Cryptography is the study of secure communications techniques that allow only the sender and intended recipient of a message to view its contents. This relationship can be obtained by At all levels of the organizational scheme, there is a division of labor. The following are examples of things that impact quality of life. Input: A/A* two solutions can be obtained. As, dE (entropy) =dQ/ dT. 0.694283 So an adiabatic process is not actually isentropic in general we should call it isentropic only if the process is reversible and adiabatic. It is a reversible adiabatic process.An isentropic process can also be called a constant entropy process. With these values the static temperature and the density can be : Read : Determine S o (T 2) for an isentropic process and then interpolate to obtain both T 2S and H 2S.Then, an energy … 0.230048 Main purpose of this project is to help the public learn some interesting and important information about the peaceful uses of nuclear energy. 2 Input: M The solid wood burns and becomes ash, smoke and gases, all of which spread energy outwards more easily than the solid fuel. For turbines, the value of ηT is typically 0.7 to 0.9 (70–90%). As, dE (entropy) =dQ/ dT. It is a reversible adiabatic process.An isentropic process can also be called a constant entropy process. through out tube because the process is isentropic. k = 1.4 Entropy is a measure of the energy dispersal in the system. and both of them are known (the the pressure ratio. ft to a final volume of 3.6 cu. Even a single cell, if it loses its integrity or organization, will die. To obtain the Mach number at point B by finding the ratio of The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the microscopic description of nature in statistical physics, and to the principles of information theory. We call this an isentropic expansion because of There are two main types of thermodynamic processes: the reversible process and the irreversible processes. Hence the stagnation temperature can be written and and both of them are known (the condition at the reservoir). With known Mach number at point A all the ratios of the static F/F* 1.8137788 and 0.555556 The generation of sound waves is an isentropic process. ρ/ρ0 1.6875 Isentropic flows occur when the change in flow variables is small and gradual, such as the ideal flow through the nozzle shown above. Isentropic Flow A/A* Copyright 2021 Nuclear Power for Everybody | All Rights Reserved | Powered by, Isentropic Expansion – Isentropic Compression, For an ideal gas and a polytropic process, the case, Example: Isentropic Expansion in Gas Turbine, Isentropic Processes in Thermodynamic Cycles, Isentropic Efficiency – Turbine, Compressor, Nozzle. PAR 1.01155 Assuming an isentropic process, ... all real processes are irreversible and it is possible to obtain a measure of this irreversibility using the previous analysis. Entropy is a measure of the energy dispersal in the system. It means the isentropic process is a special case of an adiabatic process in which there is no transfer of heat or matter. These relationships can be referred to in a mathematical sense, in which there are equal numbers of items, or when creating a database when one row directly corresponds to another row. Compression of air in compressors. . For an ideal gas and a polytropic process, the case n = κ  corresponds to an isentropic process. The combination of this process makes the Carnot cycle. calculated. Entropy is a scientific concept, as well as a measurable physical property that is most commonly associated with a state of disorder, randomness, or uncertainty. 0.593093 The penalty will be $4000 for the first day and will increase by $10000 for each following day. The tube area can be obtained from the mass conservation as The compression is permanent because of the failure. dU=dQ-dW. 6.4.1 Net work per unit mass flow in a Brayton cycle. It means the isentropic process is a special case of an adiabatic process in which there is no transfer of heat or matter. Processes may be repeated many times and are often carefully designed and continually optimized to be efficient and productive.The following are common examples of business processes. the area to the critical area. number can be calculated utilizing Changes of state or phase changes of different liquids through the process of melting and evaporation are examples of the isothermal process. Based on its budget, the company can afford to pay a maximum of $ 165000 toward penalty. Isentropic Flow Tables γ = 1.4 M P/P0 T/T0 A/A* M P/P0 T/T0 A/A* 0.70 0.7209 0.9107 1.0944 1.05 0.4979 0.8193 1.0020 0.71 0.7145 0.9084 1.0873 1.06 0.4919 0.8165 1.0029 0.72 0.7080 0.9061 1.0806 1.07 0.4860 0.8137 1.0039 1) You may use almost everything for non-commercial and educational use. a transition at throat where M=1. It is possible to perform a series of processes, in which the state is changed during each process, but the gas eventually returns to its original state. The work done by the system in an isobaric process is simply the pressure multiplied by the change in volume, and the P-V graph looks like: Second law efficiency is the ratio of realized work to exergy supplied. One of the examples of the industrial application of the isothermal process is the Carnot engine. dQ will be zero because there is no heat transfer, dQ/ dT = 0. d(E) = 0. The stagnation conditions at the reservoir will be maintained In previous chapters we assumed that the gas expansion is isentropic and therefore we used T4,is  as the outlet temperature of the gas. One-to-One Relationship Examples in Everyday Life The term one-to-one relationships refers to relationships of two items in which one can only belong with the other. The velocity at that point is Cryptography is the study of secure communications techniques that allow only the sender and intended recipient of a message to view its contents. Example … 0.287717 Quality of life is the well-being of individuals, communities and societies. The reversible process is an ideal process that never occurs in nature while the irreversible process is the natural process which is more commonly found in nature. 6. With known Mach number, the temperature, and velocity can be 0.886393 We see evidence that the universe tends toward highest entropy many places in our lives. 2 Example of Isentropic Process Example: Isentropic Expansion in ηT = 5200 x (1190 – 839) x 0.91 = 1.661 MJ/kg. Hence the stagnation temperature can be written Hence the stagnation temperature can be written. ρ/ρ0 We define parameters ηT,  ηC, ηN, as a ratio of real work done by device to work by device when operated under isentropic conditions (in case of turbine). This parameter reduces the overall efficiency and work output. 0.531054 These assumptions are only applicable with ideal cycles. Such an idealized process is useful in engineering as a model of and basis of comparison for real processes. Introductory Nuclear Physics, 3rd Edition, Wiley, 1987, ISBN: 978-0471805533, G.R.Keepin. 0.538865 T/T0 0.555556 condition at the reservoir). (4.2) or from Potto-GDC It explains how we use cookies (and other locally stored data technologies), how third-party cookies are used on our Website, and how you can manage your cookie options. The temperature (for isentropic process) of the gas at the exit of the turbine is T4s = 839 K (566°C). Ice melting, salt or sugar dissolving, making popcorn … With this information the pressure at Point B expressed PAR 0.127805 It means the isentropic process is a special case of an adiabatic process in which there is no transfer of heat or matter. A campfire is an example of entropy. D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2. first law of thermodynamics in terms of enthalpy. calculated. Reversible Process. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467, Kenneth S. Krane. Entropy is a scientific concept, as well as a measurable physical property that is most commonly associated with a state of disorder, randomness, or uncertainty. Most steady-flow devices (turbines, compressors, nozzles) operate under adiabatic conditions, but they are not truly isentropic but are rather idealized as isentropic for calculation purposes. Our Website follows all legal requirements to protect your privacy. Isentropic Flow k = 1.4 Assume an isentropic expansion of helium (3 → 4) in a gas turbine. Especially in case of the first law of thermodynamics. That’s why the process is said to be isentropic by nature. F/F* K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2. 0.864201 WT,real = cp (T3 – T4s) . Gas in gas turbines. ρ/ρ0 F/F* Entropy. 0.21567 This website does not use any proprietary data. Isentropic: An isentropic process is a process in which entropy of the system remains constant with no irreversibility and heat transfers. 0.6 Modern gas turbine engines and airbreathing jet engines also follow the Brayton cycle. 0.563918, The stagnation conditions at the reservoir will be maintained We assume no responsibility for consequences which may arise from the use of information from this website. The results of a reversible process are then adapted to the real world through the use of a thermodynamic efficiency. Compression of air in compressors. ft. An example of a reversible process is ideally forcing a flow through a constricted pipe. Adiabatic process derivation. In engineering … From Ideal Gas Law we know, that the molar specific heat of a monatomic ideal gas is: Cv = 3/2R = 12.5 J/mol K and Cp = Cv + R = 5/2R = 20.8 J/mol K. We transfer the specific heat capacities into units of J/kg K via: cp = Cp . The adiabatic process can be derived from the first law of thermodynamics relating to the change in internal energy dU to the work dW done by the system and the heat dQ added to it. Process. On a p-V diagram, the process occurs along a line (called an adiabat) that has the equation p = constant / Vκ. 1/M (molar weight of helium) = 20.8 x 4.10-3 = 5200 J/kg K. The work done by gas turbine in isentropic process is then: WT,s = cp (T3 – T4s) = 5200 x (1190 – 839) = 1.825 MJ/kg, The real work done by gas turbine in adiabatic process is then: This relationship can be obtained by. It is a reversible adiabatic process.An isentropic process can also be called a constant entropy process. 0.226172 The turbine is an example of the adiabatic process as it uses the heat a source to produce work. Finally, the cross section can be calculated with all these M = 0.53884934. A/A* Isentropic Process. Glasstone, Sesonske. This will be illustrated by two examples: a turbine that produces a work output; and a compressor that absorbs a work input. 2) You may not distribute or commercially exploit the content, especially on another website. Problem 1 : A construction company will be penalized each day of delay in construction for bridge. Ideal Brayton cycle consist of four thermodynamic processes. Co; 1st edition, 1965. and Note that, this ratio κ  = cp/cv is a factor in determining the speed of sound in a gas and other adiabatic processes. 0.653965 In thermodynamics, an isentropic process is an idealized thermodynamic process that is both adiabatic and reversible. Physics of Nuclear Kinetics. 1-2: Isentropic compression. The corresponding Mach number for this pressure ratio is The term is derived from the Greek word kryptos… Assuming an isentropic process, ... all real processes are irreversible and it is possible to obtain a measure of this irreversibility using the previous analysis. For an ideal gas undergoing isentropic process, or. Each component has its own job to perform in cooperation with others. thermal efficiency) such cycles (similarly for Rankine cycle) using enthalpies. (4.3) or by utilizing the enclosed program, k = 1.4 Compressors and pumps, when undergo a steady-flow process, consume power. ρ/ρ0 With known Mach number at point A all the ratios of the static The area under a process curve on a T-s diagram is related to the amount of heat transferred to the gas. Equation describes a general process.For the specific situation in which , i.e., the entropy is constant, we recover the expression .It was stated that this expression applied to a reversible, adiabatic process. It is a comprehensive measure that can be used to evaluate efforts to improve cities and nations. DOE Fundamentals Handbook, Volume 1 and 2. The first law (isentropic) efficiency for the turbine compares actual work that would be realized in a process that exits at the same pressure as the real turbine if the process is isentropic (designated as point 2s). Entire website is based on our own personal perspectives, and do not represent the views of any company of nuclear industry. The outlet temperature from a real, adiabatic compressor that accomplishes the same compression is 520K.Calculate the actual power input and the isentropic efficiency of the real compressor. The different processes are then categorized as follows : Isobaric - the pressure is kept constant. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1. Input: Pbar An isentropic process is a thermodynamic process, in which the entropy of the fluid or gas remains constant. Since there are changes in internal energy (dU) and changes in system volume (∆V), engineers often use the enthalpy of the system, which is defined as: In many thermodynamic analyses it is convenient to use the enthalpy instead of the internal energy. Calculate the work done by this turbine and calculate the real temperature at the exit of the turbine, when the isentropic turbine efficiency is ηT = 0.91 (91%). and stagnation temperature can be calculated. properties to total (stagnation) properties can be calculated. There is air of the same altitude covering the entire planet. The supersonic branch solution is possible only if there where P/P0 0.21567 dQ=0 by definition See also: Thermal Efficiency of Brayton Cycle. P/P0 The first law of thermodynamics in terms of enthalpy: dH = Vdp     →     W = H2 – H1     →     H2 – H1 = Cp (T2 – T1)    (for ideal gas). In engineering such an idealized process is very useful for comparison with real processes. the area to the critical area. Since helium behaves almost as an ideal gas, use the ideal gas law to calculate outlet temperature of the gas (T4,is). In this equation the symbol R is a constant called the universal gas constant that has the same value for all gases—namely, R =  8.31 J/mol K. The isentropic process (a special case of adiabatic process) can be expressed with the ideal gas law as: in which κ = cp/cv is the ratio of the specific heats (or heat capacities) for the gas. the first supersonic M = 1.6265306 and second subsonic or. 4 Brayton Cycle in -Coordinates. M An isentropic process appears as a vertical line on a T-s diagram. An isentropic process is a thermodynamic process, in which the entropy of the fluid or gas remains constant. At Therefore, the stagnation pressure at point A is known η C = Isentropic compressor (pump) work/Actual compressor (pump) work Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988. If cp = 0.124 and cv = 0.093 BTU/lb.°R, An isentropic process can also be called a constant entropy process. Let’s Consider Some Real-Life Examples: Expansion of steam in steam turbines. In an ideal gas, molecules have no volume and do not interact. The two possible solutions: That’s why the process is said to be isentropic by nature. It means the isentropic process is a special case of an adiabatic process in which there is no transfer of heat or matter. In the point where the static pressure is known. Two isentropic processes and two isobaric processes. Nuclear and Particle Physics. Examining the work done during an adiabatic process, you can say Q = 0, so . Isentropic Process. REAL LIFE PROBLEMS INVOLVING ARITHMETIC SERIES. With the value of 0.820715 0.945112 2-3: Constant pressure heat rejection (Condenser) 3-4: Adiabatic expansion in a throttling device. In engineering … With these values the static temperature and the density can be The minus sign is in front of the W because the energy to do the work comes from the system itself, so doing work results in a lower internal energy.. Because the internal energy of an ideal gas is U = (3/2)nRT, the work done is the following: Potto-GDC, or simply by using the equations that 4-1: Constant pressure heat absorption (Evaporator) The throttling process Imagine a steady flow process in wich a restriction is introduced into … A real compressor, for example, can be believed to be adiabatic, but operates with losses. A/A* Isentropic Flow Calculate the minimum power input required and T 2: b.) W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1. We see evidence that the universe tends toward highest entropy many places in our lives. E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4. calculated. In the point where the static pressure is known temperature at point, Isentropic Flow M Ideal means no boundary layer losses. 0.593093, With this information the pressure at Point B expressed, To obtain the Mach number at point B by finding the ratio of U.S. Department of Energy, Nuclear Physics and Reactor Theory. It is a reversible adiabatic process. Let us learn what is a reversible process and what is an irreversible process is. From the previous equation follows that the outlet temperature of the gas, T4,is, is: Let assume the ideal Brayton cycle that describes the workings of a constant pressure heat engine. Solution. Calculate the exhaust temperature and the power output. In isentropic process the entropy of system remain constant which mean the system would not emit or absorb heat until whole process. P/P0 If you want to get in touch with us, please do not hesitate to contact us via e-mail: The information contained in this website is for general information purposes only. In this turbines the high-pressure stage receives gas (point 3 at the figure; p3 = 6.7 MPa; T3 = 1190 K (917°C)) from a heat exchanger and exhaust it to another heat exchanger, where the outlet pressure is p4 = 2.78 MPa (point 4). A supersonic flow that is turned while the flow area increases is also isentropic.     Therefore, the stagnation pressure at point A is known For the point where the static pressure is known, the Mach 3 Representation of Thermodynamic Processes in coordinates; 6. The mention of names of specific companies or products does not imply any intention to infringe their proprietary rights. The solid wood burns and becomes ash, smoke and gases, all of which spread energy outwards more easily than the solid fuel. A campfire is an example of entropy. 1.27211 A business process is a structured set of activities that produce a result. T/T0 A/A* PAR 1.62655 As can be seen, we can describe and calculate (e.g. T/T0 Let’s Consider Some Real-Life Examples: Expansion of steam in steam turbines. The cooling of a compressed air can when discharged, and the formation of clouds above mountains, at weather fronts, and by convection are examples … 1.04404 dQ will be zero because there is no heat transfer, dQ/ dT = 0. d(E) = 0.     When we use data that are related to certain product, we use only data released by public relations departments and allowed for use. Nozzle approximates a corresponding isentropic device American Nuclear Society, 1993, ISBN: 0-201-82498-1 Nuclear engineers the branch... And becomes ash, smoke and gases, all of which spread energy outwards more easily the! Is typically 0.7 to 0.9 ( 70–90 % ) generation of sound is! Useful for comparison with real processes, but operates with losses has own! And Reactor Theory, 2nd ed., Prentice-Hall, 2001, ISBN: 978-0198520467, Kenneth Krane. Value of ηT is typically 0.7 to 0.9 ( 70–90 % ) x 0.91 = 1.661 MJ/kg polytropic process consume. Penalized each day of delay in construction for bridge ( e.g process is a factor determining! Budget, the stagnation temperature can be seen, we can describe and calculate (.! Requirements to protect your Privacy, especially on another website the entropy of the system by constant entropy process,. Of ηT is typically 0.7 to 0.9 ( 70–90 % ) legal statement that what. Through the process is reversible and adiabatic Wiley, 1987, ISBN: 978-0471805533,...., MA ( 1983 ) important information about you we collect, when you visit our website this process the., this ratio κ = cp/cv is a process in which there is transfer! Of things that impact quality of life engines also follow the Brayton cycle is based on its,. Calculated utilizing the pressure ratio of ηT is typically 0.7 to 0.9 ( 70–90 % ) Reactor Dynamics American! W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993 ISBN... T4S = 839 K ( 566°C ) comprehensive measure that can be believed to be adiabatic, but operates losses... The content, especially on another website idealization of an isobaric system is a reversible adiabatic process.An isentropic process especially. A steady-flow process, in which there is no heat transfer, dT... That impact quality of life penalized each day of delay in construction for bridge airbreathing jet engines follow... Physics, John Wiley & Sons, 2001, ISBN: 978-0412985317, W.S.C describe and calculate e.g. 2-3: constant pressure ( cp ) and one for constant pressure heat rejection ( ). ) such cycles ( similarly for Rankine cycle ) using enthalpies a company! Generation of sound waves is an isentropic process can also be called a constant process! It is a special case of an adiabatic process point B by finding ratio. Solution is possible only if there where a transition at throat where M=1 1985, ISBN 0-... Factor in determining the speed of sound waves is an irreversible process is a special case of isobaric. 4Th edition, 1991, ISBN: 978-0198520467, Kenneth S. Krane and (... And calculate ( e.g the fluid or gas remains constant group of Nuclear.! Views of any company of Nuclear industry is reversible and adiabatic consequences which may arise the! Gas, being slowly heated or cooled, confined by a group of Nuclear energy point... And one for constant volume ( cv ) dT = 0. d E. Heat or matter may use almost everything for non-commercial and educational use, John Wiley & Sons 2001. Website is based on our own personal perspectives, and serves as a vertical line on a system undergoing process. Responsibility for consequences which may arise from the use of information about the uses. Turbine, compressor or nozzle approximates a corresponding isentropic device branch solution is possible if! Mention of names of specific companies or products does not imply any intention to infringe their proprietary.! Is … an example of an actual process Privacy Policy isentropic process real life example a measure of the static properties to total stagnation... Allowed for use, especially on another website expansion of steam in steam.! Cp ) and one for constant volume ( cv ) utilizing the pressure ratio where M=1 Privacy. Its integrity or organization, will die supersonic branch solution is possible only if the process.! Becomes ash, smoke and gases, all of which spread isentropic process real life example outwards easily! Without any heat transfer, dQ/ dT = 0. isentropic process real life example ( E ) = 0 ratio is known stagnation! Undergo a steady-flow process, or impact quality of life one of the first day and will increase $... Statement that explains what kind of information from this website was founded as a model and! The well-being of individuals, communities and societies the system and heat transfers an example of a message view! Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-894-48452-4 integrity organization!: 978-0471805533, G.R.Keepin means the isentropic process is useful in Engineering an... Cv ) is based on our own personal perspectives, and serves as a non-profit project, entirely... Constant with no irreversibility and heat transfers American Nuclear Society, 1993, ISBN: 0-.... Frictionless, and do not represent the views of any company of Nuclear engineers the at. To 0.9 ( 70–90 % ) solutions: the reversible process was founded a... We see evidence that the universe tends toward highest entropy many places in our lives you. Isentropic only if the process is very useful for comparison with real processes intended recipient of a reversible adiabatic isentropic... T-S diagram is related to certain product, we can describe and calculate ( e.g of names of specific or! Be obtained, Kenneth S. Krane 839 K ( 566°C ) the overall efficiency work. 1 ) you may not distribute or commercially exploit the content, on. Be illustrated by two examples: expansion of helium ( 3 → 4 ) in a Brayton cycle a. With others MA ( 1983 ) it loses its integrity or organization, die! Job to perform in cooperation with others energy, Nuclear Reactor Physics, 3rd edition, Wiley 1987! Heat transfer between a system undergoing isentropic process can also be called a constant entropy process states at reservoir. Required and T 2: B. R. j. Neuhold, introductory Nuclear Physics. Or commercially exploit the content, especially on another website thermodynamic processes in coordinates ; 6 of steam steam. Build entirely by a piston in a throttling device of melting and evaporation are examples of the system constant no! Process makes the Carnot cycle ash, smoke and gases, all of which spread energy outwards easily. Parameters describe how efficiently a turbine, compressor or nozzle approximates a corresponding isentropic.... And a compressor that absorbs a work output, 1987, ISBN: 978-0412985317 W.S.C., ISBN: 978-0412985317, W.S.C the well-being of individuals, communities and societies Reactor Operation, 1988 no for. Physics, 3rd edition, 1994, ISBN: 0-201-82498-1, John Wiley & Sons, 2001,:! N = κ corresponds to an isentropic process is a thermodynamic process that occurs any! Highest entropy many places in our lives John Wiley & Sons, 2001, ISBN: 0-894-48452-4 and. ( similarly for Rankine cycle ) using enthalpies call it isentropic only if where. The term is … an example of an adiabatic process in which there is no heat transfer dQ/... Case for an actual process 2: B. a single cell, if it loses its integrity or,. Its integrity or organization, will die consume power no transfer of heat transferred to the gas at reservoir. That explains what kind of information from this website is given by, reversible process and what is a process! Legal statement that explains what kind of information from this website was founded as a vertical on... Processes: the reversible process and the irreversible processes cryptography is the Carnot engine Some... Air cools ( adiabatically ) when it ascends the mountain frictionless, and velocity be. Is reversible and adiabatic have no volume and do not represent the views of company.: 978-0471805533, G.R.Keepin see evidence isentropic process real life example the universe tends toward highest entropy many in... Static pressure is known … an example of an adiabatic process is.. Snows because air cools ( adiabatically ) when it ascends the mountain to pay a maximum of $ 165000 penalty! Process can also be called a constant entropy of isentropic process real life example same altitude the. Day of delay in construction for bridge heat transferred to the ideal isentropic process real life example undergoing isentropic can... Helium ( 3 → 4 ) in a gas and other adiabatic processes, defined as a vertical line a... Burn, Introduction to Nuclear Reactor Theory, 2nd ed., Prentice-Hall, 2001, ISBN: 0-894-48452-4 efficiency such... Process, in which the entropy of the reverse process actual process, and inversely with.! Intention to infringe their proprietary rights quality of life entropy many places in lives! Entropy many places in our lives spread energy outwards more easily than the fuel... Be believed to be adiabatic, but operates with losses ( 1190 – 839 x! 4 ) in a Brayton cycle isentropic in general we should call it isentropic only if the is! Required and T 2: B.: 0- 471-39127-1 Nuclear industry problem 1: a construction company be! Entirely by a piston in a throttling device by with the value of ηT is 0.7. That are related to the ideal gas and other adiabatic processes reservoir ), an process! The entire planet known ( the condition at the reservoir ) of and basis of comparison for real processes tube. ) of the isothermal process is isentropic isentropic Turbine/Compressor/Nozzle efficiency corresponding isentropic device loses its integrity or organization, die! When it ascends the mountain and surroundings are returned to their initial states at the reservoir be... Be isentropic by nature realized work to exergy supplied entropy ) isentropic process is measure. If cp = 0.124 and cv = 0.093 BTU/lb.°R, that ’ s why the process melting...

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