoxide and oxygen. The reaction is then non-stoichiometric • most practical combustion installations use atmospheric air, which carries oxygen as the primaryoxidizer. The oxygen in the air brings with it a fixed proportion of nitrogen. The combinedrequirement for oxygen with its associated nitrogen gives an air requirement that leads to the air to fuel ratio by mass or by volume An Introduction to Mechanical Engineering: Part Two

12. 2.4 Combustion – key points • for non-stoichiometric combustion, the excess air ratio is defined as the ratio of excess airsupplied to the air required for stoichiometric reaction • the product gases may be considered by proportion with or without moisture, since the moisturewill condense out of the gases when they cool down. The alternatives are known as wet and dryproducts of combustion • each reaction has an enthalpy of reaction at standard conditions, which is determined by thedifference between the sum of formation enthalpies of the reactants and products An Introduction to Mechanical Engineering: Part Two

13. 2.4 Combustion – key points • standard conditions are one atmosphere pressure and 25°C • the enthalpy of reaction is referred to as the calorific value of the fuel, and may be considered asgross, in which case the water is considered as condensed out of the gases, or as net, in whichcase the water is considered as vapour in the gases • enthalpy of reaction is directly used in flow process combustion but must be converted to internalenergy of reaction for closed process combustion An Introduction to Mechanical Engineering: Part Two

14. 2.4 Combustion – key points • the final temperature of a combustion process can be determined by an enthalpy balance (or internal energy balance for closed processes). An Introduction to Mechanical Engineering: Part Two

15. 2.5 Reciprocating compressors By the end of this section you should have learnt that: • reciprocating compressors use a piston driven in a cylinder, with a volume of gas at low pressureinduced on each cycle, which is compressed and delivered at a higher pressure • the terminology for compressors describes how the machine is constructed, and the method ofoperation. In particular, the clearance volume is significant for the operation of the compressor sinceit limits how much air can be drawn in during the induction stroke An Introduction to Mechanical Engineering: Part Two

16. 2.5 Reciprocating compressors • since a new volume of gas is drawn in at every induction, a state diagram does not represent atrue cycle, but rather a machine cycle. The p–V diagram is known as the indicator diagram of thecompressor • the compression requires work, and it is possible to calculate the ideal work assuming polytropicprocesses, and no losses to friction in the machine. This work involves heat generation, and heatthat must be lost in order to comply with the first law of thermodynamics An Introduction to Mechanical Engineering: Part Two

17. 2.5 Reciprocating compressors • the two measures of compressor efficiency are the volumetric efficiency that describes how muchthe volume drawn in is limited by the expansion of the clearance volume, and the isothermalefficiency that describes how far from the ideal isothermal compression the machine cycleprocess is • multistaging is used because of the limit of volumetric efficiency on pressure ratio. An intermediatepressure is achieved in one stage, followed by another stage to the higher pressure An Introduction to Mechanical Engineering: Part Two

18. 2.5 Reciprocating compressors • there is an ideal intermediate pressure, based on the least work done, which is found to be wheneach stage does equal work • intercooling is used in multistage compression in order to more closely approach the isothermalcondition and improve the compression work done for a given amount of work. An Introduction to Mechanical Engineering: Part Two

19. 2.6 Heat transfer – key points By the end of this section you should have learnt that: • there are three modes of heat transfer – conduction, convection and radiation • conduction heat transfer is determined by Fourier’s law of conduction. The conductivity used in thislaw depends on material properties and temperature and is defined for most materials An Introduction to Mechanical Engineering: Part Two

20. 2.6 Heat transfer – key points • the linear relationship between heat energy transferred and the temperature difference throughwhich it moves is analogous to Ohm’s law of electrical resistance. In a similar manner, the heattransferred is analogous to current transferred, the temperature difference to the potential voltagedifference, and the remaining terms are analogous to the electrical resistance, and are termed thethermal resistance An Introduction to Mechanical Engineering: Part Two

21. 2.6 Heat transfer – key points • convective heat transfer results from fluid moving from place to place and conveying andmixing material of differing temperatures. Forced convection describes situations in which thefluid is mechanically driven, by wind or machine, and natural convection describes transferdue to temperature gradients in the fluid causing buoyancy and hence naturally drivencirculation An Introduction to Mechanical Engineering: Part Two

22. 2.6 Heat transfer – key points • Newton’s law of cooling assumes a known convective heat transfer coefficient that depends onthe flow configuration. Once known, this heat transfer contribution can be treated as a thermalresistance similar to the conductive case, and combined overall thermal resistance can be used tocalculate overall heat transfer • conversely, the inverse of the overall thermal resistance divided by the overall surface area availablefor heat transfer is known as the overall heat transfer coefficient An Introduction to Mechanical Engineering: Part Two

23. 2.6 Heat transfer – key points • in the case of heat flow radially, the surface area of conduction increases with radius and leads toa logarithmic expression for the thermal resistance due to conduction • convection depends on fluid flow, and hence on laminar and turbulent flow characteristics • similar to the velocity boundary layer, there is a thermal boundary layer in situations where heattransfer is taking place. It depends on the thermal diffusivity (the thermal equivalent of viscosity),and on thermal capacity, m.cp An Introduction to Mechanical Engineering: Part Two

24. 2.6 Heat transfer – key points • the Nusselt number is a dimensionless parameter that represents convective heat transfercoefficient and provides the convective heat transfer coefficient directly. Correlationsof experimental data are made with other dimensionless numbers:the Prandtl number is used for all Nusselt number correlations and is the ratio of kinematicviscosity, , to thermal diffusivity, ; Reynolds number is used in forced convection situations; Grashof number is a dimensionless ratio that representsbuoyant and viscous forces, and is used in natural convectionsituations An Introduction to Mechanical Engineering: Part Two

25. 2.6 Heat transfer – key points • Nusselt number correlations are available in heat transfer texts from experimental evidence • radiant heat transfer is by electromagnetic radiation due to the release of energy from moleculesexcited by heat energy. It is determined according to the Stefan–Boltzmann Law of radiant heatrelease. For radiative heat transfer, two bodies at different temperatures having direct sight of eachother release and receive heat dependent on their temperatures An Introduction to Mechanical Engineering: Part Two

26. 2.6 Heat transfer – key points • the emissivity of a surface limits the amount of radiant energy released and modifies the Stefan–Boltzmann Law for surfaces that are not thermally black. A truly thermally black surface is notnecessarily coloured black, but has the property that it releases all its radiant energy due to itstemperature • it is possible to calculate combined mode heat transfer with conduction, convection and radiation,but in cases where radiant heat transfer is present, the calculation is not directly solvable due tothe fourth power of ‘T’ in the Stefan–Boltzmann Law. An Introduction to Mechanical Engineering: Part Two

27. 2.7 Heat exchangers – key points By the end of this section you should have learnt that: • heat exchangers are classified primarily as regenerators and recuperators. The recuperator is thetype involving tubes carrying one fluid surrounded by another fluid at a different temperature • recuperators are also defined by direction of flow as counter-flow or parallel-flow of the twofluids involved • thermal capacity rate is the specific heat capacity of a fluid multiplied by the amount of mass of thefluid considered, which is the mass flow rate of the fluid. It determines the temperature rise for agiven heat input An Introduction to Mechanical Engineering: Part Two

28. 2.7 Heat exchangers – key points • heat transfer theory shows how an elemental approach could be taken to the analysis of aparticular heat exchanger, but there are two methods used with overall heat transfer coefficients,which allow for simplified analysis in general cases • the temperature varies throughout a heat exchanger, the logarithmic mean temperaturedifference (LMTD) is used with a known overall heat transfer coefficient to work out either the heattransferred for the size of a heat exchanger given the heat transfer required. It can be shown that the LMTD is the correct mean to calculate the overall heat transfer An Introduction to Mechanical Engineering: Part Two

29. 2.7 Heat exchangers – key points • the collection of experimental results by Kays and London (1984) provides a method for modifyingthe LMTD for more complex heat exchangers than the simple shell-and-tube configuration • it is important to remember that the capacity rate of each fluid determines its temperature and heattransfer An Introduction to Mechanical Engineering: Part Two

30. 2.7 Heat exchangers – key points • the effectiveness ( -NTU) method relates the known data of overall heat transfer coefficient andminimum of the two capacity rates in the NTU and relies on experimental data from heat transfertexts to relate this to the ratio of actual heat transfer to maximum possible heat transfer betweenthe hottest and coldest temperatures available. Again this relies on the catalogue of data by Kaysand London • the cost of heat exchangers is the pressure drop for a given size. This must be considered in apractical heat exchanger and is determined from fluid mechanics calculations An Introduction to Mechanical Engineering: Part Two

31. 2.7 Heat exchangers – key points • fouling often occurs in practical installations and the alteration to heat transfer coefficient must be considered. An Introduction to Mechanical Engineering: Part Two

32. 2.8 Vapour power cycles – key points By the end of this section you should have learnt that: • a vapour power cycle operates on a condensable fluid in a closed cycle, receiving heat from ahot reservoir, usually a boiler, to evaporate the fluid before expanding through a turbine to a lowerpressure in order to produce work; it is then condensed to remove heat at a low pressure to a coldreservoir. A pump then increases the pressure to the high pressure side of the circuit prior to theheating part of the cycle • enthalpy changes between state points on the cycle are used to calculate heat and work from thefirst law in the form of the steady flow energy equation An Introduction to Mechanical Engineering: Part Two

33. 2.8 Vapour power cycles – key points • since vapour power cycles are widely used for power production, there are measures of theeffectiveness of employment of the energy input to obtained output power. Thermal efficiency is theratio of work output to externally supplied heat, i.e. the heat supplied from the hot reservoir. Workratio is the ratio of net work (work output less work in) to work output, and gives an indication of theloss to compression. In the case of steam vapour power cycles, the specific steam consumption is themass flow rate of steam per unit of power output, measured in kg per kW-hour An Introduction to Mechanical Engineering: Part Two

34. 2.8 Vapour power cycles – key points • the basic cycle has been improved by alterations. The basic cycle isthe Carnot cycle, which uses evaporation between saturated liquid and saturated vapour andhas expansion and compression within the vapour-liquid mixture region. This is the mostefficient cycle given any maximum and minimum temperature available, and is based on the ideaof the Carnot efficiency • the Rankine cycle is an improvement to the Carnot cycle, by simplifying thecondensation part of the cycle such that all fluid is in the saturated liquid state, and the pumpingwork is thus significantly reduced An Introduction to Mechanical Engineering: Part Two

35. 2.8 Vapour power cycles – key points • the average upper temperature can be increased by employing asuperheat part of the circuit after initial boiling, increasing the overall thermal efficiency; this alsoimproves the turbine operation by reducing expansion into the mixture region. Reheat in the circuit isincluded after the initial turbine expansion in order to avoid entering the mixture region significantlyand is used in coal-fired power stations • the Mollier chart or h–s diagram is a convenient representation of the processes in the vapour power cycle – it directly yields enthalpy changes, which are the heat and work exchanges with theworking fluid An Introduction to Mechanical Engineering: Part Two

36. 2.8 Vapour power cycles – key points • the process in the turbine is close to isentropic, and it is simple to comparethe isentropic performance with the real performance by use of the isentropic efficiency • feed heating is often employed, using some of the heat in the steam to heat the water being fed fromthe condenser to the pump. This improves the thermal efficiency by reducing the heat required fromthe boiler • feed heaters can either mix the steam with the feed water, in an open feed heater or pass the fluidsthrough a recuperator, in which the fluids are separate but exchange heat, in a closed feed heater An Introduction to Mechanical Engineering: Part Two

37. 2.8 Vapour power cycles – key points • combined heat and power is used where a quantity of heat is required for chemical processing in afactory, or where domestic heating is required for long periods of time. The thermal efficiency isartificially improved by including some of the heat lost as useful output since it is put to good use. Inthis case, steam is taken at higher temperature out of the final turbine, at a point where there is stilluseful heat in the steam. An Introduction to Mechanical Engineering: Part Two

38. 2.9 Reciprocating internal combustion engines – key points By the end of this section you should have learnt that: • internal combustion engines are either operated on the Otto cycle (working withpetrol and called spark ignition engines), or on the Diesel cycle (working withdiesel fuel and called compression ignition engines) • diesel fuel may be mainly considered as cetane, C16H34. Petrol fuel may be mainly considered tobe octane, C8H10 • both cycles are based on the ideal standard air cycle, which assumes externalheat supply and ideally enacted processes. Cycles vary from this, mainly due to thenature of heat addition by internal combustion An Introduction to Mechanical Engineering: Part Two

39. 2.9 Reciprocating internal combustion engines – key points • SI engines have air to fuel ratios of approximately 14.5:1 (near stoichiometric) and a compressionratio of approximately 8. They are quantity governed, in that the rate of air flow is adjusted to alterpower and economy • CI engines have air to fuel ratios between 20:1 and 25:1 and compression ratio in excess of 12.They are quality governed, in that the air flow is unrestricted, and the injection of fuel controls thepower and economy An Introduction to Mechanical Engineering: Part Two

40. 2.9 Reciprocating internal combustion engines – key points • there are several measures of engine performance: indicated power is the power directly from thep–V diagram; brake power is the measured power at the engine shaft; mechanical efficiency is theratio of brake power to indicated power; brake specific fuel consumption, which is the fuel requiredfor a specific brake power; volumetric efficiency, which is volume induced/swept volume, similarto that for air compressors An Introduction to Mechanical Engineering: Part Two

41. 2.9 Reciprocating internal combustion engines – key points • the compression ratio affects the combustion performance and can lead to poor combustion andhence poor mechanical behaviour if handled badly. In particular, it can lead to a noisy combustionbehaviour known as knock or diesel knock • spark timing is important for SI engines in order to provide the maximum pressure at the rightmoment in the cycle. The spark occurs a few degrees in advance of top dead centre position inorder to create maximum pressure at top dead centre An Introduction to Mechanical Engineering: Part Two

42. 2.9 Reciprocating internal combustion engines – key points • fuelling systems for SI engines rely on injection of a premixed air and fuel mixture. Carburretors were used but recently they have been superceded by fuel injection. For CI engines,injection is needed for the cycle to work – improvements have come from electronic control and higher pressures for fuel injection • the exhaust gases are ejected significantly above atmospheric pressure. This expansion canbe used in a turbocharger to drive a turbine, which in turn drives a compressor at a very high speed. This delivers air to the cylinder significantly above atmosphericpressure, increasing the volumetric efficiency. An Introduction to Mechanical Engineering: Part Two