Physics
Specific Latent Heat
Specific latent heat refers to the amount of heat energy required to change the state of a unit mass of a substance without a change in temperature. It is specific to each substance and is typically expressed in joules per kilogram. When a substance undergoes a phase change, such as from solid to liquid or liquid to gas, specific latent heat is involved in the process.
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12 Key excerpts on "Specific Latent Heat"
eBook - PDF- Sam Miller(Author)
- 2015(Publication Date)
- Cambridge University Press(Publisher)
For this reason, they can be treated as constants without much loss of accuracy. 4.5. Latent Heat: A Special Case of Specific Heat 77 4.5. Latent Heat: A Special Case of Specific Heat In Chapter 3 , we derived an expression to describe the conservation of energy when two different solid objects were placed into direct contact, or when two different liq-uids were mixed together. In this chapter, we’ve described the conservation of energy when heat is added to a parcel of gas , either at constant volume or at constant pres-sure. What we haven’t considered is the possibility of phase changes when discussing changes in the internal energy of water, such as when enough heat is added to a block of ice to cause it to melt, or when heat is added to a sample of liquid until it boils (evaporates). Table 4.1. Specific heats for dry air as a function of temperature. i Increasing temperature adds additional degrees of freedom, resulting in increased specific heat coefficients at constant pressure and constant volume. The values of both specific heats at 0 °C are included for comparison. (Values in parenthesis have been estimated from available data.) Temperature [K] Temperature [°C] c p [J/(kg K)] c v [J/(kg K)] 250 −23.2 1003 716 273.2 0 1003.8 717.0 300 26.8 1005 718 350 76.8 1008 721 400 126.8 1013 726 450 176.8 1020 733 500 226.8 1029 742 550 276.8 1040 753 600 326.8 1051 764 650 376.8 1063 776 700 426.8 1075 788 750 476.8 1087 800 800 526.8 1099 812 850 576.8 (1110) (823) 900 626.8 1121 834 950 676.8 (1132) (845) 1000 726.8 1142 855 i Hilsenrath et al. ( 1955 ). 78 The First Law of Thermodynamics You learned about phase changes in your introductory meteorology course, but here is a brief reminder of the different phase changes taking a substance from one state to another (also see Figure 4.3 ). We focus on water because of its prime impor-tance in meteorology, although the following applies to all substances.
- M J Lewis(Author)
- 1990(Publication Date)
- Woodhead Publishing(Publisher)
8Sensible and latent heat changes
8.1 INTRODUCTION
The properties to be discussed in this chapter include specific heat, latent heat and specific enthalpy.These properties play an important role in heat transfer problems when heating or cooling foods. It is necessary to know the specific heat to determine the quantity of energy that needs to be added or removed. This will give an indication of the energy costs involved and in a continuous process will have an influence on the size of the equipment.Latent heat values, which are associated with phase changes, play an important role in freezing, crystallization, evaporation and dehydration processes.8.2 SPECIFIC HEAT
The specific heat of a material is a measure of the amount of energy required to raise unit mass by unit temperature rise. As mentioned in Chapter 7 , specific heat is temperature dependent. However, for the purpose of many engineering calculations, these variations are small and an average specific heat value is used for the temperature range considered.The units of specific heat are kilojoules per kilogram per kelvin (kJ kg−1 K−1 ), kilocalories per kilogram (kcal kg−1 K−1 ) or British thermal units per pound per degree Fahrenheit (Btu lb−1 degF−1 ). From the definitions of the different thermal units, the specific heat of water in the respective units is1 .0. kcal kg −1K −1or 4.18 kJ kg−1K −1or 1 Btu lb−1degF −1In a batch heating or cooling process, the amount of heat (energy) Q required or removed is given byIn a continuous process, the rate of heat transfer is given byQ = mass × average specific heat × temperature change= MC Δ TJ or kcal or BtuQ / t = mass flow rate × specific heat × temperature rangeThe units of Q /t are joules per second (J s−1 ), i.e. watts (W), or British thermal units per hour (Btu h−1 ). This is often termed the heating or cooling duty of the heat exchanger. If it is felt that this is not a sufficiently accurate procedure, the total energy requirement can be obtained by graphical integration. Specific heat is plotted against temperature; the total heat required to raise unit mass from T 1 to T 2 is given by ∫cp dTor the area under the curve (Fig. 8.1 ) This should, in most cases, be not too far removed from the value obtained by selecting a specific heat value at the average temperature (T 1 + T 2 )/2. If the relationship between the specific heat and temperature is known in terms of temperature, then the integral ∫cpdT can be evaluated directly, (see section 8.4
eBook - PDF- P.F. Kelly(Author)
- 2014(Publication Date)
- CRC Press(Publisher)
Time for a Fixed Amount of Water Being Heated at a Constant Rate and Undergoing Phase Changes Here, the heat added [ the LHS ] is equal to the input power multiplied by the temporal duration of the plateau. The RHS is the product of the mass of the material undergoing the phase change, M , and the substance-and transition-Specific Latent Heat, L . LATENT HEAT The latent heat is the amount of heat which must be added or re-moved in order to effect the transformation of 1 kg of substance from one phase to another at the critical temperature. The SI units for latent heat are joules per kilogram [ J / kg ]. CRITICAL TEMPERATURE The critical temperature(s) for a particular material are those at which the system’s phase changes. Only at the critical temperature can the two 4 phases co-exist in equilibrium. [ The critical temperature depends on properties of the system. ] For water, the latent heats of fusion and vaporisation along with the critical temperatures [ under standard conditions 5 ] are presented in the table below. Phase Transition Latent Heat [ kJ / kg ] T C [ C ] Fusion water → ice L F = 333 0 Vaporisation water → steam L V = 2256 100 In the process illustrated in Figure 38.1, heat was added to warm and then melt the ice, to warm and then evaporate the liquid water into steam, and subsequently to further heat the steam. The reverse processes of condensation and solidification require removal of the latent heat from the system. ASIDE: When it snows on very calm winter days, the latent heat released by the condensation and solidification of water vapour can accumulate in the air nearby and produce a significant rise in the air temperature. 4 It is possible to have three phases, e.g., ice, water, and water vapour, simultaneously present in a system at a fixed temperature. 5 For example, at ambient pressure equal to 1 atm .
eBook - PDF- Richard L. Myers(Author)
- 2005(Publication Date)
- Greenwood(Publisher)
Heat transfer may cause a phase change, and no temperature change occurs as long as two phases are present. In this situation, heat is referred to as latent heat. The relationship between heat and phase changes will be examined in the next section. The relationship between heat trans- fer, Q, and the change in temperature of a substance depend s on the specific heat 86 Heat capacity of the substance. The specific heat capacity of a substance is a measure of the amount of heat necessary to raise the tem- perature of 1 g of the substance by 1°C. The specific heats of several common substances are listed in Table 6.1. Table 6.1 demon- strates that the specific heat of a substance depends on its phase. The specific heat of liquid water is approximately twice that of ice and steam. Water has one of the highest specific heats compared to other liquids. The high specific heat capacity of liquid water is directly related to its chemical structure and the presence of hydrogen bonds. The high specific heat of water explains why coastal environments have more moderate weather than areas at similar latitudes located inland. Water's high specific heat capacity means coastal regions will not experience drastic temperature changes as compared to inland regions. The relationship between heat, specific heat capacity, and temperature change of a substance is given by the equation Q = mcAT. In this equation, Q is the amount of thermal Table 6.1 Specific Heat Capacity of Some Common Substances Substance Steel Wood Ice Liquid water Steam Air Alcohol Specific Heat J/g=°C 0.45 1.7 2.1 4.2 2.0 1.0 2.5 energy (often Q is referred to simply as heat) transferred in joules, m is the mass in grams, c is the specific heat capacity of the sub- stance, and AT is the change in temperature. The temperature change is equal to the final temperature minus the initial temperature. As an application of this equation, consider what happens when heating a pot of water on the stove.
- S. Bobby Rauf(Author)
- 2021(Publication Date)
- River Publishers(Publisher)
Specifc Heat Specifc heat is defned as the amount of the heat, Q , required to change the temperature of mass “ m ” of a substance by Δ T . The symbol for specifc heat is “ c .” The mathematical formula for specifc heat of solids and liquids is: c = Q/(m. Δ T) Eq. 1-28 Or, Q = m. c. Δ T Eq. 1-29 Where, m = Mass of the substance; measured in kg , in the SI system, and in lbm in the US system Q = The heat added or removed; measured in Joules or kJ in the SI System, or in Btu’s in the US system Δ T = The change in temperature, measured in °K in the SI Systems, or in °R in the US System The units for c are kJ/(kg. °K), kJ/(kg. °C), Btu/(lbm. °F) or Btu/(lbm. °R). The thermodynamic equation involving specifc heats of gases are as follows: Q = m. c v . Δ T, when volume is held constant . Eq. 1-30 Q = m. c p . Δ T, when pressure is held constant . Eq. 1-31 Approximate specifc heat , c p , for selected liquids and solids are listed in Table 1-5 . The next case study, Case Study 1-2, is designed to expand our ex-ploration of energy related analysis methods and computational tech-niques. Some of the energy, work and heat considerations involved in this case study lay a foundation for more complex energy work and thermo-dynamics topics that lie ahead in this text. This case study also provides us an opportunity to experience the translation between the SI (Metric) 17 Introduction to Energy, Heat, and Thermodynamics Table 1-5. Approximate Specifc Heat, c p, for Selected Liquids and Solids, in kJ/ kg °K, cal/gm °K, Btu/lbm °F, J/mol °K Table 1-6. Densities of Common Materials 18 Thermodynamics Made Simple for Energy Engineers unit system and the US (Imperial) unit system. As we compare the solu-tions for this case study in the US and SI unit systems, we see that choos-ing one unit system versus another, in some cases does involve the use of different formulas.
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
An Important Point In determining and then using the specific heat of any substance, we need to know the conditions under which energy is transferred as heat. For solids and liquids, we usually assume that the sample is under constant pressure (usually atmospheric) during the transfer. It is also conceivable that the sample is held at constant volume while the heat is absorbed. This means that thermal expansion of the sample is prevented by applying external pressure. For solids and liquids, this is very hard to arrange experimentally, but the effect can be calculated, and it turns out that the specific heats under constant pressure and constant volume for any solid or liquid differ usually by no more than a few percent. Gases, as you will see, have quite different values for their specific heats under constant-pressure conditions and under constant-volume conditions. Heats of Transformation When energy is absorbed as heat by a solid or liquid, the temperature of the sample does not necessarily rise. Instead, the sample may change from one phase, or state, to another. Matter can exist in three common states: In the solid state, the mol- ecules of a sample are locked into a fairly rigid structure by their mutual attraction. In the liquid state, the molecules have more energy and move about more. They may form brief clusters, but the sample does not have a rigid structure and can flow or settle into a container. In the gas, or vapor, state, the molecules have even more energy, are free of one another, and can fill up the full volume of a container. Melting. To melt a solid means to change it from the solid state to the liq- uid state. The process requires energy because the molecules of the solid must be freed from their rigid structure. Melting an ice cube to form liquid water is a common example. To freeze a liquid to form a solid is the reverse of melting and requires that energy be removed from the liquid, so that the molecules can settle into a rigid structure.
eBook - PDF- Jean-Philippe Ansermet, Sylvain D. Brechet(Authors)
- 2019(Publication Date)
- Cambridge University Press(Publisher)
Experimentally, it is observed that the specific heat of any substance decreases to zero as the temperature tends to zero. As we will see in this chapter, this general property can be derived from what is known as the third law of thermodynamics. It was formulated by Walther Nernst in 1904. After his studies in Zürich, Berlin and Graz, he founded the Institute of physical chemistry and electrochemistry in Göttingen and received the Nobel Prize in 1920 in recognition for his work on thermochemistry. The third law was important, because at the time it was formulated, physicists faced a challenge concerning specific heat. Pierre Louis Dulong (1785–1838) and Alexis Thérèse Petit (1791–1820) established an empirical law according to which the specific heat of a metal depends on its molar mass, but not on its temperature. This temperature independence could be derived from statistical physics, using the physical concepts known at the turn of the twentieth century. This failure to predict the correct temperature dependence was one of the fundamental problems physics faced at the beginning of the twentieth century. Einstein resolved the issue by a derivation of the specific heat that was based on quantum mechanical arguments. In this chapter, we will illustrate the notion of specific heat and of latent heat with the ideal gas model. The ideal gas equation of state can be derived from empirical laws established by Robert Boyle (1621–1697), Edme Mariotte (1620–1684), Jacques Charles (1746–1823), Louis Gay-Lussac (1778–1850) and Amedeo Avogadro (1776–1856). The Boyle–Mariotte law states that at a constant temperature T, the pressure p of a dilute gas is inversely proportional to its volume V [43, 44]. Charles’ law states that at constant pressure 105 5.2 Thermal Response Coefficients p, the volume V of a dilute gas is proportional to its temperature T [45].
No longer available |Learn more- Irving Granet, Maurice Bluestein(Authors)
- 2014(Publication Date)
- CRC Press(Publisher)
Temperature is a measure of the energy contained in the molecules of a system due to their motion. When the temperature of a system is greater than that of its surroundings, some of that molecular energy is transferred to the surroundings in what we call heat. Thus, tempera-ture is a property of a system in a given state, whereas heat is associated with a change in the state of a system. Because work and heat are both forms of energy in transition, it follows that the units of work should be capable of being expressed as heat units, and vice versa. In the English system of units the conversion factor between work and heat, sometimes called mechanical equivalent of heat , is 778.169 ft.·lb f /Btu and is conventionally given the symbol J . We shall use this symbol to designate 778 ft.·lb f /Btu, because this is sufficiently accurate for engineering applications of thermodynamics. In the SI system, this conversion factor is not necessary, because the joule (N·m) is the basic energy unit. There are two forms of heat transfer: sensible heat and latent heat. Sensible heat transfer occurs when there is a temperature difference between bodies or systems and the amount Solving yields V 2 = 2 × 9.81 × 10 and V = 14.0 m/s Note that this result is independent of the mass of the body. The kinetic energy is readily found from Equation b to be equal to 10 kg × 10 m × 9.81 m/s 2 = 981 N·m. 73 Work, Energy, and Heat of heat transferred is related to the magnitude of that difference. This is the most common form. Latent heat transfer occurs when a body is changing state, such as evaporating from liquid to gas or condensing from gas to liquid. The change of phase occurs at constant temperature. This form of heat transfer is utilized in refrigeration and air conditioning systems (see Chapters 7 and 10). 2.8 Flow Work At this time, let us look at two systems, namely, the nonflow or closed system and the steady-flow or open system .
eBook - PDFAdvances in Energy Storage
Latest Developments from R&D to the Market
- Andreas Hauer(Author)
- 2022(Publication Date)
- Wiley(Publisher)
Most of the cited papers are recent review articles where the references to the original works can be found. 26.2 Fundamentals, Materials, Groups, and Properties 26.2.1 Fundamentals Three states of matter (often referred as phases) are observable in everyday life, namely solid, liquid, and gas. At well defined conditions of temperature and pressure, transi-tions among them take place. On heating, a crystalline solid becomes liquid at the so-called melting temperature, a liquid vaporizes at the boiling point corresponding to the working pressure, and a solid transforms directly into vapor at the sublimation temperature, given that the pressure is lower than the triple point of the substance. In the reverse direction (cooling), a liquid may solidify and a gas can condense either as a liquid or a solid. Other possible phase changes are those in which one crystalline form transforms into another one (solid–solid transitions) or those in which a liquid becomes a glass (non-crystalline, amorphous solid). All these transformations (except liquid–glass) are first order transitions, which are characterized by discontinuous changes in entropy and volume. There is, therefore, a latent heat (the system absorbs or gives energy to its environment) associated to the transition. Moreover, for a single component system, they take place at interrelated constant pressure and temperature. The molar (or gravimetric) energy involved in the transformation (phase transition latent heat) corresponds to the difference in molar (or gravimetric) enthalpy between the final and the initial phases. Heat must be sup-plied when a more condensed phase transforms into a more disordered one, and it is released in the reverse way. At constant pressure, the enthalpy change ( ∆ h tr ) at the transition temperature ( T tr ) relates to the entropy change ( ∆ s tr ) as:
eBook - PDFPhysical Chemistry
Thermodynamics
- Horia Metiu(Author)
- 2006(Publication Date)
- Taylor & Francis(Publisher)
And, in reasoning on this subject, we must not forget to consider that most remarkable circumstance, that the source of the heat gen-erated by friction, in these experiments, appeared evidently to be inexhaustible. It is in hardly necessary to add that anything which any insulated body, or system of bodies, can continue to furnish without limitation cannot possibly be a material substance: and it appears to me to be extremely difficult, if not quite impossible, to form any distinct idea of anything, capable of being excited and communicated, in the man-ner the heat was excited and communicated in these, except it be MOTION. 122 Heat Supplement 6.2 Joseph Black, Heat Capacity Joseph Black (1728–1799), excerpts on specific heat and latent heat from “Lectures on the Elements of Chemistry delivered in the University of Edinburgh by the Late Joseph Black, M.D. …” published from his manuscripts by John Robison (1803) (as excerpted by William Francis Magie, A Source Book in Physics (New York: McGraw-Hill, 1935)) (Excerpt from a paper posted on webserver.lemoyne.edu/faculty/paperabc. html created by Professor Carmen Giunta of Lemoyne College, Syracuse NY.) (Specific heat) A second improvement in our knowledge of heat, which has been attained by the use of thermometers, is the more distinct notion we have now than formerly, of the Distribution of heat among different bodies. I remarked formerly, that, even without the help of thermometers, we can perceive a tendency of heat to diffuse itself from any hotter body to the cooler around, until it be distributed among them, in such a manner that none of them are disposed to take any more heat from the rest. The heat is thus brought into a state of equilibrium. This equilibrium is somewhat curious. We find that when all mutual action is ended, a thermometer, applied to any one of the bodies, acquires the same degree of expansion: Therefore the temperature of them all is the same, and the equilibrium is universal.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
The conversion factor be- tween kilocalories and joules is known as the mechanical equivalent of heat: 1 kcal 5 4186 joules. T 5 T c 1 273.15 (12.1) D L 5 aL 0 DT (12.2) D V 5 bV 0 DT (12.3) Q 5 cm DT (12.4) Focus on Concepts 341 12.8 Heat and Phase Change: Latent Heat Heat must be supplied or removed to make a material change from one phase to another. The heat Q that must be supplied or removed to change the phase of a mass m of a substance is given by Equation 12.5, where L is the latent heat of the substance and has SI units of J/kg. The latent heats of fusion, vaporization, and sublimation refer, respectively, to the solid/liquid, the liquid/vapor, and the solid/vapor phase changes. 12.9 Equilibrium Between Phases of Matter The equilibrium vapor pressure of a substance is the pressure of the vapor phase that is in equilibrium with the liquid phase. For a given substance, vapor pressure depends only on temperature. For a liquid, a plot of the equilibrium vapor pressure versus temperature is called the vapor pressure curve or vaporization curve. The fusion curve gives the combinations of temperature and pressure for equilibrium between solid and liquid phases. 12.10 Humidity The relative humidity is defined as in Equation 12.6. The dew point is the temperature below which the water vapor in the air condenses. On the va- porization curve of water, the dew point is the temperature that corresponds to the actual pressure of water vapor in the air. Q 5 mL (12.5) Partial pressure of water vapor Equilibrium vapor pressure of water at the existing temperature Percent relative humidity 5 3 100 (12.6) FOCUS ON CONCEPTS Note to Instructors: The numbering of the questions shown here reflects the fact that they are only a representative subset of the total number that are available online. However, all of the questions are available for assignment via an online homework management program such as WileyPLUS or WebAssign.
- Greg F. Naterer(Author)
- 2002(Publication Date)
- CRC Press(Publisher)
In subsequent chapters, these governing equations and supplementary relations will be examined in greater detail for various types of multiphase systems. The previous heat balances were applied to a solid / liquid interface. Similar results are obtained for liquid / gas (vapor) systems, such as problems involving boiling or condensation heat transfer. For heat transfer with condensation, the latent heat of vaporization is released at the phase interface and typically conducted through the liquid film. The vapor typically condenses at or near the saturation temperature. Latent heat is released and primarily transferred from the phase interface through the liquid due to a lower vapor conductivity and decreasing temperature through the liquid. In the presence of convection with superheated vapor (above the saturation temperature), the rate of heat transfer to the interface is typically enhanced, thereby increasing the rate of growth of the condensate film. In single-phase problems with convection (Chapter 3), the wall heat flux was expressed in terms of the convective heat transfer coefficient multiplied by the wall / fluid temperature difference. Similarly, convection at the phase interface in two-phase flows can be expressed through the resulting steepened temperature gradient, analogous to the left side of Equation (5.74). This contribution to the heat exchange would not arise if the freestream vapor was at the saturation temperature (i.e., same as the temperature at the phase interface). In boiling heat transfer, latent heat is absorbed in the liquid to complete the change of phase. Heat is transferred by conduction, convection, or Phase Change Heat Transfer 265 radiation from the heating surface and extracted by liquid at the phase interface during boiling of the liquid. This absorption of latent heat from the liquid occurs in contrast to the release of latent heat from the vapor during condensation.
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