CHAPTER 1 BASIC CONCEPTS THEORY

Transcription

1 CHAPTER 1 BASIC CONCEPTS THEORY 1. Explain briefly the following terms with diagram (wherever necessary): a) Thermodynamic System, Surroundings & Boundary b) Control Volume & Control Surface c) Intensive & Extensive Property d) Path Function & Point Function e) Thermodynamic Equilibrium 2. Differentiate open system and control volume. Explain types of system with appropriate examples. 3. Discuss microscopic and macroscopic point of view in thermodynamics. OR How classical thermodynamics does differs from statistical thermodynamics. 4. Explain quasi static process with necessary diagrams. Darshan Institute of Engineering and Technology, Rajkot 1.1

2 CHAPTER 2 FIRST LAW OF THERMODYNAMICS THEORY 1. State 1 st Law of thermodynamics. Write down expressions for the first law applied to (i) a cycle and (ii) a process. What is difference between heat and work? Explain the conventional meanings for positive-ness and negative-ness for heat and work interactions between thermodynamic system and its surroundings across the system boundary. 2. State the first law of thermodynamics, its applications and limitations. 3. Define Internal Energy and prove that it is a property of the system. OR Prove that Energy is a point function of a system undergoing change of state. 4. Write continuity equation. Derive the general steady flow energy equation. Making suitable assumptions reduce the same for different engineering applications (i.e. Nozzle, Boiler, Cooling Tower, Steam or Gas Turbine, Hydraulic Turbine, Reciprocating Compressor, Rotary Compressor, Centrifugal Water Pump, Expansion Valve of Refrigerator, etc.) 5. Derive equation for (a) filling of a tank and (b) emptying of tank. 6. Explain displacement work and flow work. CLASS TUTORIAL 1. At the inlet to a certain nozzle the enthalpy of fluid passing is 2800 kj/kg, and the velocity is 50 m/s. At the discharge end the enthalpy is 2600 kj/kg. The nozzle is horizontal and there is negligible heat loss from it. a. Find the velocity at exit of the nozzle. b. If the inlet area is 900 cm 2 and the specific volume at inlet is m 3 /kg, find the mass flow rate. c. If the specific volume at the nozzle exit is m 3 /kg, find the exit area of nozzle. [Ans: m/s, kg/s, cm 2 ] [3.42, R. K. Rajput] 2. In a gas turbine unit, the gases flow through the turbine is 15 kg/s and the power developed by the turbine is kw. The enthalpies of gases at the inlet and outlet Darshan Institute of Engineering and Technology, Rajkot 2.1

3 are 1260 kj/kg and 400 kj/kg respectively, and the velocity of gases at the inlet and outlet are 50 m/s and 110 m/s respectively. Calculate: a. The rate at which heat is rejected to the turbine, and b. The area of the inlet pipe given that the specific volume of the gases at the inlet is 0.45 m 3 /kg. [Ans: 828 kw, m 2 ] [3.33, R. K. Rajput] 3. In an air compressor air flows steadily at the rate of 0.5 kg/s through an air compressor. It enters the compressor at 6 m/s with a pressure of 1 bar and a specific volume of 0.85 m 3 /kg and leaves at 5 m/s with a pressure of 7 bar and a specific volume of 0.16 m 3 /kg. The internal energy of the air leaving is 90 kj/kg greater than that of the air entering. Cooling water in a jacket surrounding the cylinder absorbs heat from the air at the rate of 60 kj/s. Calculate: a. The power required to drive the compressor; b. The inlet and output pipe cross-sectional area. [Ans: kw, m 2 ] [3.34, R. K. Rajput] 4. A centrifugal pump delivers 50 kg of water per second. The inlet and outlet pressures are 1 bar and 4.2 bar respectively. The suction is 2.2 m below the centre of the pump and delivery is 8.5 m above the centre of the pump. The suction and delivery pipe diameters are 20 cm and 10 cm respectively. Determine the capacity of the electric motor to run the pump. [Ans: 22.2 kw] [3.45, R. K. Rajput] 5. Air at a temperature of 20 C passes through a heat exchanger at a velocity of 40 m/s where its temperature is raised to 820 C. It then enters a turbine with same velocity of 40 m/s and expands till the temperature falls to 620 C. On leaving the turbine, the air is taken at a velocity of 55 m/s to a nozzle where it expands until the temperature has fallen to 510 C. If the air flow rate is 2.5 kg/s, calculate: a. Rate of heat transfer to the air in the heat exchanger; b. The power output from the turbine, assuming no heat loss; c. The velocity at exit from the nozzle, assuming no heat loss [Ans: 2010 kj/s, kw, m/s] [3.47, R. K. Rajput] 6. In a steam plant, 1 kg of water per second is supplied to the boiler. The enthalpy and velocity of water entering the boiler are 800 kj/kg and 5 m/s. The water receives 2200 kj/kg of heat in the boiler at constant pressure. The steam after passing through the turbine comes out with a velocity of 50 m/s, and its enthalpy is 2520 Darshan Institute of Engineering and Technology, Rajkot 2.2

4 kj/kg. The inlet is 4 m above the turbine exit. Assuming the heat losses from the boiler and the turbine to the surroundings are 20kJ/s, calculate the power developed by the turbine. Consider the boiler and turbine as single system. [Ans: kw] [3.35, R.K.Rajput] ASSIGNMENT PART 1 NON FLOW PROCESSES 1. A domestic refrigerator is loaded with food and the door closed. During a certain period the machine consumes 1 kw h of energy and the internal energy of the system drops by 5000 kj. Find the net heat transfer for the system. [Ans: -8.6MJ] [GTU JAN 2017] 2. A cylinder contains 0.45 m 3 of gas at 1 x 10 5 N/m 2 and 80 C. The gas is compressed to a volume of 0.13m 3. The final pressure being 5 x 10 5 N/m 2. Assume γ=1.4, R=294.2 J/Kg C. Calculate mass of gas, index of compression n, increase in internal energy of gas, heat rejected by gas during compression. [Ans: 0.433kg, 1.296, 49.9kJ, 17.54kJ] [GTU OCT 2012] m 3 of an ideal gas at a pressure of 2 MPa and 600K is expanded isothermally to 5 times the initial volume. It is then cooled to 300K at constant volume and then compressed back polytropically to its initial state. Determine the net work done and heat transfer during the cycle. [Ans: kJ, 0] 4. Calculate the final temperature, pressure, work done and heat transfer if the fluid is compressed reversibly from volume of 6m 3 to 1 m 3 when the initial temperature and pressure of fluid as 20 C and 1 bar respectively. Assume the index of compression as 1.4, Cp = and Cv = and R = KJ/kg-K. [GTU DEC 2014][Ans: K, bar, MJ, 0] Part 2 Steady Flow Energy Equation 5. A nozzle is a device for increasing the velocity of a steadily flowing stream. At inlet to a certain nozzle, the fluid parameter are Enthalpy = 2850 kj/kg, velocity = 50 m/s, area = 0.1 m 2, specific volume = 0.18 m 3 /kg at the discharge end enthalpy is 2650 kj/kg and the specific volume is 0.49 m 3 /kg. Make calculation for the velocity of fluid Darshan Institute of Engineering and Technology, Rajkot 2.3

5 at exit from the nozzle, mass flow rate of fluid and the exit area of the nozzle. The nozzle is horizontal and there is negligible heat loss from it. [Ans: m/s, kg/s, cm 2 ] [6.1, D.S.Kumar] 6. A perfect gas flows through a nozzle where is expends in a reversible adiabatic manner. The inlet conditions are 22 bar, C, 38 m/s. at exit the pressure is 2 bar. Determine the exit velocity and exit area if the flow rate is 4 kg/s. take R = 190 J/kg- K and γ = 1.35 [Ans: 726 m/s, E-3 m 2 ] [6.2, D. S. Kumar] 7. A steam turbine operates under steady flow conditions receiving steam at the following state: pressure 15 bar, internal energy 2700 kj/kg, specific volume 0.17 m 3 /kg and velocity 100 m/s. the exhaust of steam from the turbine is at 0.1 bar with internal energy 2175 kj/kg, specific volume 0.15 m 3 /kg and velocity 300 m/s. The intake is 3 meters above the exhaust. The turbine develops 35 kw and heat loss over the surface of turbine is 20 kj/kg. Determine the steam flow rate through the turbine. [Ans: kg/s] [6.6, D. S. Kumar] 8. A centrifugal pump delivers 2750 kg of water per minute from initial pressure of 0.8 bar absolute to a final pressure of 2.8 bar absolute. The suction is 2 m below and the delivery is 5 m above the center of pump. If the suction and delivery pipes are 15 cm and 10 cm dia. respectively, make calculation for the power required to run the pump. [Ans : Kw][6.9, D.S.Kumar] 9. A turbo jet engine is in flight at 250 m/s in the atmosphere at C. The engine operates with fuel-air ratio of and the fuel used has a calorific value of kj/kg. Due to incomplete combustion of fuel, only 95 % of energy is liberated by fuel. The engine losses 20 kj/kg of air, and the measurements indicate that temperature of gases at exit from the nozzle is C and the enthalpy values for air and gases are 250 kj/kg and 900 kj/ kg respectively. Neglecting potential energy changes for the flow streams, Make calculations for the velocity of exhaust jet. [Ans : m/s] [6.14, D. S.Kumar] 10. Air at 290 K temperature passes through a heat exchanger at 30 m/s velocity and its temperature gets raise to 1100 K. Subsequently the heated air enters a turbine with the same velocity and its expansion continuous till the temperature drops to Darshan Institute of Engineering and Technology, Rajkot 2.4

6 900 K. After exit from the turbine at 45 m/s further expansion occurs in the nozzle and the temperature falls to 790 K. If mass flow rate of air is 2 kg/s, determine : (a) Rate of heat transfer to air in the heat exchanger (b) Power output from the turbine and (c) Velocity at exit from the nozzle. Assume no heat loss and take Cp = kj/kg K for air. [Ans : 1620 kj/s ; kw; m/s][6.17, D.S.Kumar] 11. Steam at 6.87bar, 205 C enters in an insulated nozzle with a velocity of 50m/sec. It leaves at a pressure of 1.37bar and a velocity of 500m/sec. Determine the final enthalpy of the steam. Also clearly mentioned the applied assumptions. Use of steam table is permitted. Darshan Institute of Engineering and Technology, Rajkot 2.5

7 CHAPTER 3 SECOND LAW OF THERMODYNAMICS THEORY 1. Define below terms: a) Heat Engine b) Thermal Energy Reservoir c) Refrigerator d) Heat Pump 2. Give Kelvin-Plank and Clausius statement of 2 nd law of thermodynamics and prove their equivalency. OR Prove that violation of Kelvin-Plank statement leads to violation of Clausius statement and violation of Clausius statement leads to violation of Kelvin-Plank statement. 3. Prove that all reversible engines operating between operating between same temperatures limits have are equally efficient. 4. Explain Carnot theorem. OR State and prove Carnot s theorem for Heat Engine and also write statement of Carnot s theorem in the view of refrigerator and Heat Pump 5. Justify that Carnot cycle is impracticable. OR Identify the reasons for the impracticability of Carnot cycle. 6. State and explain the Perpetual motion machines of Second Kind. 7. State the comparisons of First law and Second law of thermodynamics. 8. Derive an expression for Carnot efficiency with usual notations. 9. Explain thermodynamics temperature scale. CLASS TUTORIAL 1. Two Carnot engines work in series between the sources and sink temperatures of 550K and 350K. If both engines develop equal power, derive the formulae to find out the intermediate temperature and determine the intermediate temperature also. 2. A heat engine produces a work equivalent to 80 kw with an efficiency of 40%. Determine the heat transfer rate to and from the working fluid. 3. A heat engine develop 10 kw power when receiving heat at the rate of 2250 kj/min. Evaluate the corresponding rate of heat rejection from the engine and its thermal efficiency. 4. A machine operating as a heat pump extracts heat from the surrounding atmosphere is driven by a 7.5 kw motor and supplies heat to a house needed for its heating in winter. Find coefficient of performance for heat pump. How this COP will be affected if the objection of the same machine is to cool house in summer requiring of heat rejection? Comment on result. Darshan Institute of Engineering and Technology, Rajkot 3.1

8 5. A reversed Carnot cycle operates at either a refrigerator or heat pump. In either case, the power input is 20.8 kw. Calculate the quantity of heat extracted from the cold body for either type of machine. In both case 3500 kj/min heat is delivered by the machine. In case of the refrigerator the heat is transferred to the surroundings while in case of heat pump, the space is to be heated. What is their respective coefficient of performances? If the temperature of cold body is 0 C for the refrigerator and 5 C for heat pump what will be respective temperatures of surrounding for refrigerator and heated space for heat pump? What reduction in heat rejection temperatures would be achieved by doubling the COP for same cold body temperature? 6. A Carnot engine receives 5000 KJ as heat from a heat source at C and rejects to atmosphere at 27 0 C. Calculate the thermal efficiency of engine and work produced by engine. If engine is irreversible and efficiency of this irreversible engine is 75% of Carnot engine, find the percentage change in heat rejection for the same heat input and temperature limit. 7. An engine manufacturer claims to have developed a heat engine with following specifications: Power developed = 75 kw Fuel burnt = 5 kg/hr Heating value of fuel = kj/kg Temperature limits = 1000 K and 400 K Is the claim of an engine manufacturer true or false? Provide your explanation. 8. A reversible engine receives heat from two thermal reservoirs maintained at constant temperature of 750 K and 500 K. The engine develops 100 kw and rejects 3600 kj/min of heat to a heat sink at 250 K. Determine thermal efficiency of the engine and heat supplied by each thermal reservoir. ASSIGNMENT 1. A refrigerator operating on reversed Carnot cycle whose C.O.P is 5. The evaporator is maintained at a temperature of -6⁰C and the power required to run the refrigerator is 3.5 kw. Determine the refrigerating effect and the condenser temperature of the refrigerator. [Answer: (1) R.E (Q2) = 17.5 kw; (2) T1 = K] D.S. Kumar 203/ Which is more effective way to increase the efficiency of a Carnot heat engine: Case-(i) to increase the source temperature T1 while the sink temperature T2 is held constant or Case-(ii) to decrease the sink temperature by the same amount while the source temperature is held constant? How this result would be affected in case of a Carnot heat pump? [Answer: for heat engine: Case- (ii) is more effective, for heat pump: Case- (i) is more effective] D. S. Kumar 206/7.16 Darshan Institute of Engineering and Technology, Rajkot 3.2

9 3. An inventor claims that his engine has the following specifications: Source temperature = 450 K Sink temperature = 280 K Power delivered = 0.15 kwh Heat supplied = 1200 kj As a patent officer, would you issues a patent for such an engine? Give your clarification. [Answer: Claim is false; the patent is not to be issued] D.S. Kumar 211/ An inventor claims that his engine absorbs 300 kj of energy from a thermal reservoir at 325 K and delivers 75 kj of work. The inventor also states that his engine has two heat rejections: 125 kj to a reservoir at 300 K and 100 kj to a reservoir at 275 K. Check the validity of his claim. [Answer: Claim of inventor is intolerable] D.S. Kumar 217/ A reversible engine is supplied 900 kj of heat from a heat source at 500 K. The engine develops 300 kj of net work and rejects heat to two heat sinks at 400 K and 300 K. Determine thermal efficiency and magnitude of heat interaction with each of the sink. [Answer: (1) η = 33.3%; (2) Heat rejected to sink at 400 K = 240 kj, heat rejected at 300 K = 360 kj] D.S. Kumar 220/ A heat engine work between hot and cold reservoir at 600 K and 300 K. The engine receives 300 kw of heat. Identify which of the following heat rejections represents reversible, irreversible and impossible cycle: (i) 250 kw, (ii) 60 kw, (iii) 150 kw [Answer: (1) Irreversible cycle; (2) Impossible cycle; (3) Reversible cycle] 7. A reversible heat engine receives heat from high temperature reservoir at T1 K and rejects heat to a low temperature sink at 800 K. A second reversible heat engine receives the heat rejected by the first engine at 800 K and rejects to a cold reservoir at 280 K. Make calculations for temperature T1: (i) for equal thermal efficiencies of the two engines; (ii) for the two engines to delivers the same amount of work. [Answer: (1) for equal thermal efficiencies, T1 = K; (2) for same amount of work, T1 = 1320 K] D.S. Kumar 224/ A reversible heat engine operates within the higher and lower temperature limits of 1400 K and 400 K respectively. The entire output from this engine is utilized to operate a heat pump. The pump works on reversed Carnot cycle, extracts heat from a reservoir at 300 K and delivers it to the reservoir at 400 K. If 100 kj/s of net heat is supplied to the reservoir at 400 K. Calculate the heat supplied to the engine by the reservoir at 1400 K. [Answer: (1) Q1 = kj/s] D.S. Kumar 233/7.41 Darshan Institute of Engineering and Technology, Rajkot 3.3

10 CHAPTER 4 ENTROPY THEORY 1. Define entropy. Prove that entropy is a property of system. 2. With usual notations prove that 3. Explain Clausius theorem. 4. State the Principle of increase of entropy. Explain application of entropy principle with any two suitable examples. 5. Explain in brief the characteristics of entropy. 6. Define the 3 rd law of thermodynamics. CLASS TUTORIAL 1. A lump of steel of mass 8 kg at 1000 K is dropped in 80 kg of oil at 300 K. Find out entropy change of steel, oil and the universe. Take specific heats of steel and oil as 0.5 kj/kg K and 3.5 kj/kg K respectively. D.S Kumar 248/8.6 [Answer: (ds) st = kj/k, (ds) oil = kj/k, (ds) uni = kj/k] kj/s of heat is supplied at a constant fixed temperature of 290 C to a heat engine. The heat rejection takes place at 8.5 C. The following results were obtained (i)215 kj/s are rejected. (ii)150 kj/s are rejected. (iii)75 kj/s are rejected. Classify which of the result report a reversible cycle or irreversible cycle or impossible results. 3. An inventor claims that he has developed a heat engine which absorbs 1200 kj and 800 kj of heat from reservoirs at 800 K and 600 K respectively and rejects 600 kj and 200 kj of heat to reservoirs at 400 K and 300 K. The engine is further stated to give an output equivalent to 1200 kj. Determine whether the engine suggested by the inventor is theoretically possible. D.S Kumar 256/8.18 [Answer: ds= kj/k, Suggested claim is theoretically not possible] 4. The connections of a reversible engine to three sources at 400 K, 300 K and 200 K. The engine draws 1200 kj of work. Determine: (1) The amount and directions of heat reservoirs with the other heat sources, (2) Make calculations for the entropy changes due to each of the heat interactions with the engine, (3) How much entropy change occurs for the cycle? [Answer: (1) Q 2 = kj, Q 3 = -200 kj; (2) ds 1 = -3 kj/k, ds 2 = +4 kj/k, ds 3 = -1 kj/k; (3) ds cycle = 0 kj/k] D.S Kumar 257/8.19 Engineering Thermodynamics ( ) Darshan Institute of Engineering and Technology, Rajkot 4.1

11 5. 1 m 3 of air is heated reversibly at constant pressure from 290 K to 580 K and is then cooled reversibly at constant volume back to initial temperature. If the initial pressure is 1 bar. Workout the net heat flow and overall (net) change in entropy. Represent the processes on T-s diagram. Take C p = kj/kg K and R = kj/kg K. [Answer: (1) Q net = kj/k; (2) ds net = kj/k] D.S Kumar 271/ kg of air at 150 kpa pressure and 360 K temperature is compressed polytropically to pressure 750 kpa according to the pv1.2 = C. Subsequently the air is cooled to initial temperature at constant pressure. This is followed by expansion at constant temperature till the original pressure of 150 kpa is reached. Sketch the cycle on p-v and T-s plot. Determine work done, heat transfer, and change in entropy during each process. D.S Kumar 272/8.33 [Answer: Process 1-2: W1-2 = kj, Q1-2 = kj, ds1-2 = kj/k; Process 2-3: W2-3 = kj, Q2-3 = kj, ds2-3 = kj/k; Process 3-1: W3-1 = kj, Q3-1 = kj, ds3-1 = kj/k] ASSIGNMENT 1. 5 kg of water at 0:C is exposed to reservoir at 98:C. Calculate the change in entropy of water, reservoir and universe. Assume specific heat of water, Cpw = kj/kg K. [Answer: dswater = kj/k; dsres = kj/k; dsuni = kj/k] 2. A small piece of steel of mass 10 kg at 800:C is dropped in bath of oil has mass 110 kg at 25:C. The specific heats of steel and oil are 0.5kJ/kg K and 3.55kJ/kg K respectively. Find out the change in entropy of steel, oil and universe. [Answer: dssteel = kj/k; dsoil = kj/k; dsuni = kj/k] 3. One inventor claims that when 2 kg of air is supplied to a magic tube at 4 bar and 20:C, two equal mass streams at 1 bar are produced, one at -20:C and the other at 80:C. Another inventor claims that it is possible to produce two equal mass streams, one at -40:C and the other at 40:C. Considering the system to be adiabatic, determine which claim is correct and why? Assume ambient conditions at 0:C. [Answer: Inventor 1: S2 > S1 Claim is acceptable, Inventor 2: S2 < S1 Claim is false] D.S Kumar 268/ One kg of air initially at 7 bar pressure and 360 K temperature expands polytropically PV 1.2 = C until the pressure reduced to 1.4 bar. Determine: (1) Final specific volume and temperature; (2) Change in intern al energy, work done and heat transfer; (3) change in entropy. Take R = kj/kg K and γ = 1.4. D.S Kumar 264/8.23 [Answer: (1) v2 = m 3 /kg, T2 = 275 K; (2) du = kj/kg, W = kj/kg, Q = kj/kg; (3) ds1-2 = kj/kg K] Engineering Thermodynamics ( ) Darshan Institute of Engineering and Technology, Rajkot 4.2

12 5. A close system contains air at pressure 1 bar, temperature 290 K and volume 0.02 m3. This system undergoes a thermodynamic cycle consisting of following three processes in series: Process 1-2: heating at constant volume till the pressure becomes 4 bar, Process 2-3: cooling at constant pressure, Process 3-1: heating at constant temperature to initial state. Represent the cycle on T-s & p-v plot and evaluate change in entropy for each process. Take R = kj/kg K and Cv = kj/kg K. D.S Kumar 271/8.32 [Answer: ds1-2 = kj/k, ds2-3 = kj/k, ds3-1 = kj/k] 6. A 40 ohms resister initially at 30 0 C and thermally insulated. The current 12 A is flow for a 1 second. The specific heat of resistor is 0.88kJ/kg K and mass of resistor is 20 gram. Calculate the change of entropy of resistor and universe. [Answer: dsresistor = J/K, dsuniverse = J/K] Engineering Thermodynamics ( ) Darshan Institute of Engineering and Technology, Rajkot 4.3

13 CHAPTER 5 ENERGY Theory 1. Define/Explain below terms: a) Available energy (Exergy) b) Unavailable energy (Anergy) c) Dead state d) Maximum work e) High grade energy and low grade energy f) Law of degradation of energy 2. Explain exergy destruction in heat transfer process. 3. Derive the expression for availability in a closed system (non-flow) at a given state. 4. Derive the expression for availability in a steady flow (open) system at a given state. 5. Explain Gouy-Stodola theorem and its applications. CLASS TUTORIAL 1. Calculate availability (available energy) and unavailability (unavailable energy) of a system that absorbs kj of heat from a heat source at 500 K temperature while the environment at 290 K temperature. D.S Kumar 287/9.1 [Answer: Availability = 6300 kj, Unavailability = 8700 kj] 2. A source at 1000 K is available for transfer of heat at the rate of 100 kw to a system at 500 K. If these temperatures remain constant. Determine entropy production during heat transfer, the increase in unavailable energy. Take ambient temperature as 300 K. D.S Kumar 289/9.6 [Answer: (1) ds net =- 6 kj/k min, (2) Increase in UAE = 1800 kj/min] 3. A system at 450 K receives 225 kj/s of heat energy from a source at 1500 K, and the temperatures of both the system and source remains constant during heat transfer process. Represent process on T-s diagram. Determine the net change in entropy, available energy of heat source and system, and decrease in available energy. [Answer: (1) dsnet = kj/s K, (2) AE1 = 180 kj/s, AE2 = 75 kj/s, (3) in AE = 105 kj /s(or in UAE)] D.S Kumar 292/ kg of water at 90⁰C is mixed with 30 kg of water at 30⁰C and the pressure remains constant during the mixing operation. Calculate the decrease in available energy. It may be presumed that the surroundings are at 10⁰C temperature and for water C pw = kj/kg K. [Answer: in AE = kj] D.S Kumar 291/9.9 Engineering Thermodynamics ( ) 5.1 Darshan Institute of Engineering and Technology, Rajkot.

14 CHAPTER 6 VAPOR POWER CYCLES THEORY 1. What do you understand by Steam Rate and Heat Rate? What are their units? 2. Derive an expression for an efficiency of Carnot vapor cycle with p-v, T-S, h-s and schematic diagram. OR Explain Carnot vapor cycle. State and explain required modifications with help of suitable diagrams to make the cycle feasible. 3. Why Carnot cycle is not practical for steam power plants? Explain in brief. Also give comparison of Carnot and Rankine vapor cycle. 4. Derive an expression for an efficiency of an ideal Rankine cycle with p-v, T-S, h-s and schematic diagram. 5. Explain effect of different operating variables on Rankine cycle performance. 6. State various methods to improve efficiency of Rankine cycle. With suitable diagrams, explain any one of them. OR What is the effect of regeneration? On the (1) specific output, (b) mean temperature of heat addition (c) cycle efficiency and (d) steam rate OR Draw ideal simple Rankine cycle with reheating on T-s and h-s diagram. Identify the reheating process and locate the increase in work done due to reheating in both graph. CLASS TUTORIAL 1. A power generating plant uses steam as working fluid and operates on an ideal Carnot cycle. Dry saturated steam at 17.5 bar pressure is supplied to the engine and it expands isentropically to a condenser pressure of 0.07 bar. Assuming the liquid to be saturated at entry to the boiler, make calculations for the work ratio, thermal efficiency and specific steam consumption. [Ans: 0.823, %, 5.39 kg/kwh] [15.2, D. S. Kumar] 2. A steam turbine working on Rankine cycle is supplied with dry saturated steam at 25 bar and the exhaust takes place at 0.2 bar. For a steam flow rate of 10 kg/s, determine: Darshan Institute of Engineering and Technology, Rajkot 6.1

15 a. Quality of steam at the end of expansion. b. Turbine shaft work. c. Power required to drive the pump. d. Work ratio and Rankine efficiency. e. Heat flow in the condenser. [Ans: 0.776, kj/kg, kw, 0.996, 28.9 %, kw] [15.4, D. S. Kumar] 3. In a thermal power plant operating on an ideal Rankine cycle, superheated steam produced at 5 MPa and 500 C is fed to a turbine where it expands to the condenser pressure of 10 kpa. If the net power output of the plant is to be 20 MW, determine: a. Heat added in the boiler per kg of water. b. Thermal efficiency of the cycle. c. Mass flow rate of steam in kg/s. d. Mass flow rate of cooling water in the condenser if the cooling water enters the condenser at 25 C and leaves at 35 C. [Ans: kj/kg, %, kg/s, kg/s] [15.7, D. S. Kumar] 4. A steam power plant uses the following cycle: Steam at boiler outlet 150 bar& 550 C Reheat at 40 bar to 550 C Condenser at 0.1 bar. Using the Mollier chart and assuming ideal processes, find the (a) Quality of steam at turbine exhaust, (b) Cycle efficiency and (c) Steam rate. [Ans: 0.88, 43.9%, 2.18 kg/kwh] [12.4, P. K. Nag] ASSIGNMENT 1. In a steam power cycle, the steam supply is at 15 bar and dry and saturated. The condenser pressure is 0.4 bar. Calculate the Carnot and Rankine efficiencies of the cycle. Neglect pump work. [May-2016] 2. A steam turbine power plant operating on ideal Rankine cycle, receives steam at 30 bar, 350 C at the rate of 2 Kg/s and it exhausts at 0.09 bar. Calculate the followings: i) Net power output, ii) Steam rate, iii) Heat rejection in condenser in KW, iv) Rankine Cycle efficiency. [Jun-2017] Darshan Institute of Engineering and Technology, Rajkot 6.2

16 3. A steam power plant operates on a theoretical reheat cycle. Steam at 25 bar pressure and 400 C is supplied to the high pressure turbine. After its expansion to dry state, the steam is reheated at constant pressure to its original temperature. Subsequent expansion occurs in the low pressure turbine to a condenser pressure of 0.04 bar. Considering feed pump work, make calculations to determine: a. Quality of steam at entry to condenser, b. Thermal efficiency and c. Specific steam consumption. Mollier Diagram is permitted. [Ans: 0.945, 37%, kg/kwh] [15.8, D. S. Kumar] 4. In a single heater regenerative cycle the steam enters the turbine at 30 bar, 400 C and the exhaust pressure is 0.1 bar. The feed water heater is a direct contact type which operates at 5 bar. Find: a. The efficiency and the steam rate of the cycle. b. The increase in mean temperature of heat addition, efficiency and steam rate as compared to the Rankine cycle (without regeneration). Pump work may be neglected. [Ans: 36.08%, 3.85 kg/kwh, 27.4 C, 1.9%, 0.39 kg/kwh] [12.13, R. K. Rajput] Darshan Institute of Engineering and Technology, Rajkot 6.3

17 CHAPTER 7 GAS POWER CYCLE THEORY 1. Define: Cycle, Air Standard Efficiency, Compression Ratio, Brake Thermal Efficiency and Mean Effective Pressure. 2. Derive an equation of air standard efficiency of following ideal gas power cycles with P-V, T-S and H-S diagram: a. Carnot Cycle b. Otto Cycle c. Diesel Cycle 3. Compare Otto, Diesel and Dual cycle for: a. Same compression ratio and heat supplied b. Same maximum pressure and temperature c. Constant maximum pressure and heat input 4. Carnot cycle is not practical Justify. 5. What are the air standard assumptions? 6. How actual Brayton cycle differs from the theoretical cycle? Explain with the help of T-S diagram. Also derive an expression for efficiency of Brayton cycle. What are the advantages of the Brayton cycle over the conventional heat engine cycles? OR State the thermodynamic process of open cycle gas turbine power plant. OR Draw Brayton cycle and derive expression for optimum pressure ratio. 7. State various methods to improve efficiency of Brayton cycle. With suitable diagrams, explain any one of them. OR What is regeneration in gas turbine plant? How it improves thermal efficiency of simple open cycle Gas Turbine Plant. Explain it with the help of schematic diagram and T-S Diagram of the cycle. OR Enlist the various components used in intercooling and reheating gas cycle based power plant. OR Draw the schematic diagram of Simple Gas Turbine cycle with intercooling. Draw T- S diagram of the cycle. CLASS TUTORIAL 1. An engine uses 6.5 Kg of oil per hour of calorific value of 30,000 kj/kg. If the Brake power of engine is 22 kw and mechanical efficiency is 85% calculate (a) indicate thermal efficiency (b) Brake thermal efficiency (c) Specific fuel consumption in Kg/B.P/hr. [Ans: 47.78%, 40.61%, kg/kw-hr] [June-2010] Darshan Institute of Engineering and Technology, Rajkot 7.1

18 2. An engine working on Otto cycle has a volume of 0.45 m 3, pressure 1 bar and temperature 30 C at the beginning of compression stroke. At the end of compression stroke, the pressure is 11 bar. 210 kj of heat is added at constant volume. Determine: a. Pressures, temperatures and volumes at salient points in the cycle. b. Percentage clearance. c. Efficiency. d. Mean effective pressure. e. Ideal power developed by the engine if the number of working cycles per minute is 210. Assume the cycle is reversible. [Ans: 600 K, m 3, 1172 K, bar, m 3, 1.97 bar, K, 0.45 m 3, %, 49.5 %, bar, 364 kw] [21.13, R. K. Rajput] 3. In an Otto cycle air at start of isentropic compression is at 20 C and 110kPa. If clearance volume is 20% of the swept volume and temperature at end of constant volume heat addition is 1400 C, find the air standard efficiency and mean effective pressure in kpa. Take C p C v = 1.4. [Ans: 51.16%, 4.61bar] [June-2011] 4. The following data pertains to a C.I. engine working on air standard Diesel cycle: Cylinder bore = 15 cm; Stroke length = 25 cm, Clearance volume = 400 cm 3 Calculate the air standard efficiency of the engine if fuel injection takes place at constant pressure for 5 % of the stroke. How this efficiency value will be affected if the fuel supply continues up to 8 % of the stroke? [Ans: %, 2 %] [12.18, D. S. Kumar][June-2015] OR Calculate the percentage loss in the ideal efficiency of a Diesel engine with compression ratio 12 if the fuel cut-off is delayed from 5% to 8%. 5. In a Diesel cycle, air a 0.1 MPa and 300 K is compressed adiabatically until the pressure rises to 5 MPa. If 700 kj/kg of energy in the form of heat is supplied at constant pressure, determine the compression ratio, cutoff ratio, thermal efficiency and mean effective pressure. [Ans: ; ; % ; MPa][12.23; D. S. Kumar] 6. In a gas turbine plant working on Brayton cycle, the air at inlet is 27 C, 0.1 MPa. The pressure ratio is 6.25 and the maximum temperature is 800 C. The turbine and compressor efficiencies are each 80 %. Find compressor work, turbine work, heat supplied, cycle efficiency and turbine exhaust temperature. Mass of air may be considered as 1 kg. Draw T-s diagram. [Ans: kj/kg, kj/kg, kj/kg, %, K] [21.38, R. K. Rajput] 7. A closed cycle ideal gas turbine plant operates between temperature limits of 800 C and 30 C and produces a power of 100 kw. The plant is designed such that there is no need for a regenerator. A fuel of calorific kj/kg is used. Calculate the mass Darshan Institute of Engineering and Technology, Rajkot 7.2

19 flow rate of air through the plant and rate of fuel consumption. Assume Cp = 1 kj/kg K and γ = 1.4. [Ans: kg/s, 4.74E-8 kg/s] [May-2016] ASSIGNMENT 1. A Carnot cycle has lowest pressure and temperature equal to 1bar & 20 C. Pressure after Isothermal compression is 4 bar. Pressure after isentropic compression is 12 bar and after Isothermal heat addition process is 6 bar. Calculate: a. The highest temperature in the cycle. b. The change in entropy during Isothermal expansion. c. Heat added to the cycle. d. Heat rejected by the cycle [Ans: K, kj/kg-k, 79.56kJ/kg, kj/kg] [Dec 2010] 2. An air standard Otto cycle is designed to operate with the following data: Maximum cycle pressure and temperature: 5 MPa and 2250 K Minimum cycle pressure and temperature: 0.1 MPa and 300 K Determine the net work output per unit mass of working fluid and the thermal efficiency. [Ans: KJ/kg; %] [12.8; D.S.Kumar] 3. The upper and lower temperature limits for an Otto cycle are 1500 K and 300 K respectively. What compression ratio is required to develop maximum work? Estimate the maximum theoretical power developed by an engine working on this cycle when the air flow rated is 0.35 kg/min. [Ans: 7.476, 1.92 kw] [12.11, D. S. Kumar] 4. An ideal Diesel engine has a diameter 150 mm and stroke 200 mm. The clearance volume is 10% of the swept volume. Determine the compression ratio and air standard efficiency of the engine if cut off takes place at 6% of the stroke. [Ans: 11, 57.52%] [Dec-2013] 5. An air-standard Diesel cycle has a compression ratio of 20, and the heat transferred to the working fluid per cycle is 1800 kj/kg. At the beginning of the compression process, the pressure is 0.1 MPa and the temperature is 15 C. Consider ideal gas and constant specific heat model. Determine a) The pressure and temperature at each point in the cycle, b) The thermal efficiency, c) The mean effective pressure. [Ans: K, 3.31bar, K, K, 4.389bar, %, 0.699bar] [Dec-2015] 6. In an ideal Brayton cycle, the ambient air at 1 bar K is compressed to 6 bar and the maximum cycle temperature is limited to 1200 K. if the heat supply is 120 MW, find (i) The thermal efficiency of the cycle (ii) work ratio (iii) power output and (iv) mass flow rate of air. Also show the cycle on p-v and T-s diagram. [Ans: 40.06%, , 48.08MW, kg/s] [May-2012, Jan-2017] Darshan Institute of Engineering and Technology, Rajkot 7.3

20 7. Find the required air-fuel ratio in a gas turbine whose turbine and compressor efficiencies are 85% and 80%, respectively. Maximum cycle temperature is 875 C. The working fluid can be taken as air (Cp = 1.0 kj/kg K, γ = 1.4) which enters the compressor at 1 bar and 27 C. The pressure ratio is 4. The fuel used has calorific value of kj/kg. There is a loss of 10% of calorific value in the combustion chamber. [Ans: 56:1] [Dec-2015] Darshan Institute of Engineering and Technology, Rajkot 7.4

21 CHAPTER 8 - PROPERTIES OF GASES & GAS MIXTURES THEORY 1. What is an ideal gas equation? What assumptions are made in deriving the ideal gas equation of state from kinetic theory of gas? 2. State the Boyle s law, Charle s and Avogadro s law for perfect gas. 3. Explain briefly Dalton s law, Gibbs-Dalton law and Amagat s law for perfect gas mixtures. 4. Derive the vander Waal s equation. 5. State the law of corresponding states and define the compressibility factor and explain its significance. CLASS TUTORIAL 1. A piston cylinder device initially contains 0.5 m3 of nitrogen gas at 400 kpa and 27 C. An electric heater within the device is turned on and is allowed to pass a current of 2 A for 5 min from a 120-V source. Nitrogen expands at constant pressure, and a heat loss of 2800 J occurs during the process. Consider nitrogen gas as ideal gas and nitrogen has constant specific heats. Take characteristics gas constant for nitrogen is 0.297kJ/kgK. Take Cp = kj/kgk for nitrogen at room temperature. Determine the final temperature of nitrogen. 2. A cylinder of 0.1 m3 volume is filled with kg of C 8 H 18 at K. Assuming that C8H18 obeys the Vander Walls equation of state, calculate the pressure of the gas in the cylinder. The Vander walls Constant a and b for C 8 H 18 are Pa (m 3 /mol) 2 and m 3 /mol, respectively. Engineering Thermodynamics ( ) Darshan Institute of Engineering and Technology, Rajkot 8.1