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Home , Thermodynamic system

Introduction Thermodynamics is a study of physical and chemical phenomena which involve and . Practically Thermodynamics is the theory of converting heat to and understanding the role of and other properties of matter in this conversion process. Interestingly, ordinary experiences of our daily such as heat, temperature, work, energy, and properties of matter have deeply rooted with thermodynamics phenomena. Historically in 1824, Nicholas Leonard Sadi Carnot an French Engineer in his famous thesis “Reflections on the motive of fire” showed that the work produced by a is proportional to the heat transferred from the boiler to the condenser, and that in general work could only be gained from heat by a transfer from a warmer to a colder body. Generally thermodynamics contains four laws; 1. Zeroth law: deals with thermal equilibrium and establishes a concept of temperature. 2. The First law: throws light on concept of . 3. The Second law: indicates the limit of converting heat into work and introduces the principle of increase of . 4. Third law: defines the of entropy. Basic Concepts and Definitions : In thermodynamics, system is the specified matter under investigation or it is a region of space which is under consideration in the analysis of a problem. In simpler way a system may be as large as ocean and as small as a test tube in the chemistry laboratory. By dictating certain conditions and System further known as; open system, and . Open System: An open system is a system that freely exchanges energy and matter with its surroundings. For example, when you are boiling vegetables in an open pan on a stove, energy and matter are being transferred to the surroundings through steam. The pan is an open system because it allows for the transfer of matter (for example adding spices/salt to the pan or tasting what is being cooked) and for the transfer of energy (for example heating the pan and allowing steam to leave the pan). Boilers, turbines, heat exchangers. Fluid flow through them and heat or work is taken out or Supplied to them. Most of the engineering and equipment are open .

Fig. Open system Closed System: A closed system is a system that exchanges only energy with its surroundings, not matter. For example, when a lid is put a beaker and contents in the beaker are boiled, the sides of the beaker will start getting foggy and misty. This fog and mist is the steam which confirms that the beaker allows for energy transfer. Thus, even though a closed system cannot allow matter transfer, it can still allow energy transfer. Car battery, Electric supply takes place from and to the battery but there is no material transfer.

Fig. Closed system Worked example: 1. Classify each of the following systems into open or closed systems. (1) Kitchen refrigerator, (2) Ceiling fan (3) Thermometer in the mouth (4) Air compressor (5) Cooker (6) Carburetor (7) Radiator of an automobile. Solution: Kitchen refrigerator: Closed system. No flow. is supplied to compressor motor and heat is lost to atmosphere. Ceiling fan: Open system. Air flows through the fan. Electricity is supplied to the fan. Thermometer in the mouth: Closed system. No mass flow. Heat is supplied from mouth to Thermometer bulb. Air compressor: Open system. Low pressure air enters and high pressure air leaves the compressor, is supplied to drive the compressor motor. Pressure Cooker: Closed system. There is no mass exchange (neglecting small steam leakage). Heat is supplied to the cooker. Carburetor: Open system. Petrol and air enter and mixture of petrol and air leaves the carburetor. There is no change of energy. Radiator of an automobile: Open system. Hot water enters and cooled water leaves the radiator. Heat energy is extracted by air flowing over the outer surface of radiator tubes. Surroundings: Anything outside the thermodynamic system is called the surroundings. To be more perfect anything outside the thermodynamic system which affects the behaviour of the system is known as surrounding. Energy: is the ability to do work. Work is when an object moves against a force and is defined by the following equation: W = F x D ………….(1) ‘W’ represents work, ‘F’ represents force, and ‘D’ represents distance. It can be as simple as picking up a cricket ball or as complicated as pushing a bus. When you are moving an object against a force (i.e. gravity), you are doing work on that object. There are many different types of energy, but the two that will be discussed here are and . Potential energy is "stored energy," energy that contains the potential to do work when released. Any object that is stationary contains potential energy. For example, if someone is standing in a cricket ground holding a ball in their hand, the ball has potential energy. Note that the ball is stationary. Kinetic energy on the other hand, is known as the energy created by movement. Now imagine that someone is still holding that same ball in their hand. By throwing the ball, potential energy is transformed to kinetic energy, because the ball is now moving and is not stationary anymore. Heat: A form of energy associated with the motion of atoms or molecules and capable of being transmitted through solid and fluid media by conduction, through fluid media by convection, and through empty space by radiation. Temperature: Heat is energy transferred between the system and the surrounding. It is a property which is used to determine the degree of coldness or hotness or level of heat intensity of a body or Temperature is the property of matter which reflects the quantity of energy of motion of the component particles. It is also termed as a measure of the intensity of heat, i.e. the hotness or coldness of a sample or object. Work: Work is defined as the energy transferred (without transfer of mass) across the boundary of a system and surrounding. In thermodynamics, the term work denotes a means for transferring energy. Work is an effect of one system on another that is identified and measured. Work done by a system is considered negative: W > 0 i.e., for example if you throw an object. Work done on a system is considered positive: W < 0 i.e., for example if you hit by a truck. Work = Force x Distance …………….(3) The Internal Energy (E): of a system is the total energy content of the system. It is the sum of the kinetic, potential, chemical, electrical, and all other forms of energy possessed by the atoms and molecules of the system. E is path independent, but Q (heat content) and W (work done) are path dependent. For an ideal , the internal energy depends only on temperature. : Imagine heating or cooling of water as shown in below Fig. 1.4.; in both the case there will be change in heat content that means while heating, heat energy will be used for boiling water (precisely temperature was enters into the system). On the other hand while cooling water, heat is released to the surrounding (precisely temperature was going out of the system). To summarize in both the reaction (cooling or heating or any other reaction to say) there will be change in the heat content. Thermodynamically this change in the heat content was known as Enthalpy (∆H) ( in Greek “heat inside”). The heat released or absorbed in the constant pressure process is called the enthalpy change for the reaction.

Fig. 1.4. Enthalpy of the process. The following conventions are used for enthalpy changes. ∆H < 0 A reaction is exothermic when heat is given out by the system and enters into the surroundings. ∆H > 0 A reaction is endothermic when heat is absorbed by the system. Enthalpy is a very important concept in thermodynamics it can be related to other parameter like as follows; for example, if we perform a at constant pressure (P) and during that reaction if change in (∆V) takes place then enthalpy of that reaction will be equal to ∆H =∆E + P∆V ………….(4) Where ∆U is the change in the internal energy for the process. Specific : The specific heat of a substance is the heat required in calories to raise the temperature of 1 gram by 1 degree Celsius. There are two kinds of specific heats: Specific heat at constant volume, Cv (the energy required when the volume is maintained constant). Specific heat at constant pressure, Cp (the energy required when the pressure is maintained constant) The specific heat at constant pressure Cp is always higher than Cv because at constant pressure the system is allowed to expand and energy for this expansion must also be supplied to the system. Types of thermodynamic processes: We say that a has occurred when the system changes from one state (initial) to another state (final). : When the temperature of a system remains constant during a process, we call it isothermal. Heat may flow in or out of the system during an isothermal process. An isothermal process in one in which the initial and final are the same. dT = 0 : No heat can flow from the system to the surroundings or vice versa. dq = 0 It can be also defined as “The process in which neither heat enters into nor goes out of the system is called adiabatic process.” In an adiabatic process, compression always results in warming and expansion in cooling. : It is a process during which the volume of the system is kept constant. For example after hot foods are sealed in glass containers during canning, the cooling of a constant volume of material helps to seal the can shut. : It is a process during which the pressure of the system is kept constant. Specific heat of : of a substance is a measure of the amount of heat needed to raise the temperature of the substance by 1 K. Heat capacity represented by C is C = mass x = m x C. If a quantity of heat dQ added to a substance increases the temperature of the substance by dT, then: dQ = C dT ………………..(5) C = dQ / dT The amount of heat needed to raise the temperature of a given mass of gas by 1 K depends on whether the gas is kept at constant volume or constant pressure. Therefore, we have to define two types of heat capacities for a gas. Heat capacity of a gas at constant pressure is represented by CP Heat capacity of a gas at constant volume is represented by CV. Hence eq. 5 can be written as

CV = dQ / dT or CP = dQ / dT ………..(6)

First law of Thermodynamics: The first law of thermodynamics simply states that “energy can be neither created nor destroyed (conservation of energy)”. The other statement of first law is “it is impossible to construct a perpetual motion which could produce work without consuming energy”. Thus power generation processes and energy sources actually involve conversion of energy from one form to another, rather than creation of energy from nothing. For example: terms of their energy conversion processes.

Automobile Engine Chemical Kinetic

Heater/Furnace Chemical Heat

Hydroelectric Gravitational Electrical

Solar Optical Electrical

Nuclear Nuclear Heat, Kinetic, Optical

Battery Chemical Electrical

As you can see conversion between and other forms of energy are extremely important, whether you are veterinarian or a mechanical engineer. During an interaction between a system and its surroundings, the amount of energy gained by the system must be exactly equal to the amount of energy lost by the surroundings. A rock falling off a cliff, for example, picks up speed as a result of its potential energy being converted to kinetic energy. The first Law of Thermodynamics tells us that energy is neither created nor destroyed, thus the energy of the universe is a constant. However, energy can certainly be transferred from one part of the universe to another. To work out thermodynamic problems we will need to isolate a certain portion of the universe (the system) from the remainder of the universe (the surroundings). For example consider the pendulum example in real there is friction and the pendulum will gradually slow down until it comes to rest. We can define the pendulum as the system and everything else as the surroundings. Due to friction there is a small but steady transfer of heat energy from the system (pendulum) to the surroundings (the air and the bearing upon which the pendulum swings). Due to the first law of thermodynamics the energy of the system must decrease to compensate for the energy lost as heat until the pendulum comes to rest. [Remember though the total energy of the universe remains constant as required by the first Law.] Mathematical form of first law:

Suppose that a closed system having internal energy E1. Now if ‘q’ quantity of is supplied to the system, then its internal energy becomes

E1 + q

If ‘W’, work is done on the system then its internal energy further increases to become E2

Therefore E2 = E1 + q+ W

E2 - E1 = q+ W ∆E = q+ W ……….(1) If the work is done by the system then first law will get the form, ∆E = q - W …………..(2). This is a statement of the First Law of Thermodynamics. In fact, it provides a definition of change in internal energy. Sign convention: When working numerical problems we will quickly become confused if we don’t adopt a universal convention for when we use a positive sign or a negative sign. Sign Convention for work, W Work is done upon the system by the surroundings W > 0 Work is done by the system on the surroundings W < 0 Let’s look at some processes to get a better feel for defining a thermodynamic system and using the proper sign convention. Example 1. Hold a piece of ice in your hand until it melts Solution A System → You Surroundings → Ice + the rest of the universe. q < 0. Heat flows out of the system (you) into the ice. Solution B System → Ice Surroundings → You + the rest of the universe. q > 0 Heat flows into the system (ice) from you. You can see that the answer changes depending upon how you define the system, but the physical reality is exactly the same, but both solutions A and B are correct. It doesn’t matter how you define the system as long as you are consistent. 2. Consider the evaporation of sweat from your body. Solution A System → The sweat Surroundings → Your body + the rest of the universe. q > 0 Heat flows into the system (sweat) from you in order to raise the kinetic energy of the sweat molecules enough to allow them to go from the liquid phase to the gas phase. Solution B System → You Surroundings → The sweat + the rest of the universe. q < 0 Heat flows out of the system (you) into the sweat. Since heat leaves your body this cools you down. That’s why we sweat after all. Significance of First law of thermodynamics: 1. It states exact relationship between heat and work. 2. It states that certain quantity of heat will produce a definite amount of work. 3. It explains that when no work is done then, ∆E = q, that means the amount of internal energy change is equal to heat absorbed by the system. 4. It states conservation of energy. Limitations of First law of thermodynamics: 1. This law does not tell about source of heat and direction of flow of heat. The first law does not indicate whether heat can flow from a cold end to a hot end or not. For example: we cannot extract heat from the ice by cooling it to a low temperature. Some external work has to be done. 2. This law is not able to explain: why natural (spontaneous) process is unidirectional. 3. It does not tell about attainment of thermodynamic equilibrium. 4. It does not tell about feasibility of the process. 5. The first law of thermodynamics gives no information about the source of heat. Viz, whether it is a hot or a cold body. 6. It does not tell why whole amount of heat energy cannot be converted into mechanical work. Worked examples 1. A system receives 300 KJ of heat from its surroundings and does 200 KJ of work on the surroundings. What is the change in its internal energy? Solution: From first law of thermodynamics equation, ∆E = q − W q = 300 K J, W= - 200 K J (work leaves the system) Hence ∆E = 300 – (-200) = 300 + 200 = 500 KJ. 2. A quantity of gas in a cylinder receives 1500 J of heat from a hot plate. At the same time 600 J of work are done on the gas by outside forces pressing down on a piston. Calculate the change in thermal energy of the gas. Solution: ∆E = q + W q = 1500 J, W = 800 J Hence ∆E = 1500 + 600 = 2100 J. 3. Calculate the internal energy change, when a system absorbs 5 KJ of heat and does 1 KJ of work. Solution: ∆U = q - w = 5 KJ - 1KJ = 4 KJ Second law of thermodynamics: The second law of thermodynamics can also be stated using Clausius, Kelvin- Planck and statements. Clausius statement: “it is impossible for a self-acting machine working in a cyclic process without any external force, to transfer heat from a cold body to hot body”. Kelvin – Planck statement: “It is impossible to construct an engine, which is operating in cyclic process extract heat energy from a reservoir and to convert it into equivalent work without rejecting some amount of heat to surrounding” Conclusions: 1. The second law of thermodynamics asserts that processes occur in a certain direction and that the energy has quality as well as quantity. 2. The second law is also used in determining the theoretical limits for the performance of commonly used engineering systems, such as heat engines and refrigerators etc. 3. All the natural process spontaneous (irreversible). 4. Increase in entropy () favours . : According to second law of thermodynamics, no engine can have 100% efficiency (because some amount of heat energy is rejected). Base on above knowledge a cycle was developed by Sadi Carnot in 1824 to have maximum efficiency for given condition. The Carnot cycle defined as “it is a theoretical proposed by Nicolas Leonard Sadi Carnot in 1824. It is the most efficient cycle for converting a given amount of thermal energy into work, or conversely, creating a temperature difference (e.g. refrigeration) by doing a given amount of work”. Carnot cycle is the best known reversible cycle. Consider a gas (shaded area in the figure) in a cylinder‐piston (closed system). The Carnot cycle has four processes: AB: Reversible isothermal expansion: The gas expands slowly, doing work on the

Surroundings. Due to the expansion volume changes from V1 to V2. During this step a amount of heat quantity transferred from the heat source at temperature T1 to the gas. The work done by the gas during this process is given by; From first law of thermodynamics dE= q – W……(2)

Since from point A to point B, temperature remains constant ‘T1’ therefore change in internal energy (dE) equals to zero. Hence eq 2 becomes q = -W Workdone 푽ퟐ 푽ퟐ 풏푹푻 푽ퟐ 풅푽 푽ퟏ 푾ퟏ = − ∫ 푷 풅푽 = ∫ 풅푽 = 풏푹푻ퟏ ∫ = 풏푹푻ퟏ 퐥퐧 푽ퟏ 푽ퟏ 푽 푽ퟏ 푽 푽ퟐ 푽ퟏ Therefore work done along curve AB = W1 = 풏푹푻ퟏ 퐥퐧 푽ퟐ BC: Reversible adiabatic expansion: The cylinder‐piston is now insulated (adiabatic) and gas continues to expand reversibly (slowly). So, the gas is doing work on the surroundings, and as a result of expansion the gas temperature reduces from source temperature T1 to sink temperature T2. Therefore work done; From first law of thermodynamics dE= q – W….(3) We know that in adiabatic process dq =0,

From eq 3 dE= – W. In this adiabatic expansion temperature drops from T1 to T2 hence internal energy also decreases Therefore eq becomes; 휕퐸 ( )푉 x ∆ T = -W 휕푇

= Cv (T1-T2) = -W or W= -Cv (T1-T2)

Hence work done along curve BC W2 = -Cv (T1-T2) CD: Reversible isothermal compression: The gas is allowed to exchange heat with a sink at Lower temperature as the gas is being slowly compressed. So, the surroundings are doing work on the system and heat is transferred from the system to the surroundings (sink) such that the gas temperature remains constant at T2.

Since from point C to point D, temperature remains constant ‘T2’ therefore change in internal energy (dE) equals to zero. Hence from first law of thermodynamics dE= q + W , since dE = 0 q = W Workdone 푉4 푉4 푛푅푇2 푉4 푑푉 푉3 푊3 = ∫ 푃 푑푉 = ∫ 푑푉 = 푛푅푇2 ∫ = − 푛푅푇2 푙푛 푉3 푉3 푉 푉3 푉 푉4 푽ퟑ Hence work done along curve CD W = − 풏푹푻ퟐ 풍풏 3 푽ퟒ DA: Reversible adiabatic compression: The gas subjected to adiabatic compression. The gas temperature is increasing from T2 to original temperature T1 as a result of adiabatic compression. The work is done on the system Therefore work done; From first law of thermodynamics dE= q + W……(4) We know that in adiabatic process dq =0,

From eq 4 dE = W……(3). In this adiabatic expansion temperature increases from T1 to T2 hence internal energy also decreases 휕퐸 Therefore eq becomes ( )푉 ∆ T = Cv (T1-T2) = W or W= Cv (T1-T2) 휕푇

Hence work done along curve DA W4 = Cv (T1-T2)

Total work done by the Carnot cycle =W= W1+W2+W3+W4 푉1 푉3 = 푛푅푇1 ln - Cv (T1-T2) − 푛푅푇2 ln + Cv (T1-T2) 푉2 푉4 푽ퟏ W = nR 퐥퐧 (T1 – T2) [Since, V1/V2 = V3/V4] 푽ퟐ Now efficiency of the Carnot cycle can be represented as follows; work it did η = quantity of heat supplied

푉1 nR ln (T1 – T2) 푉2 푉1 푛푅푇1 ln 푉2 (T1 – T2) η = 푇1

Fig. P - V diagram for Carnot cycle

Concept of Entropy: It is very interesting to understand one of the implications of second law of thermodynamics. In essence second law says that, “the level of disorder in the universe is steadily increasing. Systems tend to move from ordered behavior to more random behavior”. Another interpretation of the second law is that “heat flows spontaneously from a hotter region to a cooler region, but will not flow spontaneously the other way (unless external work)”. This applies to anything that flows: it will naturally flow downhill rather than uphill. Therefore to enjoy real essence of second law one should know concept of entropy. Entropy is the measure of randomness or disorderness of the system. But absolute value of the entropy cannot be measured as it depends on both initial and final state of the system. Thermodynamically the entropy (S) can be defined as For a thermodynamic system which involved in a quantity of ‘Q’ at a temperature ‘T’, then a change in entropy can be measured by: 퐝퐐 ∆퐒 = ……….(15) 퐓 Importantly this equation applicable only for reversible process. Because for heat quatinty is indefinite and uncertain. Units of entropy: heat change ∆S = = K J/K absolute temperature Calories per degree. In SI unit system its unit is kilo per degree kelvin. Applications of thermodynamics in the field of : Thermodynamics has very wide applications as basis of thermal engineering. Almost all process and engineering industries, agriculture, transport, commercial and domestic activities use thermal engineering. But energy technology and power sector are fully dependent on the laws of thermodynamics. For example: (i) Central thermal power plants, captive power plants based on coal. (ii) Nuclear power plants. (iii) Gas turbine power plants. (iv) Engines for automobiles, ships, airways, and spacecraft’s. (v) Direct energy conversion devices: cells, thermionic, thermoelectric engines. (vi) Air conditioning, heating, cooling, ventilation plants. (vii) Domestic, commercial and industrial lighting. (viii) Agricultural, transport and industrial machines. All the above engines and power consuming plants are designed using laws of thermodynamics. Review Questions 1. Define thermodynamics. Justify that it is the science to compute energy, energy and entropy. 2. Discuss the applications of thermodynamics in the field of energy technology. 3. Define closed, open and isolated system, give one example of each. 4. Discuss different types of thermodynamic process. 5. State thermodynamic definition of work. Also differentiate between heat and work. 6. The system does work on the surroundings when an expands against a constant external pressure – Justify the statement. 7. The pressure exerted on an ideal gas at 4.00 atm and 300 K is reduced suddenly to 2.00 atm while heat is transferred to maintain the initial temperature of 300 K. Calculate q, W, and ∆E in joules for this process. [Ans: W = −1.25 × 103 J , q = +1.25 × 103 ∆E = 0 (ideal gas undergoing an isothermal process)] 8. Define mathematically first law of thermodynamics. Discuss its limitations & significance. Vf 9. Show that, for isothermal process, W = nRT ln Vi 10. Compare different statements of second law of thermodynamics. 11. Define Carnot cycle. With neat PV diagram, derive an expression for efficiency of the Carnot cycle. 12. Derive an expression for total work done in a Carnot cycle. Objective Questions: 1. A portion of the universe which is chosen for thermodynamic investigation is called a……. i) entropy ii) surrounding iii) system iv) boundary 2. Thermodynamics studies the transformations of: i) heat into ii) mechanical energy into heat iii) heat energy into chemical energy iv) kinetic energy into potential energy The processes or systems that do not involve heat are called i) isothermal processes ii) thermal processes iii) adiabatic processes iv) none of the above 3. Thermometer in the mouth is the example for i) entropy ii) closed system iii) open system iv) isolated system 4. The processes or systems which maintain constant temperature is called i) isothermal process ii) thermal process iii) adiabatic process iv) none of the above 5. A system receives 325 KJ of heat from its surroundings and does 200 KJ of work on the surroundings. What is the change in its internal energy? i) - 125KJ ii) -220KJ iii) 410 KJ iv) 125KJ.