Department of Mechanical Engineering Indian Institute of Technology New Delhi II Semester -- 2012 – 2013
MEL 140 ENGINEERING THERMODYNAMICS
PROBLEM SET – 1: Review of Basics
Problem 1: Define Work. Explain how the force is generated in an automobile.
Problem 2: Define and classify Energy and explain the relation between a body and energy.
Problem 3: Is there any relation between energy and work? Name any device which connects energy and work.
Problem 4: An aircraft is cruising at an altitude of 9.5 km. Apply Newton’s Second Law of Motion and analyze the forces acting on the flight.
Problem 4: Recapitulate the Law of conservation of Energy and comment on the validity of the same in an aircraft engine.
Problem 5: What is Temperature and Pressure? Why and how are they measured?
Problem 6: Explain the basic structure of a common instrument.
Department of Mechanical Engineering Indian Institute of Technology New Delhi II Semester -- 2012 – 2013
MEL 140 ENGINEERING THERMODYNAMICS
PROBLEM SET – 2: Application of Thermodynamics
This problem sheet describes some inventions which created a need for thermodynamic analysis for complete understanding. Try to understand the operation of these inventions and comment on the necessity of thermodynamic analysis.
Problem1: Savery's steam pump is shown on the side. This was first operated in 1698 to pump water. Identify the use of various parts and understand the principle of operation.
Problem 2: Newcomen's steam engine is shown on the side. By 1725, the Newcomen engine was employed in many coal mines but also was used to take water to mill-wheels. Identify the use of various parts and analyze the cyclic events occurring in operation.
Problem 3: James Watt modified the Newcomen’s steam engine by incorporating a separate condensing device. This was first operated in 1775 to pump water. This is the forerunner of the steam engines used for railroads, ships and numerous other applications. Draw approximate diagram of Watt’s engine. Identify the use of various parts and analyze the cycle of operation.
Problem 5: A muscle represents an organic system that converts chemical energy into mechanical work. This system works at constant temperature. Understand the principle of operation of muscle and identify the thermodynamic superiority of muscle over steam engine. Identify a special name to signify this superiority.
Department of Mechanical Engineering Indian Institute of Technology New Delhi II Semester -- 2012 – 2013
MEL 140 ENGINEERING THERMODYNAMICS
PROBLEM SET –3: Basic Definitions in Thermodynamics
Problem1: Consider LPG stove and Electric stove as thermodynamic systems and carryout preliminary study to classify under thermodynamics.
Problem2: Which of the following can be classified as a property? Give a brief reason. (a) Colour of a filament; (b) Age of a vehicle tire; (c) Life of a bulb ;(d) Specific heat of a solid;(e) Pressure; (f) Temperature; (g) heat; (h) Calorific value of a fuel.
Problem 3: A system is subjected to a change of state from state 1 to state 2. During this change of state it is found that the change in properties T, p and v are T, p and v. Verify whether the parameters v2, T3 and p2 can be called as properties are not.
Problem 5: The p--v--T relation for Clausius gas is
q p v b RT v2
Where a, b and R are constants. Show that T is a property of gas.
Problem 4: Integrate
x2 y dx 3xydy Along the paths (a) The straight line y = m x and (b) y = x2. Are the results of (a) and (b) equal? Discuss the nature of differential.
Problem 6: Integrate
2 2 x y dx 2xydy
Along the paths (a) The straight line y = x and (b) y = x3. Why in this case, the answer for the two paths are identical.
Problem 7: Find the total differential of T using the equation
q p v b RT v2
2 1.4 and integrate the differential along (a) p=v0 + k v, (b) p v = C1 and (c) p v = C2 and prove that the change in T is independent of path of integration.
Problem 8: A tank 5m high is half full of water, and air at 130 kPa gage pressure is occupying the remaining volume. The tank is 1.5m in diameter and the contents are at 200C. (At 200C the density of air =1.178 kg/m3 and the density of water = 998 kg/m3). (a) What is the gage pressure at the top of the water? (b) What is the gage pressure at the bottom of the tank? (c) If the atmospheric pressure is 101 kPa, find the absolute pressures of (a) & (b).
Department of Mechanical Engineering Indian Institute of Technology New Delhi II Semester -- 2012 – 2013
MEL 140 ENGINEERING THERMODYNAMICS
PROBLEM SET – 4: Properties of Pure Substance
Problem1: A sealed rigid vessel has volume of 1 m3 and contains 2 kg of water at 1000C. The vessel is now heated. If a safety pressure valve is installed, at what pressure should the valve be set to have a maximum temperature of 2000C?
Problem 2: Saturated water vapor at 200 kPa is in a constant pressure piston/cylinder assembly. At this state the piston is 0.1 m from the cylinder bottom. How much is this distance if the temperature is changed to a. 2000C, b. 1000C.
Problem 3: In a refrigerator the working substance evaporates from liquid to vapor at -200C inside a pipe around the cold section. Outside (on the back or below) is a black grille, inside of which the working substance condenses form vapor to liquid at 400C. For each location find the pressure and the change in specific volume (v) if a. the substance is R-22 b. the substance is ammonia. c. n-Pentane d. Propane and e. Propene.
Problem 4: Two tanks are connected both containing water. Tank A is at 200 kPa, v =0.5 m3/kg, V= 1 m3, and tank B contains 3.5 kg at 0.5 MPa and 4000C. The valve is now opened and the two come to a uniform state. Find the final specific volume.
Problem 5: A 400-m3 storage tank is being constructed to hold LNG, liquified natural gas, which may be assumed to be essentially pure methane. If the tank is to contain 90% liquid and 10% vapor, by volume, at 100 kPa, what mass of LNG (kg) will the tank hold? What is the quality in the tank?
Problem 6: A pressure cooker (closed tank) contains water at 1000C with the liquid volume being 1/10 of the vapor volume. It is heated until the pressure reaches 2.0 MPa. Find the final temperature. Has the final state more or less vapor than the initial state?
Problem 7: Ammonia at 100C with a mass of 10 kg is in a piston/cylinder assembly with an initial volume of 1 m3. The piston initially resting on the stops has a mass such that a pressure of 900 kPa will float it. Now the ammonia is slowly heated to 500C. Find the final pressure and volume.
Problem 8: A cylinder fitted with a frictionless piston contains butane at 250C, 500 kPa. Can the butane reasonably be assumed to behave as an ideal gas at this state?
Problem 9: A spherical helium balloon 10 m in diameter is at ambient T and P, 150C and 100 kPa. How much helium does it contain? It can lift a total mass that equals the mass of displaced atmospheric air. How much mass of the balloon fabric and cage can then be lifted?
Problem 10: Is it reasonable to assume that at the given states the substance behaves as an ideal gas? a. Oxygen at 300C, 3 MPa; b. Methane at 300C, 3 MPa; c. Water at 300C, 3 MPa d. R-134a at 300C, 3 MPa; e. R-134a at 300C, 100 kPa.
Department of Mechanical Engineering Indian Institute of Technology New Delhi II Semester -- 2012 – 2013
MEL 140 ENGINEERING THERMODYNAMICS
PROBLEM SET – 5: Modes of Work Transfer
Problem1: A bulldozer pushes 500 kg of dirt 100 m with a force of 1500 N. It then lifts the dirt 3 m up to put it in a dump truck. How much work did it do in each situation?
Problem 2: Two hydraulic cylinders maintain a pressure of 1200 kPa. One has a cross-sectional area of 0.01 m2, the other one of 0.03 m2. To deliver 1 kJ of work to the piston, how large a displacement (V) and piston motion H are needed for each cylinder?
n Problem 3: A nonlinear spring has a force versus the displacement relation of F = ks(x - x0) . If the spring end is moved to x1 from the relaxed state, determine the formula for the required work.
Problem 4: The rolling resistance of a car depends on its weight as F = 0.006 mg. How long will a car of 1400 kg drive for a work input of 25 kJ?
Problem 5: The air drag force on a car is 0.225 AV2. Assume air at 290 K, 100 kPa and a car frontal area of 4 m2 driving at 90 km/h. How much energy is used to overcome the air drag driving for 30 min?
Problem 6: A cylinder fitted with a frictionless piston contains 5 kg of superheated refrigerant R-134a vapor at 1000 kPa and 1400C. The setup is cooled at constant pressure until the R-134a reaches a quality of 25%. Calculate the work done in the process.
Problem 7: Tanks A and B are connected through a valve. Tank A is rigid with a volume of 400-L and contains argon gas at 250 kPa and 300C. Cylinder B, having a frictionless piston of such mass that a pressure of 150 kPa will float it, is initially empty. The valve is opened and argon flows into B and eventually reaches a uniform state of 150 kPa and 300C throughout. What is the work done by the argon?
Problem 8: A piston/cylinder assembly contains 1 kg of liquid water at 200C and 300 kPa. There is a linear spring mounted on the piston such that when the water is heated the pressure reaches 3 MPa with a volume of 0.1 m3. a. Find the final temperature. b. Plot the process in a P–v diagram. c. Find the work in the process.
1/3 Problem 9: A balloon behaves so the pressure is P =C2V , C2 = 100 kPa/m. The balloon is blown up with air from a starting volume of 1 m3 to a volume of 3 m3. Find the final mass of the air, assuming it is at 250C, and the work done by the air.
Problem 10: Consider a piston/cylinder setup with 0.5 kg of R-134a as saturated vapor at -100C. It is now compressed to a pressure of 500 kPa in a polytropic process with n =1.5. Find the final volume and temperature, and determine the work done during the process. Problem 11: An areal soap film with surface tension formed by wetting a wire frame (initially closed) and then moving the slide wire S away from leg b by means of constant force F. (a) Show that the work done against the resisting surface tension is W = 2 ×l×b = ×A. (b) Find the work done when b = 25 cm, l = 6 cm and = 25 dyne/cm.
Problem 12: A constant force moves a 42 cm electric conductor with a velocity of 1.3 m/s orthogonally across a magnetic field whose flux density is 3.12 Weber/cm2 (1 Weber = 1 N.s.m/C). The conductor carries a current of 20 Amp. Find the force and the rate of work produced.
Problem 13: A pump is driven by an electric motor through a rotating shaft. The torque required to rotate a pump from standstill is usually greater when the pump is first started, called the start-up torque. If the pump shaft start-up torque varies with angular displacement for the first 25 revolutions of start-up according to the relationship, T = 45 Nm + 0.003 Nm/degree × , determine the shaft work required to rotate the pump through the first ten revolutions of start-up
Department of Mechanical Engineering Indian Institute of Technology New Delhi II Semester -- 2012 – 2013
MEL 140 ENGINEERING THERMODYNAMICS
PROBLEM SET – 6: Heat Transfer & First Law
Problem 1: A warm room is maintained at 200C against the colder ambient air. The wall has a thickness of 20 cm with a conductivity of 1.3 W/m K and a total surface area of the room is 100 m2. The outside wind is blowing so the convective heat transfer coefficient is 100 W/m2K. With an outer wall surface temperature of 12.10C, find out the rate of heat transfer loss from the room.
Problem 2: The room mentioned in problem 1 is heated using 2m long and 3cm diameter electrical wire. Heat is generated in the wire as a result of resistance heating, and the surface temperature of the wire is 1520C. Determine the convection heat transfer coefficient for heat transfer between the outer surface of wire and the air in the room.
Problem 3: Consider a person standing in the room discussed above. The inner surfaces of walls, floors, and the ceiling of the house are observed to be at an average temperature of 200C. Determine the rate of radiation heat transfer between this person and the surrounding surfaces if the exposed surface area and the average outer surface temperature of the person are 1.4 m2 and 320C, respectively.
Problem 4: A constant-pressure, adiabatic system contains 0.15 kg of air at 150 kPa. The system receives 20.79 kJ of paddle work. The temperature of the air is initially 278 K and finally 416 K. Find the mechanical work and the changes of internal energy and enthalpy.
Problem 5: A piston/cylinder contains R-12 at -300C, x=20%. The volume is 0.2 m3. It is 3 known that Vstop= 0.4 m , and if the piston sits at the bottom, the spring force balances the other loads on the piston. It is now heated up to 200C. Find the mass of the fluid and show the P-v diagram.Find the work and heat transfer.
Problem 6: A spherical balloon initially 150 mm in diameter and containing R-12 at 100 kPa is connected to a 30 liters un-insulated, rigid tank containing R-12 at 500 kPa. Everything is at the ambient temperature of 200C. A valve connecting the tank and balloon is opened slightly and remains so until the pressures equalize. During this process heat is exchanged so the temperature remains constant at 200C. For this range of variables the pressure inside the balloon is proportional to the diameter at any time. Calculate (a) The final pressure. (b) Work done by the R-12 during the process. (c) Heat transferred to the R-12 during the process. (Hint: This is to be solved iteratively with a suitable initial guess.)
Problem 8: Superheated vapor ammonia enters an insulated nozzle at 200C and 800 kPa, with a low velocity and at a steady rate of 0.01 kg/s. The ammonia exits at 300 kPa with a velocity of 450 m/s. Determine the temperature (or quality, if saturated) and the exit area of the nozzle.
Problem 9: A steam turbine receives steam at 15 MPa, 6000 C at a rate of 100 kg/s. In the middle section 20 kg/s is withdrawn at 2 MPa, 3500C and the rest exists at 75 kPa and 95% quality. Assuming no heat transfer and no changes in kinetic energy, find the total turbine work.
Problem 10: Steam with a specific enthalpy of 1600 kJ/kg and pressure 100 kPa enters an adiabatic compressor and the exit steam is at a pressure of 1200 kPa and has a specific enthalpy of 1700 kJ/kg. No kinetic or potential energy changes occur through the pump. Determine: (a) Pump work per kg of steam. (b) Average density of steam.
Problem 11: A simplified single-cylinder internal combustion engine that produces 15 kW of mechanical power, loses 40 kJ/min in radiated and conducted heat while using 0.72 kg/min of a fuel-air mixture which is assumed to have an enthalpy of 2600 kJ/kg of mixture. Determine the specific enthalpy of the exhaust gases, assuming that the engine is in a steady state.
Department of Mechanical Engineering Indian Institute of Technology New Delhi II Semester -- 2012 – 2013
MEL 140 ENGINEERING THERMODYNAMICS
PROBLEM SET – 7: First Law Analysis of Cyclic Units
Problem 1: The Boeing 747 is a wide body commercial airliner, often referred to by the nickname "Jumbo Jet”. It is designed to fly at an altitude of 10 km. Following are the details of the flight. Properties of Local Atmosphere: -49.90C, 26.5 kPa & 0.4135 kg/m3 The cruising speed: 913 km/h The average drag coefficient : 0.022 Flight projected area for drag : 511 m2 The total thrust required to drive this flight is to be generated by FOUR turbojet engines. Figure 1 and following table show the parts of a jet engine and properties at various locations.
State 1 2 3 4 5 6 P, kPa 29.5 397.5 T 0C -49.9 -15.0 296 1100 789 235
What is the velocity of the jet and mass flow rate of air, assuming fuel flow rate is negligible.
Problem 2: The following data and Figure 2 are for a simple steam power plant as shown in Figure. State 1 2 3 4 5 6 7 P, MPa 6.2 6.1 5.9 5.7 5.5 0.01 0.009 T 0C 45 175 500 490 40
State 6 has x6 = 0.92 and velocity of 200 m/s. The rate of steam flow is 25 kg/s, with 300 kW power input to the pump. Piping diameters are 200 mm from steam generator to the turbine and 75 mm from the condenser to the steam generator. The economizer is a low temperature heat exchanger. Determine (a) The power output of the turbine. (b) Heat transfer in the condenser, economizer and steam generator. (c) The flow rate of cooling water through the condenser, if the cooling water temperature increases from 150C to 250C in the condenser.
Figure 1
Figure 2
Department of Mechanical Engineering Indian Institute of Technology New Delhi II Semester -- 2012 – 2013
MEL 140 ENGINEERING THERMODYNAMICS
PROBLEM SET – 8: Second Law Analysis of Heat Engines & Pumps
Problem 1: A control mass containing two kilograms of helium operate on a three-process cycle consisting of constant volume (1--2); constant pressure (2--3); and constant temperature (3--1) processes. Given that p1 = 100 kPa, T1 = 300K, and v1/v3 = 5, determine (a) the pressure, volume and temperature around the cycle; (b) the work for each process; and (c) the heat added. Is this cycle represents a heat engine or heat pump?
Problem 2: Prove that a cyclic device that violates the Kelvin--Planck statement also violates the Clausius statement.
Problem 3: In a steam power plant heat is added at the rate of 1 MW at 7000C in the boiler, 0.58 MW is rejected at 400C in the condenser and the pump power is 0.02 MW. Find the plant thermal efficiency. Assuming the same pump power and rate of heat addition in the boiler, how much turbine power could be produced if the plant were running in a Carnot cycle?
Problem 4: A heat pump is to be used to heat a house in winter and reversed to cool the house in summer. The interior temperature is to be maintained at 250C. Heat transfer through the walls and roof is estimated to be 1200 kJ/hr-K. (a) If the outside temperature in winter is 30C, what is the minimum power required to drive the heat pump? (b) If the power input is the same as that in part (a) what is the maximum outside temperature for which the inside can be maintained at 250C?
Problem 5: A furnace can deliver heat QH1 at TH1 and it is proposed to use this to drive a heat engine with a rejection at Tatm instead of direct room heating. The heat engine drives a heat pump that delivers QH2 at Troom using the atmosphere as cold reservoir. Find the ratio QH2/QH1 as a function of temperatures. Is this a better set-up than direct room heating from the furnace?
Problem 6: Prove that following processes are irreversible. The flow of water over a water fall. Driving a nail into a wall. Passage of electric current through a resistor. Heat transfer due to a finite temperature difference. Exhaust stroke of an IC engine. Combustion of H2 and O2.
Problem 7: Prove that an irreversible heat pump will have lower CoP than that of a reversible heat pump working between same reservoirs.
Problem 8: A cyclic machine, receives Qh from a high temperature reservoir. It rejects heat QL to a low temperature reservoir. Following is the list of these variables for the engine measured during various trial runs. Are these cycles reversible, irreversible, or impossible?
Th, K Qh, kJ Tl, K Ql, kJ Wout, kJ Result 1000 325 400 125 200 6000 100000 300 8000 92000 1573 800 673 550 1000 9.2 200 3.2 6.75 293 0.009 263 0.08 0.01
Department of Mechanical Engineering Indian Institute of Technology New Delhi II Semester -- 2012 – 2013
MEL 140 ENGINEERING THERMODYNAMICS
PROBLEM SET – 9: Change in Entropy
Problem 1: Suppose that 1 kg of saturated water vapor at 1000C is condensed to a saturated liquid at 1000C in a constant-pressure process by heat transfer to the surrounding air, which is at 250C. What is the net increase in entropy of the water plus surroundings?
Problem 2: Calculate the change in entropy per kilogram as air is heated from 300 to 600 K while pressure drops from 400 to 300 kPa. Assume: 1. Constant specific heat. 2. Variable specific heat.
Problem 3: One kilogram of air is contained in a cylinder fitted with a piston at a pressure of 400 kPa and a temperature of 600 K. The air is expanded to 150 kPa in a reversible, adiabatic process. Calculate the work done by the air.
Problem 4: In a reversible process, nitrogen is compressed in a cylinder from 100 kPa and 200C to 500 kPa. During this compression process, the relation between pressure and volume is pV1.3 = constant. Calculate the work and heat transfer per kilogram, and show this process on p–V and T–S diagrams.
Problem 5: A piston/cylinder setup contains 1 kg of water at 150 kPa and 200C. The piston is loaded so that pressure is linear in volume. Heat is added from a 6000C source until the water is at 1 MPa and 5000C. Find the heat transfer and total change in entropy.
Problem 6: A piece of hot metal should be cooled rapidly (quenched) to 250C, which requires removal of 1000 kJ from the metal. There are three possible ways to remove this energy: (1) Submerge the metal into a bath of liquid water and ice, thus melting the ice. (2) Let saturated liquid R-22 at 200C absorb the energy so that it becomes saturated vapor. (3) Absorb the energy by vaporizing liquid nitrogen at 101.3 kPa pressure. a. Calculate the change of entropy of the cooling media for each of the three cases. b. Discuss the significance of the results.
Problem 7: A counter flow heat exchanger is used to cool air at 540K, 400kPa to 360K by using a 0.05kg/s supply of water at 200C and 200kPa. The air flow rate is 0.5 kg/s in a 10cm diameter pipe. Find the air inlet velocity, the water exit temperature, and total entropy generation in the process.
Problem 8: A mixing chamber receives 5kg/min ammonia as saturated liquid at -200C from one line and ammonia at 400C, 250kPa from another line through a valve. The chamber also receives 325 kJ/min of heat from a 400C reservoir. This should produce saturated ammonia vapour at - 200C in the exit line. What is the mass flow rate at state - 2 and what is the total entropy generation in the process?
Problem 9: An air turbine with inlet conditions 1200K, 1MPa and exhaust pressure of 100 kPa pulls a sledge over a leveled plane surface, T = 200C. The turbine work overcomes the friction between the sledge and surface. Find the total entropy generation per kilogram of air through the turbine.