12/21/2014 7:39 PM. Chapter 2. Energy and the 1st Law of Thermodynamics. Dr. Mohammad Suliman Abuhaiba, PE

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1 Chapter 2 Energy and the 1st Law of Thermodynamics 1

2 2 Homework Assignment # 2 Problems: 1, 7, 14, 20, 30, 36, 42, 49, 56 Design and open end problem: 2.1D Due Monday 22/12/2014

3 3 Work and Kinetic Energy

4 4 Potential Energy

5 5 Conservation of Energy in Mechanics

6 6 Broadening Our Understanding of Work Thermodynamic definition of work: Work is done by a system on its surroundings if the sole effect on everything external to the system could have been the raising of a weight.

7 7 Modeling Expansion or Compression Work Expansion / Compression Work (Moving Boundary Work) V2 p dv V 1 Work is process (path) dependent, and is NOT a property of the system

8 8 Sign Convention Work W > 0: Work done by system W < 0: Work done on system Power: Time rate of work

9 9 Example 2.1 A gas in a piston cylinder assembly undergoes an expansion process for which the relationship between pressure & volume is given by p.v n = Constant. The initial pressure is 3 bar, the initial volume is 0.1 m 3, and the final volume is 0.2 m 3. Determine the work for the process, in kj, if a. n = 1.5 b. n = 1.0 c. n = 0

10 10 Broadening Our Understanding of Energy Mechanical Energy: KE, PE, E Work is done by energy transfer Heat is another form of energy Expand the conservation of energy principle to accommodate thermal systems.

11 11 Broadening Our Understanding of Energy In engineering TD change in total energy of a system is made up of three macroscopic contributions: 1. change in kinetic energy, associated with motion of system as a whole relative to an external coordinate frame. 2. change in gravitational potential energy, associated with position of system as a whole in the earth s gravitational field. 3. All other energy changes are lumped together in the internal energy of the system. internal energy is an extensive property of the system.

12 12 Broadening Our Understanding of Energy Kinetic Energy KE 1 2 m( V 2 2 V1 2 ) Potential Energy PE m g( z 2 z1) Common Units: J(N m) or kj, ft lbf, Btu

13 13 Broadening Our Understanding of Energy Total Energy: An extensive property of a system Kinetic Energy (Mechanical) Potential Energy (Mechanical) Internal Energy: U or u Represents all other forms of energy Includes all microscopic forms of energy E KE PE U

14 14 Microscopic Interpretation of Internal Energy Consider a system consisting of a gas contained in a tank. Think about the energy attributed to motions and configurations of individual molecules, atoms, and subatomic particles making up the matter in the system Gas molecules move about, encountering other molecules or walls of container. Part of internal energy of gas is translational kinetic energy of molecules.

15 15 Microscopic Interpretation of Internal Energy kinetic energy due to rotation of molecules relative to their centers of mass & kinetic energy associated with vibrational motions within molecules. energy is stored in chemical bonds between atoms that make up the molecules. Energy storage on the atomic level includes energy associated with electron orbital states, nuclear spin, and binding forces in the nucleus.

16 16 Energy Transfer by Heat Sign Convention, Notation, and Heat Transfer Rate Q > 0: Heat transfer into the system Q < 0: Heat transfer Q out of the system Rate of heat transfer:

17 17 Heat Transfer Modes Conduction Q x dt A dx Radiation Q e es AT 4 b Emissivity, e, is a property of surface that indicates how effectively the surface radiates (0< e <1.0) s = Stefan Boltzmann constant

18 18 Heat Transfer Modes Convection Q ha( T T ) c b f

19 19 1 st Law of Thermodynamics Consider a system of a piston and cylinder with an enclosed dilute gas characterized by P,V,T & n.

20 20 1 st Law of Thermodynamics What happens to the gas if the piston is moved inwards?

21 21 1 st Law of Thermodynamics If the container is insulated the temperature will rise, the atoms move faster and the pressure rises. Is there more internal energy in the gas?

22 22 1 st Law of Thermodynamics External agent did work in pushing the piston inward. W = Fd = (PA) x x W = P V

23 23 1 st Law of Thermodynamics Work done on the gas equals the change in the gases internal energy, x W = U

24 24 1 st Law of Thermodynamics Let s change the situation: Keep the piston fixed at its original location. Place the cylinder on a hot plate. What happens to gas?

25 25 1 st Law of Thermodynamics Heat flows into the gas. Atoms move faster, internal energy increases. Q = heat in Joules U = change in internal energy in Joules. Q = U

26 26 1 st Law of Thermodynamics What if we added heat and pushed the piston in at the same time? F

27 27 1 st Law of Thermodynamics Work is done on the gas, heat is added to the gas and the internal energy of the gas increases! F Q = W + U

28 28 1 st Law of Thermodynamics For the gases perspective: heat added is positive, heat removed is negative. Work done on gas is positive, work done by the gas is negative. Temperature increase means internal energy change is positive.

29 29 Conservation of Energy: 1 st Law of Thermodynamics KE PE U Q W Change in amount of energy contained within the system during some time interval = Net amount of energy transferred in across the system boundary by heat transfer during the time interval - Net amount of energy transferred out across the system boundary by work during the time interval

30 30 Alternative Forms of the Energy Balance Differential Form: de Q W Time Rate Form: de dt Q W

31 31 Example 2.2 Cooling a Gas in a Piston Cylinder Four kilograms of a certain gas is contained within a piston cylinder assembly. The gas undergoes a process for which the pressure volume relationship is pv 1.5 = constant. The initial pressure is 3 bar, the initial volume is 0.1 m 3, and the final volume is 0.2 m 3. The change in specific internal energy of the gas in the process is u 2 - u 1 = kj/kg. There are no significant changes in kinetic or potential energy. Determine the net heat transfer for the process, in kj.

32 32 Example 2.3 Considering Alternative Systems Air is contained in a vertical piston cylinder assembly fitted with an electrical resistor. The atmosphere exerts a pressure of 1 bar on the top of the piston, which has a mass of 45 kg and a face area of.09 m 2. Electric current passes through the resistor, and the volume of the air slowly increases by.045 m 3 while its pressure remains constant. The mass of the air is 0.27 kg, and its specific internal energy increases by 42 kj/kg. The air and piston are at rest initially and finally. The piston cylinder material is a ceramic composite and thus a good insulator. Friction between the piston and cylinder wall can be ignored, and the local acceleration of gravity is g 9.81 m/s 2. Determine the heat transfer from the resistor to the air, in kj, for a system consisting of a. the air alone b. the air and the piston

33 Example 2.4 Gearbox at Steady State During steady-state operation, a gearbox receives 60 kw through the input shaft and delivers power through the output shaft. For the gearbox as the system, the rate of energy transfer by convection is 33 where h = kw/m 2 K is the heat transfer coefficient, A =1.0 m 2 is outer surface area of gearbox, T b = 300 K is the temperature at the outer surface, and T f = 293 K is the temperature of the surrounding air away from the immediate vicinity of the gearbox. For the gearbox, evaluate the heat transfer rate and power delivered through the output shaft, each in kw.

34 34 Example 2.5 Silicon Chip at Steady State A silicon chip measuring 5 mm on a side and 1 mm in thickness is embedded in a ceramic substrate. At steady state, the chip has an electrical power input of W. The top surface of the chip is exposed to a coolant whose temperature is 20 C. The heat transfer coefficient for convection between the chip and the coolant is 150 W/m 2 K. If heat transfer by conduction between the chip and the substrate is negligible, determine the surface temperature of the chip, in C.

35 35 Example 2.6 Transient Operation of a Motor The rate of heat transfer between a certain electric motor and its surroundings varies with time as, where t is in seconds and is in kw. The shaft of the motor rotates at a constant speed of 100 rad/s and applies a constant torque of 18 N.m to an external load. The motor draws a constant electric power input equal to 2.0 kw. For the motor, plot, each in kw, and the change in energy E, in kj, as functions of time from t = 0 to t = 120 s. Discuss.

36 36 Cycle Analysis Ecycle Qcycle Wcycle Power Cycles Q cycle W cycle Refrigeration & Heat Pump Cycles Q W in cycle W cycle Q in Q W out cycle

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