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4, Thermodynamics 12th Science 12th - Physics Syllabus 1, Introduction: 2. Thermal Equilibrium 3. Zeroth Law of Thermodynamics 4. Heat, Internal Energy and Work 4.1 Internal Energy 4.2 Thermodynamic system and Thermodynamic Process 4.3 Heat: 4.4 Change in Internal Energy of a System 5. First Law of Thermodynamics: (Work and Heat are related) 5.1 First Law of Thermodynamics 6. Thermodynamic state variables 6.1 Thermodynamic Equilibrium 6.2 Thermodynamic State Variables and Equation of State 6.3 The p-V diagram 7. Thermodynamic Process 7.1 Work Done During a Thermodynamic Process 7.2 Heat Added During a Thermodynamic Process 7.3 Classification of Thermodynamic Processes §. Heat Engines 8.1 Heat Engine 8.2 The Heat Engine Cycle and the p-V Diagram g. Refrigerators and Heat Pumps 9.1 Heat Flow from a Colder Region to a Hotter Region 9.2 Refrigerator 9.3 Performance of a Refrigerator g.4 Air conditioner 9.5 Heat Pump 10. Second Law of Thermodynamics 10.1 Limitations of the First Law of Thermodynamics 10.2 The second law of thermodynamics, statement 11. Carnot Cycle and Carnot Engine 11.1 Significance of Reversibility in Thermodynamics 41.2 Maximum Efficiency of a Heat Engine and Carnot’s Cycle 11.3 Carnot Refrigerator 11.4 The Second Law of Thermodynamics and the Carnot Cycle 12. Sterling Cycle | Theory Notes Q. What is thermodynamics? Q. What is thermal equilibrium? Q. State and explain the zeroth law of thermodynamics. Q. What is thermometry? Q. Explain the term internal energy of a system. Q. Define thermodynamic system. Give different types of systems, Thermodynamics Thermodynamics is the branch of physics that deals with the concepts of heat and temperature and the inter-conversion of heat and other forms of energy, Thermal Equilibrium When two objects are at the same temperature, they are said to be in thermal equilibrium. At thermal equilibrium, there is no transfer of heat. Zeroth Law of Thermodynamics Statement If two systems are each in thermal equilibrium with a third system, they are also in thermal equilibrium with each other. Explanation Consider three systems A, B and C. If A and C are in thermal equi- librium and systems A and B are in thermal equilibrium, then systems B and C must be in thermal equilibrium. N+ 4 = [<> B) Zeroth law helps us to compare the temperature of different objects. Thermometry Temperature is a measurable quantity and the science of measuring temperatures is called thermometry. Internal Energy 1) The energy associated with the random, disordered motion of the molecules of a system is called internal energy of that system and is denoted by U. 2) It is the total energy of all the atoms (or molecules) of the substance. 3) For an ideal monoatomic gas (Ex. argon), the internal energy consists of translational kinetic energy only while for a poly- atomic gas (Ex. carbon dioxide), the internal energy consists of translational, rotational and vibrational kinetic energy. 4) In case of liquids and solids, the internal energy also consists of the potential energy of the molecules due to the intermolecular force of attraction. Thermodynamic System Object or group of objects having ability to exchange energy with its surroundings is called a thermodynamic system. The part of the universe other than system is called its surrounding or environment and the separation between the system and the surrounding is known as boundary. Surrounding (Environment) Boundary i System a Q. What is meant by thermo- dynamic Process? Q. Explain the term ‘Heat’. ic Process ic) properties like tem There evasurable process vome thot a system (in equilibriy, ie an i ) 0. ture (T), pressure (Poe variables or thermodynamic State are called therm functions. riables have definite 2) The condit ic va. jon at which thermodynamic the system. values is known hi state oO odynamic state of a system changes, i ic 3) The process, in w! i cess. is called as thermodynamic pro es Heat fe ergy that is transferred between the system ang its ‘ending d i nce. cuvoundine due to a temperature differe Heat is always transferred from higher temperature to lowe; eal temperature. Consider a system. Let 7;and 7: be the temperature of the syste, and its surrounding respectively. <7; ; on v he hl of the surrounding (7:) is higher than the temperature of the system (7;), then the system gains energy and Q is positive. Surrounding (1) @o (a Case 2) 7; > T; If the temperature of the system (7;) ture of the surrounding (Tr), negative. is higher than the tempera- then the system loses energy and Q is Surrounding ,) (s QO Case 3) 7;=7, If the temperature the surrounding zero. € of the system (B) is equal tot he temperature of (Tz), then there is no transfer of energy and Q is Surrounding (T) Q=0 e Q. Explain, how a change in internal energy of a system can be brought about? Q. Derive the equation for work done during the expan- sion of gas. Change in Internal Energy of a System Consider a cylinder fitted with a movable, massless and frictionless piston. The gas inside the cylinder is the system. Let 7; and 7; be the temperature of the system and its environment respectively. Internal energy of the system (gas) can be charged in following ways. 1) If the cylinder is heated or cooled, temperature difference is created between the system and the environment. This causes the exchange of energy between the two. If 7; > 7%, then the system gains energy from the environment and internal energy of the system (gas) increases. If 7; > 7;, then the system loses energy to the environment and internal energy of the system (gas) decreases. Qincreases i final T=200C i initial T=100C Tttt heat 2) If the piston is quickly pushed inside the cylinder, the gas is compressed and some work is done by the piston (environment) on the gas. Therefore the system (gas) gains energy and its internal energy increases. If the gas pushes the piston out, the gas is expanded and some work is done by the gas on the piston (environment). Therefore the system (gas) loses energy and its internal energy decreases. work is — done on the gas Work Done During the Expansion of Gas Consider an ideal gas enclosed in a cylinder fitted with a movable, massless and frictionless piston. The gas inside the cylinder is the system and the cylinder along with the piston is its environment. Let A be the cross sectional area of the cylinder and p be the constant pressure exerted by the system on the piston. If the piston moves through an infinitesimal distance dx during the expansion of the gas, then the work done is- Q. Explain thermodynamic equilibrium. Q. What is the equation of state? Q. Explain p-V diagram for a gaseous system. Thermodynamic Equilibrium Thermodynamic equilibrium consists of following three equilibria - 1) Mechanical Equilibrium A system is in mechanical equilibrium if its pressure is the same throughout and does not change with time. 2) Chemical Equilibrium A system is in chemical equilibrium if its chemical composition is the same throughout and does not change with time. 3) Thermal Equilibrium A system is in thermal equilibrium if its temperature is the same throughout and does not change with time. A system which is in thermal, mechanical and chemical equi- librium it is said to be in thermodynamic equilibrium. The state of system in thermodynamic equilibrium can be repre- sented by specifying it’s (P.V.T). These quantities are independent of time. They are called thermodynamic co-ordinates or variables of state. Equation of State 1) The measurable macroscopic properties of a system in equilib- rium are called the thermodynamic state variables. 2) State variables describe the equilibrium states of a system. 3) All the state variables of a system are not always independent. 4) The mathematical relation between the state variables is called the equation of state. Ex. Ideal gas equation pV = nRT is an equation of state. It shows the relation between pressure (p), volume (V), temperature (T) and number of moles (n) of the gas. For given n, there are only two inde- pendent variables. The third variable is dependent. p-V diagram 1) The graphical representation of equation of a system (gas) is called the p-V diagram or the p-V curve or the indicator diagram of the system. 2) The ideal gas equation is - pV = nRT pe v .at constant T A typical p-V diagram for an ideal gas at constant T is shown below- The p-V curve at a constant temperature is called an isotherm. Real gases have more complicated equations of state and p-V diagrams. 3) The area under the p-V curve represents the work done during the process. The work done by gas confined to a cylinder fitted with a movable, massless, frictionless piston is given by , iF w= [aw= [pdv This equation can be represented graphically. system i at L FPA [ |dx| Fig. Gas Enclose in Cylinder Q. Define quasi static process. work (dw) = force X displacement ee =Fdx dw = p.Adx dw = p.dV {w= p(v,-V)} a) During expansion, volume of the gas increases and Pressure decreases. The work done in this case is positive. (work = area = [‘vdv) >0 1 yoy % b) During compression, volume of the gas decreases and Pressure increases. The work done in this case is negative. (work = area= [ pav) <0 2 ¥— 1 c) When the volume changes from V; to V; at constant pressure, the work done is p(V,— V). The curve is a line parallel to the volume axis. (work = area = p(V,-¥,)) > 0 d) If the volume is constant in a thermodynamic process, the work done is zero because there is no displacement. The area under P. V curve represents work done. Quasi Static Process The process in which changes in the state variables of a system occur infinitesimally slowly so that the system is always in thermo- dynamic equilibrium, is known as quasi static process. 8 Q. Prove that heat trans- ferred toa system depends on the path followed by the system to change from initial state to final state. V, and system goes to point C. Then volume increases from j, top at constant pressure p, and system goes to final state B. The are, under the curve represents the work done. i three cases is not th As the amount of work done in above © Same it is clear that the work done by a system depends not only o, the initial and final states but also on the intermediate states j.¢, the path followed. Heat Added During a Thermodynamic Process ; Consider an ideal gas enclosed in a cylinder fitted with a Movable. massless and frictionless piston. The gas inside the cylinder is the system and the cylinder along with the piston is its environment, The initial volume V, of the system can be changed to the final volume V, by following two methods. Method 1) Vi TPP F heat (our Fig. Isothermal Expansion of Gas In this method, the gas is slowly heated so that its temperature remains constant and the volume changes from V, to V,. During this isothermal heating, some amount of heat is absorbed by the system. “O>0 Method 2) In this method, the system placed in an insulated vessel is divided into two compartments by a thin, breakable partition. Y—| i The compartment X has a volume JV, and the compartment Y has a volume J;' such that 4+ V;'= V,. Initially the compartment Y is empty. If the partition is suddenly broken, the gas undergoes sudden expansion and its volume changes from V, to V;. During this free expansion, the heat absorbed by the system is zero. “Q=0 The work done in free expansion is also zero. As the amount of heat transferred in above two cases is not the same, it is clear that heat transferred to a system depends not only on the initial and final states but also on the path followed. Q. Explain reversible and irreversible thermodynamic process. Q. Give the cause of irreversibility. Q. Give the assumptions for discussion of thermodynamic process. Thermodynamics Process A} Reversible Process 7 i A thermodynamic process that can be reversed = pei ’ reverse direction is called as reversible process. Ex. ice, boiling of water etc. and 2) The path of a reversible process is the same in the forward an the backward direction. P initial stage final stage Vv Vv, y— 3) Reversible process is very slow process and hence there is no loss of energy during the process. It is ideal process. B] Irreversible Process ; i A thermodynamic process that can not be reversed or retraced in reverse direction is called as arreversible Process. Ex. punc- turing an inflated balloon, burning a candle etc. 2) The path of an irreversible process is not the same in the forward and the backward direction. P initial stage P final stage Vv V, f ' vy 3) Irreversible process is rapid and hence there is loss of energy due to friction or some other dissipative forces. An irreversible process shows hysteresis. 4) Most of the processes in the nature are irreversible process. Cause of Irreversiblity 1) Many process such as a free expansion or an explosive chemical reaction take the system to non-equilibrium states. 2) Many processes involve loss of energy due to friction, viscosity or some other dissipative forces. Assumptions for Discussion of For the discussion of thermody tions are made. 1) Most of the thermodynamic processes are reversibl quasi static in nature, They are very slow so that t in thermodynamic equilibrium during all the chan: 2) The ideal gas enclosed in a cylinder fitted with a tionless and massless piston is the system. For process, the walls of the cylinder are good thermal conductors while for an adiabatic process, they are thermally insulated. The ideal gas equation is applicable to the system Thermodynamic Process namic processes, following assump- le. They are he system is ge. movable, fric- an isothermal 3) —— 1 Q. Discuss the thermody- namics of isobaric process. Q. What is isochoric process? Q. Discuss the thermody- namics of isochoric process. Thermodynamics of Isobaric Process Consider the isobaric expansion of an ideal gas at constant pressure p. Let V, and 7, are its volume and temperature 1n the initia aint and V, and 7, are its final volume and temperature in its final state respectively. a The work done at constant pressure is given as ~ W = pdV = p(V,- Vy) We AR(Ty = Ti) soe oe 1 Dove {-: pV = nRT} The change in internal energy of a system is given as - AU = nC AT = nC, (Tj ~ To oe(2) Where C, is the specific heat at constant volume AT =(T,-T) is the change in temperature In isobaric process. According to the first law of thermodynamics - OQ = AU + Wo ue en(3) From equations (1), (2) and (3) Q=nC(T,- 1) + R(T, ~ T) “QO = (nC, + nR)(T-T) “.Q=nC,(T- T) | Where C, is the specific heat at constant pressure. uCp=C.t+R During isobaric process, temperature and internal energy of the system change. ; . The p-V diagram of an isobaric process is called an isobar. Isochoric Process 1) The process in which volume of the system remains constant is called as isochoric process. Ex. Heating a gas in a container having fixed volume. 2) During isochoric process, volume remains constant. Hence AV=0. Thermodynamics of Isochoric Process According to the first law of thermodynamics - Q=AU+W During isochoric process, AV=0. Hence work done is zero. (W =O). W = pAv} “0 = AU.........1) Thus during isochoric process, all the energy supplied to the system is converted into its internal energy. Thus internal energy of the system increases. The change in internal energy of a system is given as - AU = nC. AT..........(2) Q. What is adiabatic process? Q. Discuss the thermody- namics of adiabatic process. Where C, is the specific heat constant volume AT is the change in temperature. From equations (1) and ve = Av enc.AT The p-V diagram of an isochoric process is called an isochore, Adiabatic Process 1) The process in which heat neither enters nor leaves the system is called as adiabatic process. Ex. A process carried out in an insulated system. . 2) During adiabatic process, the heat transferred is zero. Hence 3) Adiabatic process can be brought about by rapidly changing the state of the system so that there is no time for any exchange of heat. Ex. Puncturing an inflated balloon. 4) The p-V diagram for adiabatic process is shown below When system expands adiabatically, W is positive and AU is negative, internal energy of system decrease. W=-AU While, when system is compressed W is negative and internal energy is increased. AU =—W Thermodynamics of Adiabatic Process Consider an adiabatic expansion of gas from volume V, to V;. The work done is - w= [‘pav For adiabatic change - pV’ = constant = C Q. What is heat engine? Q. What are elements of a typical heat engine? Q. Give the types of heat engines. Q. How does heat engine work? A aeneetit rms heat partly into work or mechanical energy A device that transfor is called as heat engine. Ex. Automobile engine. ee Elements of Heat Engine A typical heat engine has t i ion peepee ee of a substance that absorbs heat ang It is the system consistin : » diesel engine, the working substance ig does work, In a gasoline or dic’ ng aa a mixture of fuel vapour and air while in a steam engine it is steam, he following elements. 2) Hot and cold reservoir Hot reservoir at higher temperature substance while the cold reservoir al the heat from the working substance. source an the cold reservoir is also calle Ty provides heat to the working t lower temperature 7c receives Hot reservoir is also called d sink. 3) Cylinder The working substance is enclo frictionless and massless piston. work by displacing the piston in t ferred to the environment. sed in a cylinder with a moving, The working substance does some he cylinder. This work is trans- Types of Heat Engines There are two basic types of heat engines 1) External Combustion Engine In this engine, the working substance is heated externally. Ex. steam, engine. 2) Internal Combustion Engine In this engine, the working substance is heated internally. Ex. gasoline or diesel engine in automobiles. Working of Heat Engine Any heat engine works in following three basic steps 1) The working substance absorbs heat from a hot reservoir at higher temperature. 2) Part of the heat absorbed by the working substance is converted into work. 3) The remaining heat is transferred to a cold reservoir at lower temperature. The energy flow diagram of the heat engine is shown below- hot reservoir T, om input (Q,) Vie oo) \ output (Q,) engine cold reservoir Ty The heat Qy absorbed by the working substance, the heat Qc trans- ferred to sink and the work done W by the working substance are represented by ‘heat pipelines’. The circle represents the engine. The width of the heat pipeline is proportional to the amount of heat or work done. _ Q. Define and explain the efficiency of heat engine. Q. Explain the p-V diagram of the heat engine cycle. | 1) The ratio of the work done by the engine (output) an Pach operating cycle of the engine consists of single execution ot eal absorption, conversion to work and transfer of remaining heat to the sink. These cycles are repeated during the working of the heat engine. . The net heat absorbed (Q) per operating cycle is - 0 = On + Oc =|On|-[Qel The net work done in one operating cycle is - w= =|Ou|-|Qcl Efficiency of Heat Engine d the amount ea of heat absorbed by it (input) is called as efficiency oF thermal efficiency of the engine. efficiency(n) = - work done (output )(W) YM) Feat absorbed (input (Qu) Wy eu lel 20= 0, = 140, =! Toy] 2) Efficiency of heat engine can also be defined as the fraction of the heat absorbed that is converted into work. , 3) Heat engine can not convert all the heat absorbed into work as some heat is always lost. WH One de Oc# 0} ane 4) Efficiency of heat engine is unitless quantity. _ p-V Diagram of Heat Engine Cycle Working of a heat engine is a cyclic thermodynamic process. The p-V diagram of a typical heat engine is shown below- Section AB The cycle begins at the point A. The working substance (gas) absorbs heat at constant volume and no work is done. Temperature and internal energy of the gas increase. The pressure is increased and it goes to the point B. Section BC The gas expands, its volume increases and work is done by the system, The pressure is reduced and it goes to the point C. Section CD The excess heat is rejected to the sink by the working substance (gas) at constant volume. The internal energy of the gas decreases and it cools down. The pressure is reduced and it goes to the point D. Q. Explain the flow of energy in refrigerator with the help of a diagram. Q. Explain the performance of a refrigerator and define its coefficient of performance. —————————— The refrigerant goes through the following steps in one —_ cycle of refrigeration, Steps 1) Adiabatic Expansion The refrigerant fluid passes through a nozzle and expands into a low- pressure area. Step 2) Isobaric e i xpansion A The cool gas extracts heat from the inner compartment of the fridge. Its temperature increases at constant pressure. Step 3) Adiabatic Com i ¢ pression i The gas is compressed adiabatically by the compressor. ores done on the gas so that it is heated and converted to a liquid. Step 4) Isobaric Compression : The hot liquid passes through coils on the outside of the fridge and heat is transferred to the surrounding at constant pressure. Thus a single cycle of refrigeration is completed. Energy Flow in Refrigerator Energy flow diagram of a refrigerator is shown below - hot reservoir Q “oy cold reservoir T, c In refrigerator, heat is extracted from a cold reservoir at 7¢ mechan- ical work is done on the refrigerant by the compressor and then the total energy is rejected at the hot reservoir at 7). Performance of Refrigerator In refrigerator, the heat absorbed by the working substance is Qc and the heat rejected by it is Q,,. The work done on the refrigerant (system) is W. The ratio of the magnitude of the heat absorbed to the magnitude of the work done is called the coefficient of performance (C)P)K or quality factor or Q-value of a refrigerator. 1Oc| coefficient of performance(K ) = For refrigerator, Qc > 0,0n < Oand W < 0 “|Ocl=+ Qc,]Ou|=— Qu and|W|=- Ww First law of thermodynamics for cyclic process is - Q. Give the coefficient of performance of air conditioner. Q. Write a note on heat pump. Q. What are the limitations oj first law of thermodynamics? Q=W 2 On + Oc = W 2 W= Oct Ou 2 [W1=|cl-|n! Therefore equation (1) becomes Qcl 1Qcl__ K= Twi > [Ql-1Oul The coefficient of performance (K) of a refrige and unitless. For a typical household refrigerator Kz 5. ator is dimensionless Coefficient of Performance of Air Conditioner Working of an air conditioner and a refrigerator is exactly similar. Therefore the coefficient of performance of an air conditioner is given as - [Qc| = cote) Ke Twi Where [Qc] is the heat absorbed the working substance |W| is the work done For air conditioner, the rate of heat removed (H) and the power (P) required for removing the heat is given as - 1Qcl Hay «.|Qc|= Ht Where f is the time in which heat 1Qc| is removed. aa -|Wl= Therefore equation (1) Beeoniel |= Pr [Qc|_ Ht __ H K=Twl > Pr P For a typical air conditioner, K is 2.5 to 3. Heat Pump Heat pump is a device used to heat a larger structure like a building. Its evaporator coils absorb heat from the cold air from outside and the condenser coils release the absorbed heat inside the building. Thus heat pump keeps the building warm. Limitations of First Law of Thermodynamics According to the first law of thermodynamics, heat can be quantita- tively converted into work and vice versa. It has the following limitations. 1) First law of thermodynamics does not predict the direction of the process. Ex. Heat can flow from higher temperature to lower temperature but not from lower temperature to higher temperature on its own. The first law of thermodynamics does not predict this practical observation. 2) According to the first law heat can be converted into work and work can be converted into heat. But the complete (100%] conversion is not possible. This implies that a heat engine can not convert heat into work completely. i.e. heat engine can not have 100% efficiency. Similarly the coefficient of performance of a refrigerator can never be infinite. 20