Thermodynamics, Heat Transfer, And Fluid Flow. V.1. Thermodynamics, страница 6

It equals the total P-Vdivided by the total mass m, or the product of the pressure P and the specific volume ν, and iswritten as Pν.PVPν(1-14)mwhere:Rev. 0P=pressure (lbf/ft2)V=volume (ft3)ν=specific volume (ft3/lbm)m=mass (lbm)Page 17VmHT-01ENERGY, WORK, AND HEATThermodynamicsExample:Determine the specific P-V energy of 15 lbm of steam at 1000 psi in an 18 ft3 tank.Solution:Using Equation 1-14PνPVmPν(1000 lbf/in.2) (144 in.2/ft 2) (18 ft 3)15 lbmPν172,800 ft lbf/lbmSpecific EnthalpySpecific enthalpy (h) is defined as h = u + Pν, where u is the specific internal energy (Btu/lbm)of the system being studied, P is the pressure of the system (lbf/ft2), and ν is the specific volume(ft3/lbm) of the system.

Enthalpy is usually used in connection with an "open" system problemin thermodynamics. Enthalpy is a property of a substance, like pressure, temperature, andvolume, but it cannot be measured directly. Normally, the enthalpy of a substance is given withrespect to some reference value.

For example, the specific enthalpy of water or steam is givenusing the reference that the specific enthalpy of water is zero at .01°C and normal atmosphericpressure. The fact that the absolute value of specific enthalpy is unknown is not a problem,however, because it is the change in specific enthalpy (∆h) and not the absolute value that isimportant in practical problems. Steam tables include values of enthalpy as part of theinformation tabulated.WorkKinetic energy, potential energy, internal energy, and P-V energy are forms of energy that areproperties of a system. Work is a form of energy, but it is energy in transit.

Work is not aproperty of a system. Work is a process done by or on a system, but a system contains no work.This distinction between the forms of energy that are properties of a system and the forms ofenergy that are transferred to and from a system is important to the understanding of energytransfer systems.HT-01Page 18Rev. 0ThermodynamicsENERGY, WORK, AND HEATWork is defined for mechanical systems as the action of a force on an object through a distance.It equals the product of the force (F) times the displacement (d).W = Fd(1-15)where:W=work (ft-lbf)F=force (lbf)d=displacement (ft)Example:Determine the amount of work done if a force of 150 lbf is applied to an object until ithas moved a distance of 30 feet.Solution:Using Equation 1-15W = FdW = (150 lbf)(30 ft)W = 4500 ft-lbfIn dealing with work in relation to energy transfer systems, it is important to distinguish betweenwork done by the system on its surroundings and work done on the system by its surroundings.Work is done by the system when it is used to turn a turbine and thereby generate electricity ina turbine-generator.

Work is done on the system when a pump is used to move the working fluidfrom one location to another. A positive value for work indicates that work is done by thesystem on its surroundings; a negative value indicates that work is done on the system by itssurroundings.HeatHeat, like work, is energy in transit. The transfer of energy as heat, however, occurs at themolecular level as a result of a temperature difference.

The symbol Q is used to denote heat.In engineering applications, the unit of heat is the British thermal unit (Btu). Specifically, thisis called the 60 degree Btu because it is measured by a one degree temperature change from 59.5to 60.5°F.Rev. 0Page 19HT-01ENERGY, WORK, AND HEATThermodynamicsAs with work, the amount of heat transferred depends upon the path and not simply on the initialand final conditions of the system.

Also, as with work, it is important to distinguish betweenheat added to a system from its surroundings and heat removed from a system to itssurroundings. A positive value for heat indicates that heat is added to the system by itssurroundings. This is in contrast to work that is positive when energy is transferred from thesystem and negative when transferred to the system. The symbol q is sometimes used to indicatethe heat added to or removed from a system per unit mass.

It equals the total heat (Q) addedor removed divided by the mass (m). The term "specific heat" is not used for q since specificheat is used for another parameter. The quantity represented by q is referred to simply as theheat transferred per unit mass.qQm(1-16)where:q=heat transferred per unit mass (Btu/lbm)Q=heat transferred (Btu)m=mass (lbm)Example:Determine the heat transferred per unit mass if 1500 Btu’s are transferred to 40 lbm ofwater.Solution:Using Equation 1-16qQmq1500 Btu40 lbmq37.5 Btu/lbmThe best way to quantify the definition of heat is to consider the relationship between the amountof heat added to or removed from a system and the change in the temperature of the system.Everyone is familiar with the physical phenomena that when a substance is heated, itstemperature increases, and when it is cooled, its temperature decreases. The heat added to orremoved from a substance to produce a change in its temperature is called sensible heat.

Theunits of heat are often defined in terms of the changes in temperature it produces.HT-01Page 20Rev. 0ThermodynamicsENERGY, WORK, AND HEATAnother type of heat is called latent heat. Latent heat is the amount of heat added to or removedfrom a substance to produce a change in phase.

When latent heat is added, no temperaturechange occurs. There are two types of latent heat. The first is the latent heat of fusion. Thisis the amount of heat added or removed to change phase between solid and liquid. The secondtype of latent heat is the latent heat of vaporization. This is the amount of heat added orremoved to change phase between liquid and vapor. The latent heat of vaporization is sometimescalled the latent heat of condensation.Different substances are affected to different magnitudes by the addition of heat. When a givenamount of heat is added to different substances, their temperatures increase by different amounts.The ratio of the heat (Q) added to or removed from a substance to the change in temperature(∆T) produced is called the heat capacity (Cp) of the substance. The heat capacity of a substanceper unit mass is called the specific heat (cp) of the substance.

The subscript p indicates that theheat capacity and specific heat apply when the heat is added or removed at constant pressure.CpQ∆TcpQm∆Tcpq∆TCp=heat capacity at constant pressure (Btu/°F)cp=specific heat at constant pressure (Btu/lbm-°F)Q=heat transferred (Btu)q=heat transferred per unit mass (Btu/lbm)m=mass (lbm)∆T=temperature change (°F)(1-17)where:One lbm of water is raised 1°F and one Btu of heat is added. This implies that the specific heat(cp) of water is one Btu/lbm-°F. The cp of water is equal to one Btu/lbm-°F only at 39.1°F.By rearranging Equation 1-17 we obtain Q = mcp∆T, which is used to calculate latent heat.

Bysubstituting mass flow rate in lbm/hr, ṁ , for m, we obtain Q̇ ṁcp∆T . This equation is usedto calculate heat transfer in Btu/hr and will be useful in later chapters.Rev. 0Page 21HT-01ENERGY, WORK, AND HEATThermodynamicsExample:How much heat is required to raise the temperature of 5 lbm of water from 50°F to150°F? (Assume the specific heat (cp) for water is constant at 1.0 Btu/lbm-°F.)Solution:Qm∆Tcp=Q= cpm∆TQ= (1.0 Btu/lbm-°F)(5 lbm)(150°F - 50°F)Q= (1.0 Btu/lbm-°F)(5 lbm)(100°F)Q= 500 BtuFrom the previous discussions on heat and work, it is evident that there are many similaritiesbetween them.

Heat and work are both transient phenomena. Systems never possess heat orwork, but either or both may occur when a system undergoes a change of energy state. Both heatand work are boundary phenomena in that both are observed at the boundary of the system. Bothrepresent energy crossing the system boundary.EntropyEntropy (S) is a property of a substance, as are pressure, temperature, volume, and enthalpy.Because entropy is a property, changes in it can be determined by knowing the initial and finalconditions of a substance.

Entropy quantifies the energy of a substance that is no longeravailable to perform useful work. Because entropy tells so much about the usefulness of anamount of heat transferred in performing work, the steam tables include values of specificentropy (s = S/m) as part of the information tabulated. Entropy is sometimes referred to as ameasure of the inability to do work for a given heat transferred.

Entropy is represented by theletter S and can be defined as ∆S in the following relationships.∆S∆QTabs(1-18)∆s∆qTabs(1-19)∆S=where:HT-01the change in entropy of a system during some process (Btu/°R)Page 22Rev. 0ThermodynamicsENERGY, WORK, AND HEAT∆Q=the amount of heat transferred to or from the system during the process(Btu)Tabs=the absolute temperature at which the heat was transferred (°R)∆s=the change in specific entropy of a system during some process(Btu/lbm -oR)∆q=the amount of heat transferred to or from the system during the process(Btu/lbm)Like enthalpy, entropy cannot be measured directly.

Also, like enthalpy, the entropy of asubstance is given with respect to some reference value. For example, the specific entropy ofwater or steam is given using the reference that the specific entropy of water is zero at 32°F.The fact that the absolute value of specific entropy is unknown is not a problem because it is thechange in specific entropy (∆s) and not the absolute value that is important in practical problems.Energy and Power EquivalencesThe various forms of energy involved in energy transfer systems (such as potential energy,kinetic energy, internal energy, P-V energy, work and heat) may be measured in numerous basicunits.