MINISTRY OF SCIENCE AND TECHNOLOGY DEPARTMENT OF TECHNICAL AND VOCATIONAL EDUCATION Sample Questions & Worked Out Examples For ME 01013 BASIC ENGINEERING THERMODYNAMICS A.G.T.I (First Year) Mechanical Engineering Part I CHAPTER 1 General Introduction Basic Engineering Thermodynamics (ME 01013) CHAPTER 1 GENERAL INTRODUCTION Q1. In a steady-flow system, a substance flows at the rate of 4 kg/s. It enters at a pressure of 620 kW/m2, a velocity of 300 m/s, internal energy 2100 kJ/kg and specific volume 0.37 m3/kg. It leaves the system at a pressure of 130 kN/m2, a velocity of 150 m/s, internal energy 1500 kJ/kg and specific volume 1.2 m3/kg. During its passage through the system the substance has a loss by heat transfer of 30 kJ/kg to the surroundings. Determine the power of the system in kilowatts, stating whether it is from or to the system. Neglect any change in potential energy. Q2. Steam enters a turbine with a velocity of 16 m/s and specific enthalpy 2990 kJ/kg. The steam leaves the turbine with a velocity of 37 m/s and specific enthalpy 2530 kJ/kg. The heat loss to the surroundings as the steam passes through the turbine is 25 kJ/kg. The steam flow rate is 324000 kg/hr. Determine the work output from the turbine in kilowatts. Q3. Air passes through a gas turbine system at the rate of 4.5 kg/sec. It enters with a velocity of 150 m/s and a specific enthalpy of 3000 kJ/kg. At exits, the velocity is 120 m/s and the specific enthalpy is 2300 kJ/kg. The air has heat loss to the surroundings of 25 kJ/kg as it passes through the turbine. Determine the power developed by the turbine. Q4. During the compression stroke of an engine, the work done on the working substance in the engine cylinder is 75 kJ/kg and the heat rejected to the surroundings is 42 kJ/kg. Find the change of internal energy, stating whether it is an increase or decrease. Q5. In a non-flow process these is a heat loss of 1055 kJ and an internal energy increase of 210 kJ. How much work is done and is the process an expansion or compression? Q6. A copper vessel of mass 2 kg contains 6 kg of water. If the initial temperature of the vessel plus water is 20В°C and the final temperature is 90В°C, how much heat is added to accomplish this change, assume that these is no heat loss? Cp of copper = 394 J/kg k, Cp of water at 20В°C = 4181. 6J/kg, k, Cp of water at 90В°C = 4204.8 J/kg k. Q7. If the specific heat capacity of the material is 394 J/kg k, estimate the specific heat capacity of the solid including the water of equivalent of the calorimeters. Cp for water at 16В°C = 4184.6 J/kg k Cp for water at 32В°C = 4178.0 J/kg k Part I CHAPTER 2 Gases and Single Phase Systems CHAPTER 2 Q1. A gas whose original pressure and volume were 300 kN/m2 and 0.14 m3 is expanded until its new pressure is 60 kN/m2 while its temperature remains constant. What is its new volume? Q2. A quantity of gas whose original volume and temperature are 0.2 m3 and 303В°C, respectively, is cooled at constant pressure until its volume becomes 0.1 m3. What will be the final temperature of the gas? Q.3 A gas whose original pressure, volume and temperature were 140 kN/m2, 0.1 m3 and 25В°C, respectively, is compressed such that its new pressure is 700 kN/m2 and its new temperature is 60В°C. Determine the new volume of the gas. Q4. A quantity of gas has a pressure of 350 kN/m2 when its volume is 0.03 m3 and its temperature is 35В°C. If the value of R = 0.29 kJ/kg-K, determine the mass of gas present. If the pressure of this gas is now increased to 1.05 MN/m2 while the volume remains constant, what will be the new temperature of the gas? Q5. 2 kg of gas occupying 0.7 m3 had on original temperature of 15В°C. It was then heated at constant volume until the temperature became 135В°C. How much heat was transferred to the gas and what was its final pressure? Take Cv=0.72kJ/kgK R=0.29kJ/kgK Q6. A gas whose pressure, volume and temperature are 275 kN/m2, 0.09 m3 and 185В°C respectively, has its state changed at constant pressure until its temperature becomes 15В°C. How much heat is transferred from the gas and how much work is done on the gas during the process? Take R = 0.29 kJ/kg-K and Cp = 1.005 kJ/kg-K. Q7. 0.25 kg of air at a pressure of 140 kPa occupier 0.15 m3 and from this condition it is compressed to 1.4 mn/m2 according to the law pv1.25 = C. Determine (a) the change in internal energy of air, (b) the workdone on or by air, (c) the heat received or rejected by the air. Take Cp = 1.005 kJ/kg-K, Cv = 0.718 kJ/kg-K. Q8. A gas expands adiabatically from a pressure and volume of 700 kPa and 0.015 m3 respectively, to a pressure of 140 kPa. Determine the final volume and the work done by the gas. What is the change of the internal energy in this case? Take Cp = 1.046 kJ/kg-K, Cv = 0.752 kJ/kg-K. Q9. A gas expands according to the law PV1.3 = C from a pressure of 1 MN/m2 and a volume 0.003 m3 to a pressure or rejected by the gas during this process? Determine also the polytropic heat. Take r = 1.4, Cv = 0.718 kJ/kg-K. Q10. A quantity of gas has an initial pressure of 140 kPa and volume 0.14 m3. It is then compressed to a pressure of 700 kPa while the temperature remains constant. Determine the final volume of the gas. Q11. A quantity of gas has an initial volume of 0.06 m3 and a temperature of 15В°C. It is expanded to a volume of 0.12 m3 while the pressure remains constant. Determine the final temperature of the gas. Q12. A mass of gas has an initial pressure of 1 bar and a temperature of 200В°C. The temperature of the gas is now increased to 550В°C while the volume remain constant. Determine the final pressure of the gas. Q13. A mass of air has an initial pressure of 1.3 Mpa, volume 0.014 m3 and the temperature 135В°C. It is expanded until its final pressure is 275 kPa and its volume becomes 0.056 m3. Determine (a) the mass of air (b) the final temperature of the air. Take R = 0.287 kJ/kg K. Q14. 0.23 kg of air has an initial pressure of 1.7 Mpa and a temperature of 2000В°C. It is expanded to a pressure of 0.34 Mpa according to the law PV1.35 = constant. Determine the work done during expansion. Take R = 0.29 kJ/kg K. Q15. One kilogramme of a certain gas is at 0.11 Mpa and 15В°C. It is compressed until its volume is 0.1 m3. Calculate the final pressure and temperature if the compression (a) isothermal (b) adiabatic. Calculate also, the work done, change of internal energy and heat transfer in each case. Distinguish between positive and negative quantities. Take Cp = 0.92 kJ/kg-K, Cv = 0.66 kJ/kg.K. Q16. A certain mass of air, initially at a pressure of 480 kN/m2 is expanded adiabatically to a pressure of 94 kPa. It is then heated at constant volume until it attains its initial temperature, when pressure is found to be 150 kN/m2. State the type compression necessary to bring the air back to its original pressure and volume, using the information, calculate the value of Оі. If the initial temperature of the air is 190В°C, determine the work done/kg of air during the adiabatic expansion. Take R = 0.29 kJ/kg-K. Q17. A quantity of air occupies a volume of 30 liter at a temperature of 38В°C and a pressure of 104 kN/m2. The temperature of the air can be raised, (i) By heating at constant volume unitl the pressure is 208 kN/m2 (ii) By adiabatic compression until the volume is 6 liter. Find, for each case, the final temperature, the external work done, the change of internal energy, and the heat transferred. Take R = 0.29 kJ/kg-K, Оі = 1.4 Part I CHAPTER 3 Gas Power Cycles CHAPTER 3 Q1. One kg of air is taken through a constant volume cycle thus: 1-2 Compressed adiabatically through a volume ratio of 6:1, the initial pressure and temperature being 103 kN/m2 and 100В°C, respectively. 1-3 Heated at constant volume until the pressure is 3450 kN/m2. 3-4 Expanded adiabatically to its original volume. 4-1 Cooled at constant volume to its original state. Calculate and tabulate the values of the pressure, volume and temperature for each of the state points 1, 2, 3 and 4. Calculate the amount of heat transferred to the air between state points 2 and 3. For air R = 0.287 kJ/kg-K, Оі = 1.4. Q2. In an ideal constant volume cycle the pressure and temperature at the beginning of compression are 97 kN/m2 and 50В°C, respectively. The volume ratio of compression is 5:1. The hat supplied during the cycle is 930 kJ/kg of working fluid. Determine: (a) the maximum temperature attained in the cycle: (b) the thermal efficiency of the cycle; (c) the work done during the cycle/kg of working fluid. Assume Оі = 1.4 and Cv = 0.717 kJ/kg-K. Q3. In an ideal constant pressure cycle, using air, the overall volume ratio of the cycle is 8:1. Adiabatic compression begins at 2/7th of the compression stroke when the conditions of the air are 100 kN/m2, 0.084 m3 and 28В°C. If Оі = 1.4 and Cp = 1.006 kJ/kg-K, determine: (a) the pressure, volume and temperature at the state point of the cycle: (b) the heat received / cycle (c) the work done / cycle (d) the thermal efficiency of the cycle. Q4. A gas turbine operating on a simple constant pressure cycle has a pressure compression ration of 8:1. The turbine has a thermal efficiency of 6% of the ideal. The fuel used has a calorific value of 43 MJ/kg. If Оі = 1.4, determine: (a) the actual thermal efficiency of the turbine; (b) the specific fuel consumption of the turbine in kg/k W-h. Q5. An engine uses air as the working substance. At the beginning of compression the pressure is 90 kN/m2 and the temperature is 40В°C. During the adiabatic compression the volume is reduced to one-sixteenth of its value at the beginning of the compression stroke. Heat is then added at constant pressure until the Q6. An oil engine works on the ideal Diesel cycle. The overall compression ratio is 11:1 and constant pressure energy addition ceases at 10% of the stroke. Intake conditions are 96 kN/m2 and 18В°C. The engine uses 0.05 m3 of air/s. If Оі = 1.4, determine. (a) the thermal efficiency of the cycle; (b) the indicated power of the engine. Q7. A dual combustion cycle has an adiabatic compression, volume ratio of 15:1 the conditions at the commencement of compression are 97 kN/m2, 0.084 m3 and 28В°C. The maximum pressure of the cycle is 6.2 MN/m2 and the maximum temperature of the cycle is 1320В°C. If Cp = 1.006 kJ/kg-K and Cv = 0.717 kJ/kg-K determine. (a) the pressure, volume and temperature at the corners of the cycle (b) the work done/cycle. Q9. Prove that the air standard efficiency of an engine working on the constant 1 volume (Otto) cycle is given by: 1- Оі в€’1 . Where r = volume ratio of r compression and Оі = the adiabatic index. Calculate the air standard efficiency of an engine working on this cycle, if the pressure at the beginning and end of the compression are 103.5 kPa and 827.5 kPa, respectively. Take Оі = 1.4. Q10. 0.5 kg of air is taken through a constant pressure cycle. Conditions at the beginning of adiabatic compression are 96.5 kPa and 15В°C. The pressure ratio of compression is 6. Constant pressure heat addition occur after adiabatic compression until the volume is double. If Оі = 1.4 and R = 0.287 kJ/kg-K determine (a) the thermal efficiency of the cycle (b) the heat received per cycle (c) the work done per cycle. Q11. A Diesel engine has a clearance volume of 0.00025 m3 and a bore and stroke of 125.5 mm and 200 mm respectively. A charge of air at 100 kPa and 20В°C is taken into the cylinder and compressed adiabatically (Оі = 1.4). After combustion at constant pressure the temperature is 1090В°C, the expansion which follows is adiabatic. Find (a) the temperature and pressure at the end of compression (b) the temperature and pressure after expansion (c) the ideal thermal efficiency of the engine. Q12. In an ideal dual combustion cycle conditions at the commencement of adiabatic compression are 93 kPa, 0.05 m3 and 24В°C, respectively. The adiabatic compression volume ration is 9:1. The constant volume heat addition pressure ratio is 1.5 and the constant pressure heat addition volume ratio is 2. If Cp = 105 kJ/kg-K and Cv = 0.775 kJ/kg-K, determine (a) the pressure, volume and temperature at the state points of the cycle, (b) the thermal efficiency of the cycle (c) the work done per cycle. Part II CHATPER 1 Engine Trials Sample Questions CHATPER 1 Q1. During a test on a four-stroke cycle oil engine the following data and results were obtained: Mean height of indicator diagram 21 mm indicator spring number, 27 kN/m2/mm swept volume of cylinder, 14 litres Speed of engine, 6.6 rev/s Effective brake load, 77 kg Effective brake radius, 0.7 m Fuel consumption, 0.002 kg/s Calorific value of fuel, 44000 kJ/kg Cooling water circulation, 0.15 kg/s Cooling water inlet temperature, 38В° C Cooling water outlet temperature, 71В° C Specific heat capacity of water, 4.18 kJ/kg-K Energy to exhaust gases, 33.6 kJ/s Determine the indicated and brake outputs and the mechanical efficiency. Draw up an overall energy balance in kJ/s and as a percentage. Q2. The diameter and stroke of single cylinder gas engine, working on the constant volume cycle, are 200 mm and 300 mm, respectively, and the clearance volume is 2.73 litres. When running at 300 rev/min, the number of firing cycle/min was 135, the indicated mean effective pressure was 518 kN/m2 and the gas consumption 8.8 m3/hr. Calorific value of the gas used = 16350 kJ/m3. Determine: (a) the air standard efficiency; (b) the indicated power developed by the engine; (c) the indicated thermal efficiency of the engine. Assume П’ = 1.4. Q3. During a trial on a six cylinder petrol engine, a Morse test carried out as the means of estimating the indicated power of the engine. When running at full load, all cylinders in, the brake power output was 52 kW. The measured brake power outputs, in kW, when each cylinder was cut out in turn and the load reduced to bring the engine back to its original speed were as follows: 1 2 3 4 5 6 40.5 40.2 40.1 40.6 40.7 40.0 From this data, estimate: (a) the indicated power of the engine; (b) the mechanical efficiency of the engine. Q4. In a test on a single-cylinder oil engine operating on the four-stroke cycle and fitted with a simple rope brake, the following reading were taken:Brake wheel diameter 600 mm Rope diameter 25.4 mm Speed 450 rpm Dead weight on rope 20 kg Spring balance reading 3.25 kg Area of indicator diagram 410 mm2 Length of indicator diagram 64 mm Spring constant 100 kN/m2/mm Bore 120 mm Stroke 150 mm Brake specific fuel consumption 0.30 kg/kW-hr of Oil Cv = 41700 kJ/kg. Calculate the bp, ip, mechanical efficiency and indicated thermal efficiency of the engine. Q5. During a trial on a four-cylinder, compression ignition oil engine, a Morse test was carried out in order to estimate the indicated power of the engine. At full load, with all cylinders working , the engine developed a brake power of 45 kW. The measured brake power outputs, when each cylinder was cut in turn and the load reduced to bring the engine back to the original speed, were, as follows: 1 2 3 4 31 32 31.8 31.2 (kW) Form this data, estimate: (a) the indicated power of the engine; (b) the mechanical efficiency of the engine; Q6. During a test on a four-stroke, single cylinder gas engine, the following observations were made: Calorific Value of gas, 18850 kJ/m3 Gas consumption 4.95 m3/h Speed 5 rev/s Effective brake diameter 0.9 m Dead weight on brake 400 N Spring balance reading 40 N Jacket Cooling water 204 kg/h Temperature rise of jacket 30В° C Cooling water Indicated mean effective pressure 455 kN/m2 Cylinder diameter 165 mm Piston Stroke 305 mm Specific heat capacity of water, 4.18 kg/kg-k Determine:(a) the mechanical efficiency (b) the indicated thermal efficiency (c) the brake thermal efficiency (d) Draw up an energy balance for the engine in kJ/s. Q7. In a trial o a single-cylinder, four-stroke cycle oil engie: 250 mm bore by 450 mm stroke, the following results were recorded; During of trial, 30 min; Total revolution, 7962; Average dead load on brake, 940 N; Average spring balance reading, 110 N; Brake radius, 1m; Average indicated mean effective pressure, 565 kN/m2; Total fuel used, 2.9 kg of calorific value, 44000 kJ/kg; Total jacket water, 200 kg; Inlet temperature, 17В° C Outlet temperature, 67В° C; specific heat capacity of water 4.18 kJ/kg-K Calculate:- (a) the indicated power; (b) the brake power; ( c) the mechanical efficiency; (d) the brake thermal efficiency; (e) the percentage energy loss to the jacket. Q.8. A six cylinder, four-stroke cycle, marine oil engine has cylinder diameter of 610 mm and a piston stroke of 1250 mm. When the engine speed is 2 rev/s it uses 340kg of fuel oil of calorific value 44200 kJ/kg in one hour. The cooling water amounts to 19200 kg/h, entering at 15В° C and leaving at 63В° C. The torque transmitted at the engine coupling is 108 kN-m and indicated mean effective pressure is 775 kN/m2. Determine: (a) the indicated power (b) the brake power (c) the percentage of the energy lost to the cooling water; (d) the brake thermal efficiency; (e) the mechanical efficiency; (f) the brake mean effective pressure; (g) the fuel used/kW-h, on a brake power basis. Specific heat capacity of water 4.18 kJ/kg-K. Q.9. In a test on a two-stroke, heavy-oil engine, the following observations were made; Oil consumption, 4.05 kg/h Calorific value of oil, 43000 kJ/kg; Net brake load, 597 N; Mean brake diameter 1 m; Mean effective pressure 275 kN/m2; Cylinder diameter, 0.20 m, Stroke, 0.250 m; Speed 6 rev/s; Specific heat capacity of water 4.18 kJ/kgK Calculate: (a) the mechanical efficiency; (b)the indicated thermal efficiency; (c ) the brake thermal efficiency; (d) the quantity of jacket water required per minute if 30 % of the energy supplied by the fuel is absorbed by this water. Permissible rise in temperature is 25В° C. Part II CHAPTER 2 Steam and Two Phase Systems Sample Questions CHAPTER 2 Q1. Determine the specific liquid enthalpy specific enthalpy of evaporation and specific enthalpy of dry saturated steam at 0.5 MN/m2. Q2. Determine the saturation temperature, specific liquid enthalpy, specific enthalpy of evaporation and specific enthalpy of dry saturated steam at a pressure of 2.04 MN/m2. Q3. Determine the specific enthalpy of steam at 2 MN/m2 and with a temperature 275В° C Q4. Determine the specific enthalpy of steam at a pressure of 2.5 MN/m2 and with a temperature of 320В° C Q5. Determine the specific enthalpy of wet steam at a pressure of 70 kN/m2 and having a dryness fraction of 0.85. Q6. Determine the specific volume of water at saturation temperature for a pressure of 4.0 MN/m2. Q7. 1.5 kg of steam originally at a pressure of1 MN/m2 and temperature 225В° C is expanded until the pressure becomes 0.28 MN/m2. The dryness fraction of the steam is then 0.9. Determine the change of internal energy which occurs. Q8. A closed vessel of 0.6 m3 capacity contains dry saturated steam at 350 kN/m2. The vessel is cooled until the pressure is reduced to 200 kN/m2. Calculate: (a) the mass of steam in the vessel, (b) the final dryness of the steam, (c) the amount of heat transferred during the cooling process. Q9. Steam at 4 MN/m2 and dryness fraction 0.95 received heat at constant pressure until its temperature becomes 350В° C. Determine the heat received by the steam/kg. Q10. A quantity of dry saturated steam occupies 0.2634 m3 at 1.5 MN/m2. Determine the final condition of the steam if it is compressed until the volume is halved; (a) if the compression is carried out in an isothermal manner; (b) if the compression follows the law PV = constant. In case (a) determine the heat rejected during the compression. Q11. A quantity of steam at a pressure of 2.1 MN/m2 and 0.9 dry occupies a volume of 0.2562 m3. It is expanded according to the law PV1.25 = constant to a pressure of 0.7 MN/m2. Determine;(a) the mass of steam present, (b) the external work done, (c) the change of internal energy, (d) the heat exchange between the steam and surrounding, stating the direction of transfer. Q12. (a) Determine the volume occupied by 1 kg of stem at a pressure of 0.85 MN/m2 and having a dryness fraction of 0.95. (c) This is expanded adiabatically to a pressure of 0.17 MN/m2, the law of expansion being PV1.13 = constant. Determine, (i) the final dryness fraction of the steam, (ii) the change of internal energy of the steam during the expansion.