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 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 q p v b RT v2 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.