12 THERMODYNAMICS Zeroth law of thermodynamics Two systems separately in thermal equilibrium with a third system are in thermal equilibrium with each other. Isotherm It is the graph connecting pressure and volume for an isothermal process. Internal energy When heat is given to a system, the kinetic energy and potential energy of its molecules increases. Internal energy is the sum of kinetic energy and potential energy. First law of thermodynanics The energy supplied to a system is used to increase the internal energy of the system and for doing work.ie, Q = U + W Isothermal process Adiabatic It is the graph connecting pressure and volume for an adiabatic process. It is steeper than isotherm. Its slope is times the slope of isotherm. It is a process in which temperature of the system is a constant. Isobaric process It is a process in which pressure of the system is a constant. Isochoric process: It is a process in which volume of the system is a constant. Thermodynamic variables: A thermodynamic system is characterized by pressure, volume and temperature. These variables are called thermodynamic variables. For an isothermal process For an adiabatic process: PV = constant OR TV = constant OR T P = constant. Phase diagram It is the graph connecting pressure and temperature. Pressure is taken along the Y axis and temperature is taken along X axis. Triple point It is the point in phase diagram, at a particular temperature and pressure where solid, liquid and gaseous states of a substance co-exist. PV = constant OR P 1 V 1 =P 2 V 2 Unique Learning Centre, Ulloor, Tvpm. Phone: 0471 2441488 Page 1
Phase diagram showing triple point of water and CO 2 are given. Work done in an adiabatic process W = - ] where is initial temperature and is the final temperature. Adiabatic wall is an insulating wall that does not allow the flow of heat. Diathermic wall is a conducting wall that allows the flow of heat from one system to another. Quasi static process Specific heat of a gas at constant volume It is the amount of heat required to rise the temperature of 1kg of a gas through one kelvin keeping the volume constant. Specific heat of a gas at constant pressure It is the amount of heat required to rise the temperature of 1kg of a gas through one Kelvin keeping the pressure constant. The unit of molar specific heat is Jmol -1 K -1. If the system which is in mechanical and thermal equilibrium with its surroundings undergoes change in conditions very slowly, then it can keep the equilibrium as such. This type of a change is called quasi-static process. Example for non-equilibrium states: Free expansion of a gas in vacuum, A mixture of gases undergoing an explosive chemical reaction. Heat engine is a device that converts heat energy to mechanical energy. C p greater than C v Mayer s relation C p C v =R Reversible process It is a process which can be reversed such that the system and surroundings pass exactly through the same stages as in the original process with no change anywhere else in the universe. Cyclic process It is a process in which the system undergoes changes, passes through different stages and finally arrives at the initial stage. Work done in an isothermal process W = RT ln = 2.303 RT log[ where is initial volume and is the final volume. Internal combustion engine : In it the fuel is burned in a cylinder of fixed volume.eg: petrol engine, diesel engine In an external combustion engine, the fuel is burned outside.eg : steam engine. Carnot s engine Main Parts Working substance It is an ideal gas taken in a cylinder whose base is conducting and walls are nonconducting. It is provided with a tight, frictionless piston. Hot reservoir(source) It is a body at high temperaturet 1 K. The working substance absorbs a quantity of heat Q 1. Unique Learning Centre, Ulloor, Tvpm. Phone: 0471 2441488 Page 2
Cold reservoir(sink) It is a cold body at a low temperature T 2 K. The working substance rejects a quantity of heat Q 2 to it. Insulating stand It is a stand made of an insulator. Steps of working Isothermal expansion The cylinder containing ideal gas is kept on the hot reservoir. The gas is allowed to expand isothermally. The conditions of the gas changes from P 1,V 1,T 1 to P 2, V 2, T 1. Work done by the gas, W 1 2 = Q 1 = R ln Adiabatic expansion The cylinder containing ideal gas is kept on the insulating stand. The gas is allowed to expand adiabatically.the conditions of the gas changes from P 2, V 2,T 1 to P 3, V 3, T 2. Work done by the gas, W 2 3 = - ] Isothermal compression The cylinder containing ideal gas is kept on the cold reservoir. The gas is compressed isothermally. The conditions of the gas changes from P 3, V 3, T 2 to P 4, V 4, T 2.The gas rejects heat equal to Q 2 to the cold body. Work done on the gas, W 3 4 = Q 2 = R ln Adiabatic compression The cylinder containing ideal gas is kept on the insulating stand. The gas is allowed to expand adiabatically. The conditions of the gas changes from P 4 V 4 T 2 to P 1 V 1 T 1.Thus the initial state is arrived. Hence the process is cyclic. Work done on the gas, W 4 1 = - ] The PV diagram showing these changes is given below. Efficiency of the engine, ƞ= Refrigerator : = 1- In a refrigerator,reverse Carnot cycle is performed. The working substance is called refrigerant(freon).here a quantity of heat Q 2 is absorbed from a cold body(freezer unit) and a quantity of heat Q 1 is rejected to a hot body(atmosphere). The work is done by the compressor pump. Coefficient of performance, = Second law of thermodynamics Kelvin s statement: No process is possible whose sole result is the absorption of heat from a reservoir and conversion of it to work. Claussius Statement: No process is possible whose sole result is the transfer of heat from a colder object to a hotter object. Temperature less than absolute zero is not possible. Source of mechanical energy produced when work is done by a gas during an isothermal expansion The energy required for doing mechanical work is obtained as heat by the gas from surroundings. Source of mechanical energy when a gas does work during an adiabatic expansion The source of work is the internal energy of the gas. During an adiabatic compression, although no heat is given, the temperature rises Work is done on the gas during this process which increases internal energy. Hence temperature increases. Unique Learning Centre, Ulloor, Tvpm. Phone: 0471 2441488 Page 3
When a gas at high pressure suddenly expands, it cools. During expansion, the gas does work against high pressure. Internal energy decreases, hence temperature decreases. Two isotherms never intersect If they intersect it means that pressure and volume of a gas are the same at two different temperatures which is impossible. Kitchen cannot cooled by leaving the door of a refrigerator open. Conditions for isothermal process Walls of container must be perfectly conducting The process must be very slow. Essential conditions for adiabatic process The walls of contains must be perfectly non conducting The process must be very fast. 3. In the figure below, two systems A and B are separated by an insulating fixed wall and insulated from surroundings by insulated wall. Choose the correct option regarding above information. (a) The pressure of A and B will change with time. (b) The temperatures of A and B will change with time. (c) The thermodynamics states of A and B will not change with time. (d) All the above. 4. The two gases are separated by a fixed diathermic wall with initial states as (, ) and (, `). Multiple choice Questions: 1. According to initial theory, the heat was considered as fluid called Caloric. The caloric (a) flows from hotter to colder body (b) flows from colder to hotter body (c) could flow in either direction, depending on height of the bodies. (d) None of the above 2. Choose the correct options. (a) Thermodynamics laws were established before molecular picture of matter was established. (b) Thermodynamics deals with conversion of heat into other forces of energy. (c) Thermodynamics deals with macroscopic variables like volumes, temperature, mass etc. (d) All of the above Choose the correct statements. (a) The thermodynamic states of A and B will not change with time. (b) There will be a flow of energy between the two systems until the equilibrium is attained. (c) The states of the two systems will change until the equilibrium is attained. (d) Both (b) and (c ) 5. If two systems are in thermal equilibrium with each other, it means their (a) Masses are equal, temperature may be unequal. (b) temperatures are equal. (c) masses and temperatures are equal (d) None of the above 6. If a system is in thermodynamics equilibrium with its surroundings,it means (a) Temperature of the system and surroundings must be same. Unique Learning Centre, Ulloor, Tvpm. Phone: 0471 2441488 Page 4
(b) Pressure, volume, temperature of the system and surroundings must be same. (c) pressure, volume, temperature of systems and surroundings may be different. (d) None of the above 7. Choose the correct option. (a) Zeroth law gives the concept of temperature. (b) Temperature measures hotness of the body (c) Heat flows from higher temperature to low temperature until thermal equilibrium is attained. (d) All of the above 8. According to zeroth law, which physical quantity must have same value for the two systems to be in thermal equilibrium? (a) Pressure (b) temperature (c ) volume (d) composition 9. Internal energy (U) of a gas depends on the (a) kinetic energy of the system (b)molecular kinetics and potential energies (c )disordered energy associated with the random motion of the molecules (d) Both (b) and ( c) 10. For an ideal gas, internal energy depends on (a) only molecular kinetic energy (b) only potential energy of the molecules (c ) Both kinetic and potential energies of the molecules. (d)none of the above 11. Choose the state variable from the given options. (a) heat (b) work (c )Internal energy (d) All of these 12. Choose the correct option. (a) is path dependent (b) is a state variable (c ) is a state variable (d) None of these 13. According to first law of thermodynamics (a) any process that involves energy conservation is possible in nature (b) + (c) Both (a) and (b) (d) Neither (a) or (b) 14. Choose the correct option. (a) U is state variable (b) is path independent (c ) are path dependent. (d) All of the above 15. ( ) (a) path dependent (b) path independent (c )equal to (d) Both (b) and ( c) 16. Work done ( ) by a gas to move the piston in a system against a constant pressure is (a) (b) (C ) (d) + 17. For isothermal expansion of an ideal gas, (a) + (b) + (c ) + (d) Both (b) and (c ) 18. Heat capacity of a substance depends on (a) the mass of the substance (b) the temperature of the substance (c )Both (a) and (b) (d) Neither (a) or (b) 19. An ideal gas having molar specific heat capacity at constant volume is 3/2 R,the molar specific heat capacities at constant pressure is (a) (b) (c ) (d) Unique Learning Centre, Ulloor, Tvpm. Phone: 0471 2441488 Page 5
20. Specific heat capacity of water (a) depends on mass of water (b) depends on temperature (c )remains constant (e) None of the above 21. Choose the correct option. (a) = ( U internal energy) (b) = + (c) = (d) All of the above 22. A system is provided with 200 of heat and the work done by the system on the surrounding is 40J. Then its internal energy (a) increased by 600 J (b) decreases by 800 J (c ) increased by 800 J (d) decreased by 50 J 23. Extensive state variables (a) indicate size of a system (b ) become half, if we divide a system into two equal parts (c ) are internal energy,mass and volume (d) All the above 24. Intensive state variables 25. (a) Do not become half, when system is divided into two equal parts. (b) pressure,temperature, density are intensive state variables (c) Both (a) and (b) (d) (d) Neither (a) or (b) In the above figure, initially system is at (, ), the system wants to reach at (, ). Choose the correct option. (a) The system could reach from initial to final state through quasi - static process by changing the external pressure by very small amount and left the system equalise its pressure with surroundings and continue process slowly, in this way its pressure could reach at (b) In the similar process as stated in option (a) the system can reach at temperature (c) Both (a) and (b) (d) Neither (a) nor(b) 26. In an isothermal process, for an ideal gas (a) =0 (c) 0, constant (b) (d) None of these 27. In an isothermal process, for an ideal gas (a) U = 0 (b) 0 (C) 0 (d) V = 0 28. In an isothermal expansion, (a) 0 (b) + (c) 0 (d) Both (a) and (b) 29. In an isothermal compression, (a) 0 (b) (c) 0 (d) Both (a) and (b) 30. In adiabatic process, 31. (a) 0 (b), 0 (c) 0 (d) None of these Among given curves which one could represent isothermal process? (a) Curve A Unique Learning Centre, Ulloor, Tvpm. Phone: 0471 2441488 Page 6
(b) Curve B (c) Curve C (d) None of the curves could represent isothermal process 32. A gas is taken from to by two processes, one is isothermal and other is adiabatic.choose the correct option for P-V graph for the two processes? 37. 1 of an ideal gas goes from an initial state A to final state via two processes. It first undergoes isothermal expansion from volume to 3 and then its volume is reduced from 3 to at constant pressure. The correct ( ) diagram representing the two processes is (a) = (b) > (c) < (d) Information is insufficient 33. In adiabatic process, (a) Δ Δ (b) constant (c) Temperature changes (d) All of these 34. A gas is compressed isothermally to half of its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Then, (a) Compressing the gas through adiabatic process will require more work to be done 38. For isochoric process, (a) 0 (c)volume is constant (b) (d) All of these 39. Figure below shows two paths that may be taken by a gas to go from a state A to a state C. (b) Compressing the gas isothermally or adiabatically will require the same amount of work (c) Which of the case (whether compression through isothermal or through adiabatic process) requires more work will depend up on the atomicity of the gas. (d) compressing the gas isothermally will require more work to be done 35. An adiabatic process must be a (a) Quasi-static process (b)quasi-dynamic process (c )Very slow process (d )Very fast process 36. In an adiabatic process, when pressure is increased by %, if decreased by about = 3/2,then the volume (a) % (b) % (c ) 4% (d) % In process AB,400 of heat is added to the system and in process,100 of heat is added to the system.the heat absorbed by the system in the process. Will be (a) 300 (b) 380 (c ) 500 (d) 460 40. For isobaric process, (a) )= ( - ) (b) + (c) = p is fixed (d) All the above 41. A container having 1 of a gas at a temperature 27 C has movable piston which maintains constant pressure of 1 atm in Unique Learning Centre, Ulloor, Tvpm. Phone: 0471 2441488 Page 7
container. The gas is compressed until temperature becomes 127 C The Work done is ( for gas is 7.03 cal/mol K) (a) 703 (b) 814 (c ) 121 (d) 2035 42. A thermodynamic system undergoes cyclic process as shown figure. The work done by the system in the cycle is (a) Working substance takes heat from hot reservoir (b) Working substance does work, = on the environment (c) > (d) All of the above 46. Choose the correct option regarding above refrigerator. (a) (b) zero (c) (d) 2 43. moles of an ideal gas undergoes a process and as shown in the figure. The maximum temperature of the gas during the process will be (a) (b) (c) (d) 44. Choose the correct option for the curve shown below. 45. (a) For the process ABCD, Δ = 0 (b) For the process ABCDA, W is negative (c) Both (a) and (b) (d) None of the above (a) The heat extracted by working substance is (b) The heat released by working substance to hot reservoir is greater the (c) Work done on the system is (d) All of the above 47. The temperature inside a refrigerator is and the room temperature is. The amount of heat delivered to the room for each joule of electrical energy consumed ideally will be (a) (c) (b) (d) 48. According to second law of thermodynamics, (a) a heat engine cannot have efficiency equal to 1 (b) a refrigerator (or heat pump) could have infinite value of coefficient of performance (c) a heat engine can convert heat fully in work (d) Heat can flow from cold to hot body 49. Irreversibility arises (a) because most of the process are not quasistatic (b) Because resistive force, exist everywhere around us (c) Both (a) and (b) (d) Neither (a) or (b) 50. Reversibility is not possible because of Choose the correct option regarding above heat engine. (a) resistive force present everywhere (b) every process around us is Quasi-static (c ) gases are viscous Unique Learning Centre, Ulloor, Tvpm. Phone: 0471 2441488 Page 8
(d ) gases have density 51. According to Carnot, which type of engine working between two temperatures and have maximum efficiency? (a) Reversible engine (b ) Irreversible engine (c )External combustion engine (d)diesel engine 52. Carton engine is a (a) irreversible (b) Petrol engine (c ) reversible (d) Diesel engine 53. Here, is a irreversible heat engine and R is a reversible heat engine working between two temperatures and. We have coupled the two engines in a way that act as a heat engine and R as a refrigerator. ( > ) If η, it could mean for system (a) ) > ) (b) The system extracts ( ) heat from cold reservoir and changing it completely into work (c) Option (c) violates second law of thermodynamics, so η (d) All of the above 54. A Carnot engine having an efficiency of = heat engine is used a refrigerator. If the work done on the system is 10 J, the amount of energy absorbed from the reservoir at lower temperature is (a) 1 J (b) 100 J (c) 99 J (d) 90 J 1. (b) HINTS AND EXPLANATIONS According to initial theory caloric flows from colder to hotter body. Caloric was assumed to flow from colder body to hotter body. It was assumed to be fine invisible fluid filling the pores of substance. It was assumed that colder body has more caloric as compared to hotter body, so it flows from colder to hotter body 2. (d) Thermodynamic is a macroscopic science. It deals with bulk system and does not go into the molecular constitution of matter. It concepts and laws were formulated in the nineteenth century before the molecular picture of matter was firmly established. Thermodynamic description of a gas avoids the molecular description altogether. Instead the state of a gas in thermodynamic is specified by macroscopic variables such as pressure, volume temperature mass and composition that are felt by our sense perceptions and are measurable. 3. (c) The thermodynamic states of A and B will not change with time. It means both the systems are in thermal equilibrium separately. A adiabatic wall is an insulating wall. 4. (d) The energy flows between two systems until they both attain equilibrium and finally the state variables of two systems become constant. Diathermic wall is conducting wall. 5. (b) If two systems are in thermal equilibrium with each other, it means their temperatures must be same. Masses may be equal or unequal. 6. (a) If a system is in thermodynamic equilibrium with its surroundings it means that its state variables will not change with time which is possible only when systems temperature is surroundings. Unique Learning Centre, Ulloor, Tvpm. Phone: 0471 2441488 Page 9
7. (d) For example, a book lying on table does not work itself. It does not rise itself by lowering its internal energy U. Heat flows from body A to body B because temperature of body A is higher. At thermal equilibrium, = A in equilibrium with C A in equilibrium B in equilibrium with C with B zeroth law. 8. (b) According to zeroth law, temperature should be the physical quantity that will be for two systems to be in thermal equilibrium. According to this law. If and 9. (d) Internal energy of gas depends on the molecular kinetic and potential energies associated with (random motion) of the molecules of the gas. 10. (a) For an ideal gas internal energy depends only on the molecular kinetic energy. 11. (c) Internal energy is a state variable. Heat and work are not state variables. Heat and work are related to changing the state but not to actual state of system. 12. (d), are not state variable, they are cause and effect. depends on final state and initial state only, it does not depends on path (i.e., how change is brought about). So is path independent. 13. (c) According to first law, any process that involves energy conservation is possible in nature but in reality there are many process that are allowed by first law but never happen in nature. According to first law, = + In = + = 0 0 = + If is negative, then is positive. Theoretically possible, but not observed partially. 14. (d) Internal energy is a state variable and depends on the initial and final states only, it is path independent. It means that, if one has to go from (, ) to (, ) it can take any path but for every path will be same. and are path dependent. 15. (d) = and it is path independent. 16. (c) Work done against constant pressure, Volume = )) = = for constant -----(i) Force on piston = (Pressure)(area) = Let piston moves a distance Work = Force = )) ) = = finite work, = very small work 17. (d) For isothermal expansion, = 0 = +ve + ve 18. (c) Unique Learning Centre, Ulloor, Tvpm. Phone: 0471 2441488 Page 10
S depends on the mass of the substance and its temperature. Heat capacity, S = If given mass is increased, then S increases. 19. (b) = = + = + 20. (b) Specific heat capacity of water depends on temperature as shown figure. 21. (d) = = = Using first law of thermodynamics At constant, = 0 = = = From ideal gas equation, = = 1, = At constant p, p = R = = + 22. (c) = + 200 cal = 200 4.2 = 840, = + 40 From first law of thermodynamics, = + 23. (d) = = 840 40 = 800 The internal energy of the system increases by 800. Extensive state variables indicate size of a system. Their value becomes half when system is divided into two equal parts. Mass, internal energy and volume are the examples of extensive state variables. 24. (c) Temperature, pressure and density are intensive variable as they do not depend on size or extent of gas taken. Intensive variable does not change when size of sample is changed. 25. (c) When piston is pushed slowly for short times p increases from to +, system is left undisturbed to equalize with surroundings, here temperature changes from to +. Like the process is continued to achieve pressure and temperature.in the process, there may be a requirement of heating the cylinder to increase temperature. At every stage difference of pressure temperature between system and surroundings is very small. 26. (c) In an isothermal process for an ideal gas, = constant, = 0 and = 0 For example that expansion of gas in a metallic cylinder of high specific heat capacity kept in a hot reservoir is an isothermal process. 27. (c) The internal energy of an ideal gas depends only on its internal kinetic energy (of motion of molecules / atoms) and that depends on its temperature. So, for isothermal process internal energy of an ideal gas will remain constant = 0 28. (d) In process when temperature is constant, it is isothermal T = constant Change in = = 0 Option (a) is correct. Unique Learning Centre, Ulloor, Tvpm. Phone: 0471 2441488 Page 11
Work done = = As in expansion volume increases is is positive. Pressure p is positive = (positive) (positive) = positive option (b) is correct, 0 as work is done by. Both option (a), (b) are correct adiabatically simultaneously to half of its initial volume i.e., 29. (b) In compression, volume decreases = = = =log = as, < 30. (b) In adiabatic process, there is no exchange of, heat between system and surroundings. =0 By first law of thermodinamics = + = 0 = 31. (a) Curve A could represent an isothermal process where,. In isothermal process, temperature is constant. = At constant temperature, = constant So, with decreasing pressure, must increase to keep product constant. In curve, decreases with increasing. 32. (c) For the same and Slope of isothermal, ) < ) 33. (d) For adiabatic process, = 0 = = = and = constant As internal energy changes, the temperature must change. = 34. (a) The solution of this question can be understood by plot ting a ( ) graph for the compression of a gas isothermal and The isothermal curve is less steeper than the adiabatic curve. So area under the (p - V) curve for adiabatic process has more magnitude than isothermal curve. Hence work done in adiabatic process will be more than in isothermal process. 35. (d) An adiabatic process is a fast process. It occurs speedily so that heat does not have sufficient time to leave or enter the system. 36. (a) = K ( Poisson s equation) / = = constant Taking logarithm on both side + log = log + = 0 Unique Learning Centre, Ulloor, Tvpm. Phone: 0471 2441488 Page 12 = 100 = 100 = % Minus (-) sign implies that volume decreases by % 37. (d) According to question, first gas goes volume to 3 at constant pressure. In isothermal expansion, curve is recta hyperbola. 38. (a) An isochoric process is a constant volume process. In an isochoric process, = constant = 0 Work done = p = 0 From first law of thermodynamics, = + = + 0 =
39. (d) = 3 ( ) = 3 = 3 + ) = 2 = = 2 3 + 2 = 0 Process AB is isochoric so no work is done. Heat added to be system is 400 = + = 0 = = 400 Change in internal energy is 400. Process BC is isobaric and the work done = ) = 6 10 4 10 2 10 ) = 6 10 2 10 = 120 Heat added to be system is = 100 J. = + = (100 120) = 20 Change in internal energy is 20. Total increase in internal energy is going from state A to state C 400 20 = 380 J Work done in process AC is the area under the curve. Area of the trapezium = + ) ) = 6 10 + 2 10 ) 4 10 2 10 ) = 8 10 2 0 80 = + And the change in internal energy in process AC, we have = 380 J and = 80 J = + = 380 + 80 460 J 40. (d) Isobaric process, pressure is fixed. = + = ) = ) 41. (b) Work done at constant pressure is = p = P is pressure, the volume change, R is the gas constant, the change in temperature and n is number of moles. n = 1, = 127 = 400 = 27 = 300, R = 8.31 / = 1 8.31 400 300) W = 831 Option (b), i.e., 814 is closest. 42. (b) = + 3 ) = 2 43. (a) equation for path, = + 3 = 3 = = 3 for maximum temperature, 0 3 = 0 = and p = 3 Therefore, at these values = = 44. (b) The work done for the process ABCD, = (Area under the loop ABCDA) For process pressure has increased, volume is same. So temperature also increases. internal energy increases = positive 45. (d) Working substance take heat from hot reservoir and do some work W. Rest amount of heat = is rejected to the sink. Hence, working substance could move the wheels of a vehicle in doing some work. Hot reservoir has higher temperature 46. (d) An external work W has to be done to suck heat from the cold reservoir and = ( + ) is given to the hot reservoir. 47. (c) On removal of from refrigerator box, temperature of refrigerator interior become lower as compared to outside. Unique Learning Centre, Ulloor, Tvpm. Phone: 0471 2441488 Page 13
The amount of heat delivered to the room for each joule of energy consumed. = = = ) ) = 48. (a) Second law puts limitation on the efficiency of a heat engine and on the coefficient of performance of a refrigerator. Heat engine cannot have efficiency equal to 1 and a refrigerator cannot have infinite value of coefficient of performance. 49. (c) Most of the processes are irreversible due to two effects i. Most of the processes are not quasi - static and possess non-equilibrium states through a process. ii. Resistive forces appear everywhere around us that can be minimized but cannot be eliminated completely, they results in the loss of mechanical energy 50. (a) Reversibility is not possible because of resistive forces present everywhere and no process around us is quasi - static. 51. (a) Reversible engine has maximum efficiency. For reversible engine, according to Carnot efficiency is maximum. When heat is absorbed, it is done at constant temperature so that internal energy do not increase. During temperature change process, heat is not absorbed or released to surroundings. Process occurs slowly for least energy loss to surrounding. 52. (c) Process starts from,, and reverses back to,, after doing work (given by area enclosed ). Here,, reverse back, work done is not reversed back. Carnot engine is reversible engine working between two temperatures. 53. (d), are equipments. Efficiency of equipment is based on the work done by equipment = W = W In given figure, heat flows for R is shown assuming R as refrigerator. When heat flows, W for R is reversed, it is engine. In given system, > > (a) correct < ) < ) ) > ) (b) correct The coupled system takes heat - W from temperature reservoir and gives it back heat.. ) - ) = ------- (i) Observing net work done by coupled system + ) ----- (ii) coupled system takes heat W -W from temperature reservoir and converts completely to work. (c) correct 54. (d) This violates second law of thermodynamics. So, actually is true statement efficiency of reversible engine is more than efficiency of irreversible engine. (d) correct = = 100J and = 10 100 = 10 = 100 10 = 90 Unique Learning Centre, Ulloor, Tvpm. Phone: 0471 2441488 Page 14