Unit 1 Part 2 Thermal Sciences PDF MEA1112

Thermal Sciences MEA1112 Unit I- Part-II  Unit-1 part -II Thermodynamic Concepts of Heat and Work; Types of Work Interactions, First Law of thermodynamics for control mass and control volume, Energy as a Property, Internal Energy, Enthalpy, Specific heats.  ENERGY TRANSFER BY...

Thermal Sciences MEA1112 Unit I- Part-II  Unit-1 part -II Thermodynamic Concepts of Heat and Work; Types of Work Interactions, First Law of thermodynamics for control mass and control volume, Energy as a Property, Internal Energy, Enthalpy, Specific heats.  ENERGY TRANSFER BY HEAT Heat is defined as the form of energy that is transferred between two systems (or a system and its surroundings) by virtue of a temperature difference. The direction of energy transfer is always from the higher temperature body to the lower temperature one. Once the temperature equality is established, energy transfer stops. Heat is energy in transition. It is recognized only as it crosses the boundary of a system. Consider the hot baked potato. The potato contains energy, but this energy is heat transfer only as it passes through the skin of the potato (the system boundary) to reach the air, as shown in Fig. 1 Once in the surroundings, the transferred heat becomes part of the internal energy of the surroundings. Thus, in thermodynamics, the term heat simply means heat transfer.  Work – The Thermodynamics Concept In mechanics, when a body moving along a path is acted on by a resultant force that may vary in magnitude from position to position along the path, the work of the force is written as the scalar product (dot product) of the force vector F and the displacement vector of the body along the path ds. This work concept applies to systems for which applied forces affect only their overall velocity and position. However, systems of engineering interest normally interact with their surroundings in more complicated ways, with changes in other properties as well. Thermodynamics also deals with phenomena not included within the scope of mechanics, so it is necessary to adopt a broader interpretation of work. Thermodynamic definition of work: Work is done by a system on its surroundings if the sole effect on everything external to the system could have been the raising of a weight. Raising of a weight is, in effect, a force acting through a distance, so the concept of work in thermodynamics is an extension of the concept of work in mechanics. However, the test of whether a work interaction has taken place is not that the elevation of a weight has actually taken place, or that a force has actually acted through a distance, but that the sole effect could have been an increase in the elevation of a weight.  ENERGY TRANSFER BY WORK Consider figure showing two systems labeled A and B. In system A, a gas is stirred by a paddle wheel: the paddle wheel does work on the gas. In principle, the work could be evaluated in terms of the forces and motions at the boundary between the paddle wheel and the gas (Mechanics concept). By contrast, consider system B, which includes only the battery. At the boundary of system B, forces and motions are not evident. Rather, there is an electric current, I driven by an electrical potential difference existing across the terminals a and b. This type of interaction at the boundary can be classified as work follows from the thermodynamic definition of work. Imagine the current is supplied to a hypothetical electric motor that lifts a weight in the surroundings.  Energy Transfer by Work-contd.. It is also a form of energy in transit like heat. Energy can cross the boundary of a closed system in the form of heat or work. Therefore, if the energy crossing the boundary of a closed system is not heat, it must be work. For example: A rising piston, a rotating shaft, and an electric wire crossing the system boundaries. Specifically, work is the energy transfer associated with a force acting through a distance. Heat and work are directional quantities. The formal sign convention for heat and work interactions : Heat transfer to a system and work done by a system are positive; heat transfer from a system and work done on a system are negative.  Heat and Work Similarities: Both are recognized at the boundaries of a system as they cross the boundaries. That is, both heat and work are boundary phenomena. Systems possess energy, but not heat or work. Both are associated with a process, not a state. Unlike properties, heat or work has no meaning at a state. Both are path functions (i.e., their magnitudes depend on the path followed during a process as well as the end states). Dissimilarities: In heat transfer temperature difference is required. In a stable system there cannot be work transfer, however, there is no restriction for the transfer of heat. The sole effect external to the system could be reduced to rise of a weight but in the case of a heat transfer other effects are also observed.  Path and Point function Path functions have inexact differentials designated by symbol δ. Therefore, a differential amount of heat or work is represented by δQ or δW, respectively, instead of dQ or dW. Properties, however, are point functions (i.e., they depend on the state only, and not on how a system reaches that state), and they have exact differentials designated by the symbol d. For example: A small change in volume, is represented by dV, and the total volume change during a process between states 1 and 2 is ΔV, regardless of the path followed. The total work done during process 1–2, however, is:  Food for thought (a) A well-insulated electric oven is being heated through its heating element. If the entire oven, including the heating element, is taken to be the system, determine whether this is a heat or work interaction. (b) in the above problem, if the system is taken as only the air in the oven without the heating element.  Types of work 1. Electrical work 2. Mechanical work 3. Moving boundary work 4. Flow work 5. Gravitational work 6. Acceleration work 7. Shaft work 8. Spring work Electrical Work In an electric field, electrons in a wire move under the effect of electromotive forces, doing work.  Mechanical Forms of work In mechanics work done by a system is expressed as a product of force (𝐹) and displacement (𝑠): 𝑊 = 𝐹. d𝑠 If the force is not constant, the work done is obtained by adding the differential amounts of work, The pressure difference is the driving force for mechanical work. Two Requirements for a work interaction between a system and its surroundings to exist: (1) there must be a force acting on the boundary, (2) the boundary must move. Therefore, the presence of forces on the boundary without any displacement of the boundary does not constitute a work interaction. Likewise, the displacement of the boundary without any force to oppose or drive this motion (such as the expansion of a gas into an evacuated space) is not a work interaction since no energy is transferred.  Moving Boundary Work / Displacement Work / 𝒑𝒅𝑽 - Work In many thermodynamic problems, mechanical work is the form of moving boundary work. The moving boundary work is associated with real engines and compressors. Contd. When the piston moves through and infinitesimal distance 𝑑𝑠 in a quasi-equilibrium manner, the force applied on piston is, 𝐹=𝑝𝐴 Then differential work transfer through a displacement of 𝑑𝑠 during this process, 𝛿𝑊 = 𝐹. 𝑑𝑠 = (𝑝 𝐴). 𝑑𝑠 = 𝑝 𝑑𝑉 When piston moves out from initial state 1 to final state 2 with volume changing from 𝑉1 to 𝑉2, The total boundary work done by the system will be, This work transfer during a process is equal to the area under the curve on a 𝑝 − 𝑉 diagram as shown in Fig.1. pdV work in various Quasi-static process Constant volume process (Isochoric): V=C W1-2=p dV=0 Constant pressure process (Isobaric): p=C Constant temperature Process (isothermal): PV=C Contd. Polytropic Process (Isochoric): pVn=C; where n is a constant 𝑐𝑝 if n=𝛾, i.e. p 𝑉 𝛾 =C: the process is called Adiabatic process (𝛾 = ) 𝑐𝑣  Flow Work Flow energy or flow work refers to work required to push a certain mass of fluid into and out of the control volume. It is necessary for maintaining continuous flow through a control volume. Consider a fluid element of volume Fig.2 𝑉, entering the control volume through a cross sectional area A as shown in Fig. If 𝑝 is the fluid pressure acting uniformly at the imaginary piston at the entrance of the control volume, the force applied on the fluid element by imaginary piston is: 𝐹=𝑝𝐴 If the fluid is pushed by a distance L, then the flow work will be: 𝑊𝑓 = (𝑝 𝐴) 𝐿 = 𝑝 𝑉 Flow work at the entrance, 𝑊𝑓1 = 𝑝1𝑉1 Flow work at the exit, 𝑊𝑓2 = 𝑝2𝑉2  Shaft Work Energy transmission with a rotating shaft is very common in engineering practice. Often the torque T applied to the shaft is constant, which means that the force F applied is also constant. For a specified constant torque, the work done during n revolutions is determined as follows: A force F acting through a moment arm r generates a torque T as: T=F×r The power transmitted through the shaft is the shaft work done per unit time, which can be expressed as: 𝑊sh = 2πnT kW Fig.3 where n is the number of revolutions per unit time.  Paddle Work/Stirring work As the weight is lowered and the paddle wheel turns, there is work transfer into the fluid system which gets stirred. Since the volume of the system remains constant, ∫pdV=0 Fig.4  Spring Work It is common knowledge that when a force is applied on a spring, the length of the spring changes (Fig. 5). When the length of the spring changes by a differential amount dx under the influence of a force F, the work done is : 𝛿𝑊 = 𝐹. 𝑑x For linear elastic springs: F=kx where k is the spring constant. Hence, the work done is expressed as: where where x1 and x2 are the initial and the final displacements of the spring, respectively, Fig.5 measured from the undisturbed position of the spring.  Free Expansion Work (Fig.6). (Fig.6), Fig.6  Other Forms of Work Work Done on Elastic Solid Bars: Work Associated with the Stretching of a Liquid Film: Problem: (Figure below). (see Figure) Problem  First Law of thermodynamics: Background ✓ First Law of Thermodynamics-Energy cannot be created or destroyed during a process; it can only change from one form to another. ✓ Is it good enough? ✓ Example ▪ Consider a room whose door and windows are tightly closed, and whose walls are well-insulated so that heat loss or gain through the walls is negligible. Now let’s place a refrigerator in the middle of the room with its door open, and plug it into a wall outlet. You may even use a small fan to circulate the air in order to maintain temperature uniformity in the room. Now, what do you think will happen to the average temperature of air in the room? Will it be increasing or decreasing? Or will it remain constant? ▪ If we take the entire room—including the air and the refrigerator—as the system, which is an adiabatic closed system since the room is well-sealed and well-insulated, the only energy interaction involved is the electrical energy crossing the system boundary and entering the room. ▪ The conservation of energy requires the energy content of the room to increase by an amount equal to the amount of the electrical energy drawn by the refrigerator, which can be measured by an ordinary electric meter. ▪ The refrigerator or its motor does not store this energy. ▪ This energy must now be in the room air, and it will manifest itself as a rise in the air temperature.  1st Law of Thermodynamics ❑ The first law of thermodynamics, also known as the conservation of energy principle. ❑ It provides a sound basis for studying the relationships among the various forms of energy and energy interactions. ❑ It states that “Energy can neither be created nor destroyed; it can only change its form.” Total energy of an isolated system in all its form remains constant. ❑ The first law of thermodynamics cannot be proved mathematically but no process in nature is known to have violated the first law of thermodynamics. ❑ It is the relation of energy balance and is applicable to any kind of system (open or closed) undergoing any kind of process. ❑ A major consequence of the first law is the existence and the definition of the property total energy E.  First Law Applied to a Cyclic Process For a cyclic process, I Law of Thermodynamics can be stated as: “When a system undergoes a thermodynamic cycle then the net heat supplied to the system from the surroundings is equal to net work done by the system on its surroundings.” Mathematically, ❖Area 1-a-2-b-1 represents the net work delivered by the system. ❖Since the system regains its initial state, there is no change in the energy stored by the system.  Joule’s Experiment The first law can be illustrated by considering the following experiment: Joule conducted a number of experiments involving different types of work interactions and found that the work expended was proportional to increase in thermal energy, i.e. 𝑄∝𝑊 ∴ 𝑄 =𝑊/𝐽 ∴ 𝑊 = 𝐽𝑄 Where, 𝐽 = Joule’s equivalent or mechanical equivalent of heat.  First Law Applied to a Process The first law of thermodynamics is often applied to a process as the system changes from one state to another. According to first law of thermodynamics: Where, Δ𝐸 = Δ𝑈 + Δ𝐾𝐸 + Δ𝑃𝐸 + 𝑜𝑡ℎ𝑒𝑟 𝑓𝑜𝑟𝑚𝑠 𝑜𝑓 𝑒𝑛𝑒𝑟𝑔𝑦 = Net change in total energy of the system. In differential form: If a closed system undergoes a change of state during which both heat and work transfer are involved, the net energy transfer will be stored or accumulated within the system. If Q is the heat transfer to the system and W is the work transferred from the system during process, the net energy transfer (𝑄 − 𝑊) will be stored in the system. Energy-A Property of the system Similarly: Hence:  Internal energy Macroscopic form of Energy: It includes macroscopic K.E. and P.E. of a system. Microscopic form of Energy: It refers to the energy stored in the molecular and atomic structure of the system, which is called molecular internal energy. Energy in storage is neither heat nor work and is given the name “Internal Energy” or “Stored Energy” of the system. Hence: Δ𝐸 = Δ𝑈 + Δ𝐾𝐸 + Δ𝑃𝐸 + 𝑜𝑡ℎ𝑒𝑟 𝑓𝑜𝑟𝑚𝑠 𝑜𝑓 𝑒𝑛𝑒𝑟𝑔𝑦 = Net change in total energy of the system.  Control Mass & Control Volume Air Compressor Connected to a Storage Tank The system boundary shown on the figure encloses the compressor, tank, and all of the piping. Case-I: This boundary might be selected if the electrical power input were known, and the objective of the analysis were to determine how long the compressor must operate for the pressure in the tank to rise to a specified value. Since mass does not cross the boundary, the system would be a control mass. Case-II: A control volume enclosing only the compressor might be chosen if the condition of the air entering and exiting the compressor were known, and the objective were to determine the electric power input. First Law Applied to a Control mass (Closed system) Most closed systems in practice are stationary, i.e. they do not involve kinetic energy and potential energy during the process. Thus the stationary systems are called nonflow systems. And the first law of thermodynamics is reduced to: In differential form: In the present of only p.dV work: In Integral form: Also for a cyclic process Δ𝑈 = 0, as the system regains its original state hence, 𝑄−𝑊=0 ∴𝑄=𝑊  Enthalpy At constant pressure:  Specific heat cv According to I law of thermodynamics Specific heat Specific heat cp Perpetual Machine of I kind 1. below Fig Example 1 below 2. 2. 3. 4.