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Join date : 2009-10-23  Subject: THERMODYNAMICS PROBLEMS Fri Oct 30, 2009 7:34 pm Section-1: Mechanical and Thermodynamic Systems ----------------------------------------------------------------------------------------------------------------------------------------------------------------• Free Body Diagram --------------------------------------------------------------------------------1-1-1 Two thermo books, each with a mass of 1 kg, are stacked one on top of another. Neglecting the presence of atmosphere, draw the free body diagram of the book at the bottom to determine the vertical force on its (a) top and (b) bottom faces in kN. [Manual Solution] Answers: (a) 0.01 kN, (b) 0.02 kN Anim. 1-1-1 (click) --------------------------------------------------------------------------------1-1-2 Determine (a) the pressure felt on your palm to hold a textbook of mass 1 kg in equilibrium. Assume the distribution of pressure over the palm to be uniform and the area of contact to be 25 cm2. (b) What-if-Scenario: How would a change in atmospheric pressure affect your answer? [Manual Solution] Answers: (a) 3.92 kN/m2 --------------------------------------------------------------------------------1-1-3 The lift-off mass of a Space Shuttle is 2 million kg. If the lift off thrust (the net force upward) is 10% greater than the minimum amount required for a lift-off. Determine the acceleration. [Manual Solution] Answers: (a) 10.79 m/s2 Figure 1-1-3 --------------------------------------------------------------------------------1-1-4 A body weighs 0.05 kN on earth where g = 9.81 m/s2. Determine its weight on (a) the moon, and (b) on mars with g = 1.67 m/s2 and g = 3.92 m/s2 respectively. [Manual Solution] Answers: (a) 0.008 kN (b) 0.02 kN --------------------------------------------------------------------------------1-1-5 Calculate the weight of an object of mass 50 kg at the bottom and top of a mountain with (a) g = 9.8 m/s2 and (b) 9.78 m/s2 respectively. [Manual Solution] Answers: (a) 0.49 kN, (b) 0.489 kN --------------------------------------------------------------------------------1-1-6 According to Newton's law of gravity the value of g at a given location is inversely proportional to the square of the distance of the location from the center of the earth. Determine the weight of a textbook of mass 1 kg at (a) sea level and in (b) an airplane cruising at an altitude of 45,000 ft. Assume earth to be a sphere of diameter 12,756 km. [Manual Solution] Answers: (a) 9.81 N, (b) 9.77 N --------------------------------------------------------------------------------1-1-7 The frictional force on a block of mass mA resting on a table (see Fig. P1. is given as F = m N, where N is the normal reaction force from the table. Determine the maximum value for mB that can be supported by friction. Assume the pulley to be frictionless. [Manual Solution] Answers: mBmax = m mA-------------------------------------------------------------------------------- Anim. 1-1-7 (click) 1-1-8 If the block A in the above problem sits on a wedge with an angle q with the horizontal, how would the answer change? [Manual Solution] Anim. 1-1-8 (click) --------------------------------------------------------------------------------1-1-9 A block with a mass of 10 kg is at rest on a plane inclined at 25o to the horizontal. If ms= 0.6, determine the range of the horizontal push force F if the block is (a) about to slide down, and (b) about to slide up. [Manual Solution] --------------------------------------------------------------------------------1-1-10 A vertical piston cylinder device contains a gas at an unknown pressure. If the outside pressure is 100 kPa, determine (a) the pressure of the gas if the piston has an area of 0.2 m2 and a mass of 20 kg. Assume g = 9.81 m/s2. (b) What-if-Scenario: How would the answer in (a) changes if the orientation of the device is changed upside down. [Manual Solution] Answers: (a) 101 kPa, (b) 99 kPa.-------------------------------------------------------------------------------- Anim. 1-1-10 (click) 1-1-11 Determine the mass of the weight necessary to increase the pressure of the liquid trapped inside the piston cylinder device to 120 kPa. Assume the piston to be weightless with an area of 0.1 m2, the outside pressure to be 100 kPa and g = 9.81 m/s2. [Manual Solution] Answers: 203.9 kg. --------------------------------------------------------------------------------1-1-12 A piston with a diameter of 50 cm and a thickness of 5 cm is made of a composite material with a density of 4000 kg/m3. (a) If the outside pressure is 101 kPa, determine the pressure inside the piston-cylinder assembly if the cylinder contains air. What-if-Scenario: (b) How would the answer change if the piston diameter was 100 cm instead? (c) Would the answers change if the cylinder contains liquid water instead? [Manual Solution] Answers: (a) 104.8 kPa --------------------------------------------------------------------------------1-1-13 Air in the accompanying piston-cylinder device is in equilibrium at 200 °C. If the mass of the hanging weight is 10 kg and the piston diameter is 10 cm, (a) determine the pressure of air inside. Assume g = 9.81 m/s2. (b) What-if-Scenario: How would the answer change if the gas was hydrogen instead? Molar mass of air is 29 kg/kmol and that of hydrogen is 2 kg/kmol. Neglect piston mass and friction. [Manual Solution*] Answers: (a) 87.5 kPa, (b) No change Anim. 1-1-13 (click) --------------------------------------------------------------------------------1-1-14 A vertical hydraulic cylinder has a piston with a diameter of 100 mm. If the ambient pressure is 100 kPa, determine the mass of the piston if the pressure inside is 1000 kPa. [Manual Solution] Answers: 720.2 kg. --------------------------------------------------------------------------------1-1-15 Determine the pull force necessary on the rope to reduce the pressure of the liquid trapped inside the piston cylinder device to 80 kPa. Assume the piston to be weightless with a diameter of 0.1 m, the outside pressure to be 100 kPa, and g = 9.81 m/s2. [Manual Solution] Answers: 0.157 kN Anim. 1-1-15 (click) --------------------------------------------------------------------------------• Thermodynamic Systems (Sec. 1 Continued) (A Generic Thermo System) --------------------------------------------------------------------------------1-1-16 As shown in the figure below, electric current from the photo-voltaic cell runs an electric motor. The shaft of the motor turns the paddle wheel inside the water tank. Identify the system-surroundings interactions for the following systems: (a) cell (b) motor (c) tank and (d) the combined system that includes all these three subsystems. [Manual Solution] Figure 1-1-16 --------------------------------------------------------------------------------1-1-17 Identify the interactions between your body and the surroundings when you sleep. [Manual Solution*] --------------------------------------------------------------------------------1-1-18 Identify the interactions between your room and the surroundings, assuming the doors and windows are closed. [Manual Solution] --------------------------------------------------------------------------------1-1-19 Pulled by an external force, a rigid body accelerates. Treating the body as a thermodynamic system, determine the modes and signs of energy transfer across the boundary. [Manual Solution] Anim. 1-1-19 (click) --------------------------------------------------------------------------------1-1-20 During the free fall of a rigid body, identify the interactions between the body and its surroundings. [Manual Solution] --------------------------------------------------------------------------------1-1-21 A rigid body slides down a ramp under its own weight. Determine the sign of (a) work and (b) heat transfer resulting from friction. [Manual Solution] --------------------------------------------------------------------------------1-1-22 An electric adaptor for a notebook computer (converting 110 volts to 19 volts) operates 10oC warmer than the surrounding temperature. Determine the sign of each energy interactions. [Manual Solution] Figure 1-1-22 --------------------------------------------------------------------------------1-1-23 A block of ice dropped into a tank of water as shown in Fig. 1-1-23 begins melting. Identify the interactions for the (a) ice as a system (b) water in the tank as a system (c) water and ice together as a system. Compare the combined system with the extended system in terms of interactions with the surroundings. [Manual Solution] Figure 1-1-23 --------------------------------------------------------------------------------1-1-24 A gas trapped in a piston-cylinder assembly expands as it is heated by an electrical resistance heater placed inside the cylinder. Treating the gas and the heater as the system, identify (a) the interactions with its surroundings and (b) the signs of all energy transfers. [Manual Solution] Anim. 1-1-24 (click) --------------------------------------------------------------------------------1-1-25 A piston-cylinder device contains superheated vapor at atmospheric pressure. The piston is pulled by an external force until the pressure inside drops by 50%. Determine the sign of boundary work transfer treating the vapor as the system. [Manual Solution] --------------------------------------------------------------------------------1-1-26 A warm cup of coffee gradually cools down to room temperature. Treating the coffee as the system, determine the sign of heat transfer during the cooling process. [Manual Solution] Anim. 1-1-26 (click) --------------------------------------------------------------------------------1-1-27 A hot block of solid is dropped in a tank of cold water, which is at the temperature of the surrounding. Determine the sign of heat transfer treating (a) the block as the system (b) the water as the system and (c) the entire tank (with the block and water) as the system. [Manual Solution] Anim. 1-1-27 (click) --------------------------------------------------------------------------------1-1-28 In order to keep a room cool, a student turns on a fan, and opens the refrigerator door. Treating the room as a closed system, identify the possible (a) energy interactions and (b) determine the sign of each energy transfer. [Manual Solution*] --------------------------------------------------------------------------------1-1-29 An insulated tank containing high pressure nitrogen is connected to another insulated tank containing oxygen at low pressure. Determine the possible interactions as the valve is opened and the two gases are allowed to form a mixture by treating (a) one of the tanks as a system and (b) two tanks together as a single system. [Manual Solution] Anim. 1-1-29 (click) --------------------------------------------------------------------------------1-1-30 Water flows through a pipe of constant diameter at steady state. Assuming the exit and inlet at the same level, identify the interactions between (a) the open system and (b) its surroundings. If the exit was at a higher elevation, would your answers change? [Manual Solution] --------------------------------------------------------------------------------1-1-31 Water is accelerated by a nozzle attached at the end of a garden hose. Identify the interactions, treating the nozzle as an open system. [Manual Solution] Anim. 1-1-31 (click) --------------------------------------------------------------------------------1-1-32 Air is decelerated by passing it through a diffuser (inverse of a nozzle) at the inlet of a jet engine. Identify the interactions between the diffuser and its surroundings. [Manual Solution] Anim. 1-1-32 (click) --------------------------------------------------------------------------------1-1-33 A steam turbine produces shaft work as steam flows through it, entering at a high pressure and a high temperature, and leaving at a relatively low pressure. Identify the interactions between the turbine (as an open system) and its surroundings. [Manual Solution] Anim. 1-1-33 (click) --------------------------------------------------------------------------------1-1-34 Identify the possible interactions for a steam turbine with poor insulation. [Manual Solution] --------------------------------------------------------------------------------1-1-35 The pressure of a liquid flow is raised by a pump driven by an electrical motor. Identify the interactions treating (a) the pump as an open system and (b) the pump and the motor as a combined system. [Manual Solution] -------------------------------------------------------------------------------- Anim. 1-1-35 (click) 1-1-36 A pumping system raises water from the ground level to the roof of a ten story building. Identify the interactions between the entire system (pump and the piping's) and its surroundings. [Manual Solution] --------------------------------------------------------------------------------1-1-37 A compressor raises the pressure of a gas flow. The temperature of the gas is also increased as a result. Identify the possible interactions between the compressor and its surroundings. [Manual Solution] Anim. 1-1-37 (click) --------------------------------------------------------------------------------1-1-38 In a heat exchanger (see accompanying animation) a flow of hot air is cooled by a flow of water. Identify the interactions treating (a) the entire heat exchanger as the system and (b) one of the streams as the system. [Manual Solution] Anim. 1-1-38 (click) --------------------------------------------------------------------------------1-1-39 In a mixing chamber (see accompanying animation), a hot water flow mixes with a cold water flow. Identify the possible interactions treating (a) the entire mixing chamber as the system and (b) one of the flows as the system. [Manual Solution] Anim. 1-1-39 (click) --------------------------------------------------------------------------------1-1-40 A pressure cooker containing water is heated on a stove. Determine the interactions and signs of heat and work transfer, if any, as steam is released. [Manual Solution] Anim. 1-1-40 (click) --------------------------------------------------------------------------------1-1-41 As you blow a balloon, what are the interactions between the balloon as a system and its surroundings? [Manual Solution] --------------------------------------------------------------------------------1-1-42 Hot water fill up a bath tub. As the water level rises, determine the interactions treating the water in the tub as the system. (Hint: Do not forget the boundary work.) [Manual Solution] --------------------------------------------------------------------------------1-1-43 Air rushes in to fill an evacuated tank as the valve is opened. Determine the interactions treating (a) the tank as the system and (b) the tank and the air that eventually enters in the system as the system. [Manual Solution] Anim. 1-1-43 (click) --------------------------------------------------------------------------------Section-2: Interactions - Mass, Heat, and Work Transfer ----------------------------------------------------------------------------------------------------------------------------------------------------------------• Mass Interactions Across System Boundary (Mass Transfer) --------------------------------------------------------------------------------1-2-1 Air with a density of 1 kg/m3 flows through a pipe of diameter 20 cm at a velocity of 10 m/s. Determine (a) the volume flow rate in L/min and (b) Mass flow rate in kg/min. Use the PG flow state daemon to verify your answer. [Manual Solution] [TEST Solution] Figure 1-2-1 Answers: (a) 5.2 L/min, (b) 18.84 kg/min --------------------------------------------------------------------------------1-2-2 Water flows through a variable-area pipe with a mass flow rate of 10,000 kg/min. Determine the minimum diameter of the pipe if the flow velocity is not to exceed 5 m/s. Assume density of water to be 1000 kg/m3. Use the SL flow state daemon to verify your answer. [Manual Solution] [TEST Solution] Answers: 0.206 m --------------------------------------------------------------------------------1-2-3 Steam at 400oC enters a nozzle with an average velocity of 20 m/s. If the specific volume and the flow area at the inlet are measured as 0.1 m3/kg and 0.01 m2 respectively, determine (a) the volume flow rate in m3/s, and (b) the mass flow rate in kg/s. Use the PC flow state daemon to verify your answers. [Manual Solution] [TEST Solution] Answers: (a) 0.2 m3/s, (b) 2 kg/s Anim. 1-2-3 (click) --------------------------------------------------------------------------------• Work Interactions (Sec. 2 Continued) (Work Transfer Modes) --------------------------------------------------------------------------------1-2-4 A bucket of concrete with a mass of 5000 kg is raised without any acceleration by a crane through a height of 20 m. (a) Determine the work transferred into the bucket. (b) What happens to the energy as it is transferred to the bucket? (c) Also determine the power delivered to the bucket if it is raised at a constant speed of 1 m/s. [Manual Solution] Answers: (a) 981 kJ, (c) 49.05 kW --------------------------------------------------------------------------------1-2-5 The accompanying figure shows a body of mass 50 kg being lifted at a constant velocity of 1 m/s by the rope and pulley arrangement. Determine power delivered by the shaft. [Manual Solution] Answers:0.49kW Anim. 1-2-5 (click) --------------------------------------------------------------------------------1-2-6 (a) Determine the constant force necessary to accelerate a car of mass 1000 kg from 0 to 100 km/h in 6 seconds. (b) Also calculate the work done by the force. (c) Show that the work done by the force equals the change in kinetic energy of the car. Neglect friction. (d) What-if scenario: How would the answer in part (b) change if the acceleration was achieved in 5 seconds? [Manual Solution] Answers: (a) 4.63 kN, (b) 385.8 kJ, (c) No change (d) 312.46 kJ --------------------------------------------------------------------------------1-2-7 A driver locks the brake of a car traveling at 140 km/h. Without an anti-lock-brake, the tires immediately start skidding. If the total mass of the car, including the driver is 1200 kg. Determine (a) the deceleration and (b) the stopping distance for the car and (c) the work transfer (include sign) treating the car as the system. Assume the friction coefficient between rubber and pavement to be 0.9. Neglect viscous drag. [Manual Solution] Answers: (a) 8.83 m/s2, (b) 85.6 m, (c) 907.3 kJ Figure 1-2-7 --------------------------------------------------------------------------------1-2-8 A car delivers 200 hp to a winch used to raise a load of 1000 kg. Determine the maximum speed of lift. [Manual Solution] Answers: 15.2 m/s --------------------------------------------------------------------------------1-2-9 A truck of mass 10 tonnes (metric) is traveling at a velocity of 65 miles per hour. Determine (a) kinetic energy (b) how high a ramp is necessary to bring it to a stop if the mechanical energy remains constant? [Manual Solution] [TEST Solution] Answers: (a) 4.220 MJ, (b) 43.04 m --------------------------------------------------------------------------------1-2-10 A block of mass 100 kg is dragged on a horizontal surface with static and kinetic friction coefficients of 0.15 and 0.09 respectively. Determine (a) the pull force necessary to initiate motion (b) the work done by the pull force and (c) the work done against the frictional force as the block is dragged over a distance of 5 m (d) What is the net work transfer between the block and its surroundings? [Manual Solution] Answers: (a) 0.15 kN, (b) -0.44 kJ, (c) 0.44 kJ, (d) 0 Anim. 1-2-10 (click) --------------------------------------------------------------------------------1-2-11 In the accompanying figure, determine (a) the work done by the force F acting at an angle of q = 20o in moving the block of mass 10 kg by a distance of 3 m if ms = 0.5 (b) What is the sign of the work transfer if the block was treated as a system? (c) If the block comes to rest at the end of the process, describe what happens to the work done by the force? [Manual Solution] Answers: (a) -0.129 kJ Anim. 1-2-11 (click) --------------------------------------------------------------------------------1-2-12 Twenty 50 kg suitcases are carried by a horizontal conveyor belt at a velocity of 0.5 m/s without any slippage. If ms = 0.9, (a) determine the power required to drive the conveyor. Assume no friction loss on the pulleys. (b) What-if scenario: How would the answer change if the belt was inclined upward at an angle of q = 10o? [Manual Solution] Answers: (a) 4.905 kW (b) 0.416 KW --------------------------------------------------------------------------------1-2-13 A person with a mass of 70 kg climbs the stairs of a 50 m tall building. (a) What is the minimum work transfer if you treat the person as a system? Assume standard gravity. (b) If the energetic efficiency (work output/heat released by food) of the body is 30%, how many Calories are burned during this climbing process? [Manual Solution] Answers: (a) 34.34 kJ, (b) 27.4 kcal Figure 1-2-13 --------------------------------------------------------------------------------1-2-14 A person with a mass of 50 kg and an energetic efficiency of 35% decides to burn all the calories consumed from a can of soda (140 calories) by climbing stairs of a tall building. Determine the maximum height of the building necessary to ensure that all the calories from the soda can is expended in the work performed in climbing. [Manual Solution] Answers: 418 m --------------------------------------------------------------------------------1-2-15 The aerodynamic drag force Fd in kN on an automobile is given as Fd = 1/2000 cd A r V2 [kN], Where cd is the non-dimensional drag coefficient, A is the frontal area in m2, r is the density of the surrounding air in kg/m3, and V is the velocity of air with respect to the automobile in m/s. Determine the power required to overcome the aerodynamic drag for a car with cd = 0.4 and A = 7 m2, traveling at a velocity of 100 km/h. Assume the density of air to be r = 1.2 kg/m3. [Manual Solution] Answers: 36 kW Figure 1-2-15 --------------------------------------------------------------------------------1-2-16 The rolling resistance of the tires is the second major opposing force (next to aerodynamic drag) on a moving vehicle and is given by Fr = f W [kN] where f is the rolling resistance coefficient and W is the weight of the vehicle in kN. Determine the power required to overcome the rolling resistance for a 2000 kg car traveling at a velocity of 100 km/h, if f = 0.007. [Manual Solution] Answers: 3.815 kW --------------------------------------------------------------------------------1-2-17 Determine (a) the power required to overcome the aerodynamic drag and (b) rolling resistance for a truck traveling at a velocity of 120 km/h, if cd = 0.8, A = 10 m2, r = 1.2 kg/m3, f = 0.01, and m = 20,000 kg. Plot the power requirement - aerodynamic, rolling friction and total - against velocity within the range from 0 to 200 km/h. [Manual Solution] [TEST Solution] Answers: (a) 177.78 kW (b) 65.4 kW --------------------------------------------------------------------------------1-2-18 Determine (a) the power required to overcome the aerodynamic drag (b) rolling resistance for a bicyclist traveling at a velocity of 21 km/h, if cd = 0.8, A = 1.5 m2, r = 1.2 kg/m3, f = 0.01 and m = 100 kg. Also determine (c) the metabolic energetic efficiency (work output/energy input) for the bicyclist if the rate at which calories are burned is measured at 650 Calories/h. [Manual Solution] Answers: (a) 0.14 kW, (b) 0.06 kW, (c) 26.45% --------------------------------------------------------------------------------1-2-19 Determine (a) the work transfer involved in compressing a spring with a spring constant of 150 kN/m from its rest position by 10 cm, and (b) What is the work done in compressing it further by another 10 cm? [Manual Solution] Answers: (a) -0.75 kJ, (b) -3 kJ --------------------------------------------------------------------------------1-2-20 An object with a mass of 200 kg is acted upon by two forces, 0.1 kN to the right and 0.101 kN to the left. Determine (a & b) the work done by the two faces and (c) the net work transfer as the system (the object) is moved by a distance of 10 m. [Manual Solution] Answers: (a) 1 kJ, (b) -1.01 kJ, (c) -0.01 kJ --------------------------------------------------------------------------------1-2-21 A gas trapped inside a piston-cylinder device receives 20 kJ of heat while it expands performing a boundary work of 5 kJ. At the same time 10 kJ of electrical work is transferred into the system. Evaluate (a) Q and (b) W with appropriate signs. [Manual Solution] Answers: (a) 20 kJ, (b) -5 kJ Anim. 1-2-21 (click) --------------------------------------------------------------------------------1-2-22 A piston-cylinder device containing a fluid is fitted with a paddle wheel stirring device operated by the fall of an external weight of mass 50 kg. As the mass drops by a height of 5 m, the paddle wheel makes 10,000 revolutions. Meanwhile the piston (frictionless and weightless) of 0.5 m diameter moves out by a distance of 0.7 m. Find the net work transfer for the system if the pressure outside is 101 kPa. [Manual Solution] Answers: -1.52 kJ --------------------------------------------------------------------------------1-2-23 A gas in a vertical piston-cylinder device has a volume of 0.5 m3 and a temperature of 400 K. The piston has a mass of 50 kg and a cross-sectional area of 0.2 m2. As the gas cools down to atmospheric temperature the volume decreases to 0.375 m3. Neglecting friction and assuming atmospheric pressure to be 100 kPa. Determine (a) the work transfer during the process. (b) What-if-Scenario: How would the answer in (a) change if the piston weight was considered negligible? [Manual Solution] Answers: (a) -12.81 kJ, (b) -12.51 kJ Anim. 1-2-23 (click) --------------------------------------------------------------------------------1-2-24 A 10 m3 insulated rigid tank contains 20 kg of air at 25oC. An electrical heater within the tank is turned on which consumes a current of 5 Amps for 30 min from a 110 V source. Determine the work transfer in kJ. [Manual Solution] Answers: -990 kJ Anim. 1-2-24 (click) --------------------------------------------------------------------------------1-2-25 A paddle wheel stirs a water tank at 500 rpm. The torque transmitted by the shaft is 20 N-m. At the same time an internal electric resistance heater draws 2 Amps of current from a 110 V source as it heats the water. Determine (a) the total rate of work transfer in kW and (b) What is the total work transfer in one hour? [Manual Solution] Answers: (a) -1.267 kW, (b) -4561.2 kJ --------------------------------------------------------------------------------1-2-26 Determine the power transmitted by the crankshaft of a car transmitting a torque of 0.25 kN-m at 3000 rpm. [Manual Solution] Answers: 78.54 kW --------------------------------------------------------------------------------1-2-27 Determine the boundary work transfer in blowing a balloon to a volume of 0.01 m3. Assume that the pressure inside the balloon equal to the surrounding atmospheric pressure, 100 kPa. [Manual Solution] Answers: 1 kJ --------------------------------------------------------------------------------1-2-28 Air in a horizontal piston-cylinder assembly expands from an initial volume of 0.25 m3 to a final volume of 0.5 m3 as the gas is heated for 90 s by an electrical resistance heater consuming 1 kW of electric power. If the atmospheric pressure is 100 kPa, determine (a) the boundary work transfer and (b) the net work transfer. (c) What-if-Scenario: How would the answers change if the cylinder contained oxygen instead? [Manual Solution] Answers: (a) 25 kJ, (b) -65 kJ, (c) No change Anim. 1-2-28 (click) --------------------------------------------------------------------------------1-2-29 A vertical piston-cylinder assembly (see figure) contains 10 L of air at 20oC. The cylinder has an internal diameter of 20 cm. The piston is 2 cm thick and is made of steel of density 7830 kg/m3. If the atmospheric pressure outside is 101 kPa, (a) determine the pressure of air inside the cylinder. The air is now heated until its volume doubles. (b) Determine the boundary work transfer during the process. (c) What-if-Scenario: How would the answers change if the piston weight was neglected? [Manual Solution] Answers: (a) 102.5 kPa, (b) 1.025 kJ, (c) 101 kPa, 1.01 kJ Anim. 1-2-29 (click) --------------------------------------------------------------------------------1-2-30 Air in the accompanying piston-cylinder device is initially in equilibrium at 200 °C. The mass of the hanging weight is 10 kg and the piston diameter is 10 cm. As air cools due to heat transfer to the surroundings, the piston moves to the left, pulling the weight up. Determine (a) the boundary work and (b) the work done in raising the weight for a piston displacement of 37 cm. (c) Explain why the two are different. [Manual Solution] Answers: (a) -0.254 kJ, (b) 0.036 Anim. 1-2-30 (click) --------------------------------------------------------------------------------1-2-31 An insulated, vertical piston-cylinder assembly (see figure) contains 50 L of steam at 105 oC. The outside pressure is 101 kPa. The piston has a diameter of 20 cm and the combined mass of the piston and the load is 75 kg. The electrical heater and the paddle wheel are turned on and the piston rises slowly by 25 cm. Determine (a) the pressure of air inside the cylinder during the process (b) the boundary work performed by the gas and (c) the combined work transfer by the shaft and electricity if the net energy transfer into the cylinder is 3.109 kJ. [Manual Solution] Answers: (a) 123.42 kPa, (b) 0.97 kJ, (c) -4.13 kJ Anim. 1-2-31 (click) --------------------------------------------------------------------------------1-2-32 Steam is compressed from p1 = 100 kPa, vol1 = 1 m3 to p2 = 200 kPa, vol2 = 0.6 m3. The external force exerted on the piston is such that pressure increases linearly with a decrease in volume. Determine (a) the boundary work transfer (b) Show the work by shaded areas in a p-v diagram. [Manual Solution] Answers: (a) -220 KJ (b) -59.03 kJ --------------------------------------------------------------------------------1-2-33 A gas in a piston-cylinder assembly is compressed (through a combination of external force on the piston and cooling) in such a manner that the pressure and volume are related by pVn = constant. Given an initial state of 100 kPa and 1 m3 and a final volume of 0.5 m3. Evaluate the work transfer if (a) n = 0 (b) n = 1 and (c) n = 1.4 and (d) Plot a p-V diagram for each processes and show the work by shaded areas. [Manual Solution] Answers: (a) -50 kJ, (b) -69.31 kJ, (c) -79.8 kJ Anim. 1-2-33 (click) --------------------------------------------------------------------------------1-2-34 In the preceding problem the piston has a cross-sectional area of 0.05 m2. If the atmospheric pressure is 100 kPa and the weight of the piston and friction are negligible, plot how the external force applied by the connecting rod on the piston varies with the gas volume for (a) n = 0 (b) n = 1 and (c) n = 1.4. [Manual Solution] --------------------------------------------------------------------------------1-2-35 Determine the total work done by a gas system following an expansion process as shown in the accompanying p-V diagram. (needs a diagram from Naag, pg 54). [Manual Solution] --------------------------------------------------------------------------------1-2-36 A piston-cylinder device contains 0.03 m3 of nitrogen at a pressure of 300 kPa. The atmospheric pressure is 100 kPa and the spring resisting the piston motion has a spring constant of 256.7 kN/m. Heat is now transferred to the gas until the volume doubles. If the piston has a diameter of 0.5 m, determine (a) the final pressure of nitrogen (b) the work transfer from nitrogen to the surroundings and (c) the fraction of work that goes into the atmosphere. [Manual Solution] Answers: (a) 500 kPa, (b) 12 kJ, (c) 25% Anim. 1-2-36 (click) --------------------------------------------------------------------------------1-2-37 A 100 kg block of solid is moved upward by an external force F as shown in the accompanying figure. After a displacement of 10 cm, the upper surface of the block reaches a linear spring at its rest position. The external force is adjusted so that the displacement continues for another 10 cm. If the spring constant is 100 kN/m and acceleration due to gravity is 9.81 m/s2. Determine (a) the work done by the external force and (b) What fraction of the energy transferred is stored in the spring? [Manual Solution] Answers: (a) 0.696 kJ, (b) 71.8% Figure 1-2-37 --------------------------------------------------------------------------------1-2-38 The rate of energy transfer due to flow work at a particular cross-section is 20 kW. If the volume flow rate is 0.2 m3/min. Determine the pressure at that location. [Manual Solution] Answers: 6 MPa --------------------------------------------------------------------------------1-2-39 At the inlet of a steam turbine the flow state is as follows: p1 = 1 MPa, V1 = 30 m/s, mdot1 = 9 kg/s and A1 = 0.1 m2. Determine the rate of energy transfer due to flow work. [Manual Solution] Answers: 3 MW Anim. 1-2-39 (click) --------------------------------------------------------------------------------1-2-40 Nitrogen in a horizontal piston-cylinder assembly expands from an initial volume of 0.10 m3 to a final volume of 0.5 m3 as the gas is heated for 5 minutes by an electrical resistance heater consuming 1 kW of electric power. If the pressure remains constant at 150 kPa, and 70 kJ of heat is lost from the cylinder during the expansion process, determine (a) the boundary work transfer, (b) electrical work transfer, and (b) the net energy transfer into the system through heat and work. [Manual Solution] Answers: (a) 60 kJ, (b) -300 kJ, (c) 170 kJ Anim. 1-2-40 (click) --------------------------------------------------------------------------------• Heat Interactions (Sec. 2 Continued) (Heat Transfer Modes) --------------------------------------------------------------------------------1-2-41 If a therm of heat costs \$1.158 and a kW.h of electricity costs \$0.106 compare their prices on the basis of GJ. [Manual Solution] [TEST Solution] Answers: Heat: \$10.976/GJ; Electricity: \$29.444/GJ --------------------------------------------------------------------------------1-2-42 The heating value (maximum heat released as a fuel is burned with atmospheric air) of diesel is 43 MJ/kg. Determine the minimum fuel consumption necessary to accelerate a 20 ton (short ton) truck from 0 to 70 mph speed. Assume that all the work done by the engine is used to raise the kinetic energy of the truck and the efficiency of the engine is 35%. [Manual Solution] Heating Values of Common Fuels Answers: (a) 0.59 kg --------------------------------------------------------------------------------1-2-43 A gas station sells gasoline and diesel at \$2.00/gallon and \$1.75/gallon respectively. If the following data are known about the two fuels, compare the prices on the basis of MJ of energy. Heating value: gasoline 47.3 MJ/kg, diesel 46.1 MJ/kg; density: gasoline 0.72 kg/L, diesel 0.78 kg/L. [Manual Solution] Answers: Gasoline: \$0.0155/MJ; Diesel: \$0.0129/MJ --------------------------------------------------------------------------------1-2-44 Consider three options for heating a house. Electric resistance heating with electricity priced at \$0.10/kWh, gas heating with gas priced at \$1.10/Therm and oil (density 0.8 kg/L, heating value 46.5 MJ/kg) heating with oil priced at \$1.50/gal. Energetic efficiencies are 100% for the electrical heating system, 85% for the gas heating system and 80% for the oil heating system. Determine the cost of delivering 1 GJ of energy by each system. [Manual Solution] Answers: \$27.77, \$12.27, \$13.33 --------------------------------------------------------------------------------1-2-45 The USA consumed about 21 MMbd (million barrels per day) of crude oil (density 0.82 kg/L, heating value 47 MJ/kg), 67% of which is utilized in the transportation sector. Determine how many barrels of oil can be saved per year, if the fuel consumption in the transportation sector can be reduced by 20% through the use of hybrid technology. [Manual Solution] Energy Use in 2003:USA vs. World Answers: 1.027 billion barrels --------------------------------------------------------------------------------1-2-46 In 2003, the US consumed 20 MMbd of crude oil, 21.9 tcf (trillion cubic feet) of natural gas, and 1 billion tons (short) of coal. The Btu equivalents are as follows:- 1 bbl crude oil: 5.8 million Btu; 1 Mcf gas: 1.03 million Btu; 1 ton coal: 21 million Btu. Compare the energy consumption in the consistent unit of Quad (1 Quad = 10^15 Btu). [Manual Solution] Answers: 42.34 Quad, 22.557 Quad, 21 Quad --------------------------------------------------------------------------------1-2-47 In 2002, US produced 3.88 trillion kWh of electricity. If coal (heating value 24.4 MJ/kg) accounted for 51% of the electricity production at an average thermal efficiency (electrical work output/heat input) of 40%, determine the total amount of coal (in short tons) consumed by the power plants in 2002. [Manual Solution] Answers: 0.804 billion short tons --------------------------------------------------------------------------------Section-3: State and Properties (System vs. Flow State), (Properties Classified) --------------------------------------------------------------------------------1-3-1 Classify (thermodynamic, extrinsic or system) the following properties (a) m (b) v (c) p (d) T (e) r (f) KE (g) ke (h) mdot and (i) V. [Manual Solution] --------------------------------------------------------------------------------1-3-2 Compare the moles of atoms in kmols in a 1 in3 block of copper with that in an identical block of aluminum. [Manual Solution] Answers: 0.002295 kmol, 0.00164 kmol Anim. 1-3-2 (click) --------------------------------------------------------------------------------1-3-3 Determine the mass of one molecule of water. Assume the density to be 1000 kg/m3. [Manual Solution] Answers: 2.99x10-26kg --------------------------------------------------------------------------------1-3-4 One kmol of nitrogen is mixed with 2 kg of oxygen. Determine the total amount in (a) kg and (b) kmol. [Manual Solution] Answers: (a) 30 kg , (b) 1.625 kmol --------------------------------------------------------------------------------1-3-5 2 kg of hydrogen is mixed with 2 kg of oxygen. If the final mixture has a volume of 3 m3. Determine (a) molar mass (b) specific volume and (c) the molar specific volume of the final mixture. [Manual Solution] Answers: (a) 3.76 kg/kmol, (b) 0.75 m 3/kg, (c) 2.82 m 3/kmol --------------------------------------------------------------------------------1-3-6 A 4 m x 5 m x 6 m room contains 120 kg of air. Determine (a) density (b) specific volume (c) moles and (d) specific molar volume of air. Assume molar mass of air to be 29 kg/kmol. [Manual Solution] Answers: (a) 1 kg/m3, (b) 1 m3/kg, (c) 4.138 kmol, (d) 29 m3/kmol --------------------------------------------------------------------------------1-3-7 10 kg of water (density 1000 kg/m3) and 5 kg of ice (density 916 kg/m3) are at equilibrium at 0oC. Determine the specific volume of the mixture. [Manual Solution] Answers: 0.001 m3/kg Figure 1-3-7 --------------------------------------------------------------------------------1-3-8 If equal volume of iron and copper (look up Table A-1 for densities) are melted together, determine (a) the specific volume and (b) density of the alloy. Assume no change in the final volume. (c) What-if scenario: How would the answers change if equal masses of iron and copper were melted together? [Manual Solution] Answers: (a) 0.000122 m3/kg, (b) 8190 kg/m3,(c) 0.000123 m3/kg, 8128.45 kg/m3, --------------------------------------------------------------------------------1-3-9 What is the atmospheric pressure in kPa if a mercury barometer reads 750 mm. Assume r = 13,600 kg/m3. [Manual Solution] Answers: 100.062 kPa Figure 1-3-9 --------------------------------------------------------------------------------1-3-10 Determine the height of a mountain if the absolute pressure measured at the bottom and top are 760 mm and 720 mm of mercury. Assume r= 13,600 kg/m3 and rair = 1.1 kg/m3. [Manual Solution] Answers: 495 m --------------------------------------------------------------------------------1-3-11 A bourdon gage measures the pressure of water vapor at the top of a cylindrical tank with a height of 6 m to be 300 kPa. Determine (a) the absolute pressure at the bottom of the tank if 50% of the tank is filled with water vapor (b) What is the error if the variation of pressure in the vapor phase is neglected? Assume rvap = 2.16 kg/m3. [Manual Solution] Answers: (a) 430.49 kPa, (b) -0.015 % --------------------------------------------------------------------------------1-3-12 Determine the readings of the two Bourdon gages if the inner tank (see figure) has a pressure of 500 kPa, the outer tank a pressure of 50 kPa and the atmosphere a pressure of 100 kPa. [Manual Solution] Answers: -50 kPag or 50 kPav, 450 kPag Figure 1-3-12 --------------------------------------------------------------------------------1-3-13 Two closed chambers A and B are connected by a water manometer. If the gage pressure of chamber A is 10 mm of mercury vacuum and the height difference of the water columns is 10 cm. Determine the pressure in tank B if rwater = 923 kg/m3 , rvap = 2.16 kg/m3. [Manual Solution] Answers: 2.238 kPa --------------------------------------------------------------------------------1-3-14 Air flows through a Venturi meter as shown in the accompanying figure. Determine the difference in pressure between point A and B if the height difference of the water columns is 3 cm. Assume rair = 1.2 kg/m3 and rwater = 1000 kg/m3. [Manual Solution] Answers: 0.294 kPa Figure 1-3-14 --------------------------------------------------------------------------------1-3-15 Determine the height of the oil in the thin tube necessary to support a weight of 1000 kg in a hydraulic lift with the tube diameters of 1.4 m and 1 cm. Assume roil = 780 kg/m3 and rwater = 1000 kg/m3. [Manual Solution] Answers: 0.832 m --------------------------------------------------------------------------------1-3-16 The maximum blood pressure of a patient requiring blood transfer is found to be 110 mmHg. What should be the minimum height of the ivy to prevent a back flow? Assume rblood = 1050 kg/m3. [Manual Solution] Answers: 1.4237 m --------------------------------------------------------------------------------1-3-17 The temperature assigned for the ice and steam points are 0 and 100 in the Celsius scale and 32 and 212 in the Fahrenheit scale. Both scales use a linear division. (a) Show that the two scales are related by C /5 = (F - 32)/9. (b) At what temperature do they show the same reading? [Manual Solution] Answers: (b) -40oC Anim. 1-3-17 (click) --------------------------------------------------------------------------------1-3-18 The temperature T on a thermometric scale is defined in terms of property x by the function T = a ln x + b , where a and b are constants. The values of x are found to be 1.8 and 6.8 at the ice point and the steam point, the temperatures of which are assigned numbers 0 and 100 respectively. Determine the temperature corresponding to a reading of x = 2.4 in this thermometer. [Manual Solution] Answers: 21.6 --------------------------------------------------------------------------------1-3-19 Two liquid-in-glass thermometers are made of identical materials and are accurately calibrated at 0oC and 100oC. While the first tube is cylindrical, the second tube has a conical bore, 15% greater in diameter at 0oC than at 100oC. Both tubes are subdivided uniformly between the two calibration points into 100 parts. If the conical bore thermometer reads 50oC. What will the cylindrical thermometer read? Assume the change in volume of the liquid proportional to the change in temperature. [Manual Solution*] Figure 1-3-19 --------------------------------------------------------------------------------1-3-20 The signal (e.m.f.) produced by a thermocouple with its test junction at ToC is given by e = aT + bT2 [mV], where a = 0.2 mV/o C and b = -5.1 x 10-4 mV/oC2. (a) Draw a graph of e against T within the range of -200oC to 500oC. Suppose you define a new scale after your name. The temperature in your scale is assumed to be linearly related to the signal through T'= a' + b' e with T'= 25 at ice point and T' = 150 at the steam point. (b) Find the values of a' and b', and plot T ' against T. [Manual Solution*] --------------------------------------------------------------------------------1-3-21 [TEST] A cup of coffee (system mass 1 kg) at 30oC rests on a table of height 1 m. An identical cup of coffee rests on the floor at a temperature of 25oC. Determine (a) the difference in the stored energy in the two systems (b) What fraction of the difference can be attributed to potential energy? Use the SL (solid/liquid) system state daemon. Assume properties of coffee to be similar to those of water. [TEST Solution] Answers: (a)-20.93 kJ, (b) 0.047% Figure 1-3-21 --------------------------------------------------------------------------------1-3-22 [TEST] Using the SL system state daemon, determine the change in stored energy (E) in a block of copper of mass 1 kg due to (a) an increase in temperature from 25oC to 100oC (b) an increase in velocity from 0 to 30 m/s and (c) an increase in elevation by 100 m. (d) What-if-Scenario: How would the answer in (a) change if the working substance was granite instead? [TEST Solution] Answers: (a) 28.95 kJ, (b) 0.45 kJ, (c) 0.981 kJ, (d) d) 76.27 kJ Anim. 1-3-22 (click) --------------------------------------------------------------------------------1-3-23 [TEST] For a 1 kg block of copper determine the equivalence rise in stored energy by 1 kJ in terms of (a) increase in temperature (b) increase in velocity from rest and (c) an increase in height. (d) What-if-Scenario: How would the answer in (a) change if it was an aluminum block? Use the SL (Solid/Liquid) system state daemon. (Hint: enter e2 as '=e1+1'.) [TEST Solution] Answers: (a) 2.59oC, (b) 44.7 m/s, (c) 102 m, (d) 1.11oC --------------------------------------------------------------------------------1-3-24 [TEST] A piston cylinder device contains 0.01 m3 of nitrogen at 500 kPa and 30oC. Determine the change in stored energy (E) if (a) the pressure is doubled without a change in temperature (b) temperature is increased to 60oC at constant pressure. Use the IG (ideal gas) volume state daemon. [TEST Solution] Anim. 1-3-24 (click) --------------------------------------------------------------------------------1-3-25 [TEST] Determine the specific volume of the gas in a 1m3 chamber filled with (a) hydrogen (b) carbon-dioxide. The pressure inside is 1 atm and the temperature is 25oC. Use the ideal gas model. [TEST Solution] Answers: (a) 12.11 m3/kg, (b) 0.56 m3/kg -------------------------------------------------------------------------------- Figure 1-3-25 1-3-26 [TEST] A piston cylinder device contains 0.01m3 of steam at 500 kPa and 300oC. Determine the change in stored energy (E) if (a) the pressure is increased to 1 MPa at constant temperature (b) temperature is increased to 400oC at constant pressure. Use the PC (phase-change) system state daemon. [TEST Solution] --------------------------------------------------------------------------------1-3-27 [TEST] A granite rock of mass 1000 kg is situated on a hill at an elevation of 1000 m. On a sunny day its temperature rises to 95oC. (a) Determine the maximum useful work that can be extracted from the rock if the atmospheric temperature is 30oC. (b) Compare the potential energy of the rock with its stored exergy. Use the SL system state daemon. [TEST Solution] --------------------------------------------------------------------------------1-3-28 [TEST] A tank contains 2000 kg of water at 1000 kPa and 70oC. Determine (a) the stored exergy and (b) the stored energy in the water. Assume standard atmospheric conditions. [TEST Solution] -------------------------------------------------------------------------------- Anim. 1-3-28 (click) 1-3-29 [TEST] A tank contains 5 kg of carbon dioxide at 2000 kPa and 25oC. Using the IG (ideal gas) system state daemon, determine (a) the stored exergy and (b) the stored energy in the gas. Assume the atmospheric conditions to be 100 kPa and 25oC. (c) How do you explain the sign of the stored energy calculated by the daemon? [TEST Solution] Answers: (a) 576 kJ, (b) -282 kJ --------------------------------------------------------------------------------1-3-30 [TEST] Steam flows into a turbine with a mass flow rate of 6 kg/s at a temperature of 500oC and a pressure of 1500 kPa. If the inlet area is 0.25 m2, determine (a) Jdot (b) Edot (c) Udot (d) KEdot (e) Hdot (f) WFdot at the inlet. Use the PC (phase-change) flow state daemon. Neglect potential energy. [TEST Solution] Anim. 1-3-30 (click) --------------------------------------------------------------------------------1-3-31 [TEST] In the above problem determine the flow rate of (a) entropy and (b) exergy into the turbine if the atmospheric conditions are 100 kPa and 25oC. [TEST Solution] --------------------------------------------------------------------------------1-3-32 [TEST] The cooling water in a power plant is discharged into a lake at a temperature of 35oC with a flow rate of 1000 kg/min. Determine the rate of discharge of exergy. [TEST Solution]     THERMODYNAMICS PROBLEMS Page 1 of 1
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