Resources for our learning

1. ME 200 L4: Energy in Transition: Work and HeatSpring 2014 MWF 1030-1120 AMJ. P. Gore, Reilly University Chair Professorgore@purdue.eduGatewood Wing 3166, 765 494 0061Office Hours: MWF 1130-1230TAs: Robert Kapaku rkapaku@purdue.edu Dong Han han193@purdue.edu

2. Resources for our learning • Fundamentals of Engineering Thermodynamics, Moran, Shapiro, Boettner and Bailey, Seventh Edition. • Read assigned sections before coming to class. • Group class email will be used frequently to communicate. Also use http://www.purdue.edu/mixable • Class participation welcome and essential. • Given the size of the class, smaller groups of ~10 students to be formed soon. Special opportunities offered to individual ME200 Peer Mentor to lead a group. • Other Instructors, T. A. s, Classmates, Organized Learning Groups such as www.purdue.edu/si • Homework: Submission, grading, and return policies will be announced in the class.

3. Example Problem • Given: A gas in a Piston-Cylinder device undergoes a polytropic process pv1.3=const. from P1=60 lbf/in2 (or 413.69 kPa) and v1= 6 ft3/lbm (0.3746 m3/kg) to P2=20 lbf/in2 (or 137.896 kPa) • Find: Work done by the gas and v2 and work done on the atmosphere if its pressure is at 14 lbf/in2 • System: Piston cylinder device • Assumptions: Polytropic process, constant mass. • Derive the expression for 1W2 for the polytropic process

4. Work done by the gas as it depressurizes Work done on the atmosphere as the gas depressurizes

5. Energy Transfer by Heat • The symbol Q denotes energy transferred across the boundary of a system because of a temperature difference also known as heat transfer. The rate of energy transfer by heat = Note the dot • Q > 0,to the system • Q < 0, from the system • Q = 0, adiabatic • Any energy transfer that is not because of a DT is defined as Work (W).

6. Heat Transfer by Conduction • Conduction is the transfer of energy from more energetic particles of a substance to less energetic adjacent particles due to interactions between them. Always in direction of decreasing temperature. • The time rate of energy transfer by conduction is quantified by Fourier’slaw. • Example problem: Heat transfer through a window: (Eq. 2.31) • Winter time shown where outdoors is cooler than indoors. • Summer time, the is reversed and so is the sign of

7. (Eq. 2.33) Thermal Radiation Black surface at 400K; > 1 m2 • Net radiation exchange between a surface at Tb and a surface at Ts (< Tb) is shown at right. Hot surface, 1000K, 1 m2 • Net energy is transferred in the direction of the arrow and quantified by • where • Ais the area of the smaller surface, • e is a property of the surface called its emissivity, • s is the Stefan-Boltzman constant. Million! 0.16 Million! Black surface>1 m2 but only the part that “sees” the 1 m2 matters.

8. Convection • Convection is energy transfer between a solid surface and an adjacent gas or liquid by conduction! • The bulk flow within the gas or liquid determines the • The rate of energy transfer by convection is quantified by Newton’s law of cooling.

9. Convection • Transistors use electrical energy transferred to them by the power supply as work and dissipate that energy as heat! Ais the area of the transistor’s surface • Energy is transferred in the direction of the arrow and quantified by • h is a parameter called the convection heat transfer coefficient defined as: • Units of h are W/m2-K, units of k are W/m-K

10. Mechanical Energy Transfer by Work • Energy can be transferred to and from a system by mechanical work. • You have studied work in mechanics and those concepts are retained in the study of thermodynamics. • However, thermodynamics requires a broader interpretation of work to allow exchanges with other forms of energy.

11. Illustrations of Work • When a spring is compressed, energy is transferred to the spring by work. • When a gas in a closed vessel is stirred, energy is transferred to the gas by work. • When a battery is charged electrically, energy is transferred to the working medium by work. • Internal combustion engines drive piston and turn flywheels to generate work. • Gas turbines convert chemical energy into mechanical energy and then into work.

12. Sign Conventions and Units of Work & Power • The symbol W denotes an amount of energy transferredby work. • Ft-lbm-ft/(s2); m-kg-m/(s2) = m-N which lead to • ft-lbf and Btu; Joules, kJ, MJ • Since engineering thermodynamics is often concerned with engines whose purpose is to deliver work, it is convenient to regard the work done by a system as positive. • W > 0: work done by the system • W < 0: work done on the system The same sign convention is used for the rate of energy transfer by work – called power- units are Btu/hr in British, Watt, kW, MW in SI and Horsepower in both.

13. An object of mass 80 lb (or 36.29 kg), initially at rest, experiences a constant horizontal acceleration of 12 ft/s2 (or 3.6576 m/s2) due to the action of a resultant force that is applied for 6.5 s. Determine the work of the resultant force, in ft-lbf, in Btu, in J and kJ. Given m = 80 lb or 36.29 kg V1 = 0 ft/s or 0 m/s a = 12 ft/s2 or 3.6576 m/s2 t = 6.5 s Find W in ft-lbf and Btu? And W in J and kJ Sketch Assumptions The 80 lb (36.29 kg) mass is the system. Motion is horizontal, so the system experiences no change in potential energy. The horizontal acceleration is constant. Basic Equations R z m x Mechanical Work Example 13

14. Solution R z m x Mechanical Work Example 0 SI System British System (1) Work does not depend on the units we use to measure it! Different numerical values are assigned to identical work in different measuring systems! (2) See Conversion factors on inside cover of book. 10.255 kJ = 9.71 Btu because 1Btu=1.0551 kJ or 1 kJ = 0.9478 Btu 14

15. Sign Convention • Our sign convention for work is easy to remember: • Work done by a system is considered to be useful to mankind, so is defined to be positive. • Therefore work done by the accelerator on the particle is positive. • Of course, if the work for “the system” defined as “the particle” is to be calculated, then it is negative but equal in magnitude to the work done by the accelerator.

16. Piston Cylinder Systems • Piston cylinder systems are widely used • There function is to transfer expansion and compression energy change into linear motion and eventually rotary motion. Applications: I. C. engines, hydraulic jacks, bicycle air-pump, balloon inflator etc. Stroke=Crank circle diameter. The cylinder length must clear the end to end motion of the connecting rod. The clearance volume defines the compression ratio. The BDC volume defines the cylinder capacity. The pressure, temperature and volume within the cylinder are related and determine power output.

17. Expansion and Compression Work The above derivation is applicable to experimental pressure volume traces (see Fig. 2.5 in text) as well as theoretical approximations to processes for defining the system behavior. Work is a path function and can not be evaluated by just knowing the end states 1 and 2. Also, in writing the above equations, the assumption that the pressure in the cylinder is uniform through out the volume has been made. This makes the work a quasi-steady approximation to reality. None the less, this approximation has been found to be very useful in industry.

18. Expansion and Compression Work If gas volume decreases, work is negative and is done on the gas. If gas volume increases, work is done by the gas on the piston and hence on the connecting rod and the crank shaft etc. Practice these derivations

19. Examples of work functions involving different processes: Shaft Work τ – torque ω – angular velocity (rad/s)

20. Examples of work functions involving different processes: Spring Work k – spring constant xi – displacement from equilibrium

21. Examples of work functions involving different processes: Work done by “flowing” electrons Electric Power i – electric current (amp) – potential difference (V) R – resistance (ohms) Ohm’s Law 21

22. Additional examples of work Torsion of a solid bar See eq. 2.18 2. Stretching of a liquid film See eq. 2.19 3. Charging of Electrolytic cell, Electric Field, Magnetic Field Work done by electromotive force Work done by dielectric in a uniform electric field Work done by magnetic material in a field

23. Summary • Kinetic Energy and Potential Energy are macro- scale mechanical energies of a mass. • Internal Energy is an extensive property of a working substance and is defined by composition, temperature, and pressure. • Internal Energy changes by heat transfer and work interactions. • Heat Transfer is a result of temperature difference and is by conduction, convection and radiation.

24. Summary • We defined gravitational potential energy and change in this quantity and its relation to the distance of an object from the earth’s center or surface. • We defined kinetic energy using the concept of force times the displacement being equal to the work done. • We introduced the Conservation of Mechanical Energy principle involving a balance between the kinetic energy and the potential energy exchange and defined Mechanical Work and the sign convention associated with it.

25. Summary • We defined expansion and contraction work and • calculated work associated with a process in a piston cylinder device. • We learned the potential for extension of our mechanical work knowledge metaphorically to electrical, magnetic, surface tension, torsion and other work interactions. • We learned about calculation of “Pdv” work for experimental P-v diagrams as well as idealized P-v compression and expansion processes. Understand the positive and negative work sign convention intuitively.