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Chapter 2 Lecture 02: Work and Energy Today’s Objectives: • • • • • • Be able to distinguish between work and energy. Be able to calculate Kinetic Energy Be able to calculate Potential Energy Be able to calculate Work done by an acting force Be able to calculate Power Be able to calculate Work done by gases undergoing changes of state. • Be able to explain the concept of Internal Enegy Reading Assignment: • Read Chap 2. Sections 1-5 Homework Assignment: From Chap 2: Problems 6, 20, 24, 32 Sec 2.1: Reviewing Mechanical Concepts of Energy Work, Heat, and Energy Energy is conserved, but can be converted to different types Ways to Transfer Energy Into or Out of A System Work – transfers by applying a force and causing a displacement of the point of application of the force. Mechanical Waves – allow a disturbance to propagate through a medium. Heat – is driven by a temperature difference between two regions in space. Matter Transfer – matter physically crosses the boundary of the system, carrying energy with it. Electrical Transmission – transfer is by electric current. Electromagnetic Radiation – energy is transferred by electromagnetic waves W = PE = KE = U 3 Sec 2.2: Broadening Our Understanding of Work Thermodynamics “Work” Physics definition of work is W = F s But, in thermodynamics often we are working with fluids (non-solids), so we need a broader definition. “Work is done by a system on its surroundings if the sole effect on everything external to the system could have been done by raising (or dropping) a weight.” 4 Sec 2.2: Broadening Our Understanding of Work Joule’s Experiment (1845-Salford, England) Joule dropped a known mass and measured the change in temperature of the water. The experiment was conducted in the basement of his family’s brewery, where there was a constant ambient temperature. The friction of the water molecules rubbing together caused the temperature to increase. Joule’s Equipment - Manchester 5 Sec 2.2.1: Sign Convention 6 Work Sign Convention W > 0 : Work done BY the system W < 0 : Work done ON the system Sign is not inherently important, but this is the convention. Vf W PdV Vi W < 0 : Work done ON the system (System is compressed) W > 0 : Work done BY the system (System expands) Sec 2.2 .2: Power Power = Rate of Energy Transfer Book’s convention: Dot above symbol represents the rate. The rate of work can be expressed as 7 Sec 2.2 : Work 8 Work Properties Work is NOT a property of a system like V, T, or E. Work occurs when the system undergoes a process. A differential of a property is exact. V Vf Vi dV V f Vi The differential of work depends upon the path. W Vf V Vi pdV Sec 2.2 : Work 9 But, work depends on the process. For “Bobby” work depends on the path, since friction is a nonconservative force. Sec 2.2 : Work So, we need to have a PV relationship for the process. The process of changing volume is NOT necessarily in equilibrium. - He balloon popping, gas does not instantly mix with air - Gas cylinder rupture, pressure inside is higher then outside for some time, t For this class, we will used an idealized process, that are completely reversible. We call this type of process - quasi-equilbirium - quasi-static 10 Sec 2.2 : Work 11 V V V Non-quasi-static Process Consider a box initially divided in half. - Initially, one is filled with gas, the other a vacuum. - The divider is then removed. - The gas takes some time to fill the new volume. During that time, there are different local values for P in the volume. There is also likely some heat generated, as the process is irreversible. Thermodynamics ≠ Kinetics Sec 2.2 : Work 12 V V V V V V V V Quasi-static Now we move the wall slowly, such that the gas is able to adjust instantly. This is a reversible quasi-static process. 13 V Example (2.34): Air contained within a piston-cylinder assembly undergoes three processes in series. Evaluate W. Process 1-2: Compression at constant pressure from p1=10 psi, V1=4.0 ft3 to state 2 Process 2-3: Constant volume heating to state 3, where p3=50 psi Process 3-1: Expansion to the initial state, during which the p-V relationship is pV = constant. 50 P psi 10 V ft 3 4 14 Sec 2.3: Broadening Our Understanding of Energy 15 Energy Physics energy types Kinetic Energy: Energy of objects in motion Potential Energy: Energy of objects in a field (g,E,B) Internal Energy Spring Chemical Pressure Pressure can be a form of energy if P> Patm Thus, the general energy equation is E PE KE U P Patm 16 Example Problem (2.37) A 10 V battery supplies a constant current of 0.5 amp to a resistance for 30 min. a) Determine the resistance, in ohms. b) For the battery, determine the amount of energy transfer to work, in kJ. Solution: 17 Example Problem (2.31) Air contained within a piston-cylinder assembly is slowly heated. As shown in Fig P2.31, during the process the pressure first varies linearly with volume and then remains constant. Determine the total work in kJ. P (kPa) Solution: 2 150 100 3 1 50 0.030 0.045 0.070 V (m3) 18 End of Lecture 02 • Slides that follow show solutions to Example problems. 19 Example (2.34): Air contained within a piston-cylinder assembly undergoes three processes in series. Evaluate W. Process 1-2: Compression at constant pressure from P1=10 psi, V1=4.0 ft3 to state 2 3 50 Process 1-2: Isobaric Process W12 PdV P V2 V1 V2 P psi V1 since: 10 1 2 V ft 3 4 PV 1 1 PV 3 3 then : V2 V3 and V2 V3 P1 V1 P3 10 psi 3 3 V2 4 ft 0.8 ft 50 psi W12 10 psi0.8 4 ft 3 144 ft 2 in2 BTU 778 ftlb f 5.92BTU 20 Example (2.34): Air contained within a piston-cylinder assembly undergoes three processes in series. Evaluate W. Process 2-3: Constant volume heating to state 3, where P3=50 psi Process 3-1: Expansion to the initial state, during which the P-V relationship is PV = constant. 50 3 Process 2-3: Isovolumetric Process P psi 10 2 1 V ft 3 4 V23 0 W23 0 21 Example (2.34): Air contained within a piston-cylinder assembly undergoes three processes in series. Evaluate W. Process 2-3: Constant volume heating to state 3, where P3=50 psi Process 3-1: Expansion to the initial state, during which the P-V relationship is PV = constant. 50 3 Process 3-1: Isothermic Process P psi V1 W31 V3 10 2 1 V ft 3 C PdV dV C ln V3 V V1 W31 P1V1 ln 4 W31 10 psi 4 ft 3 V1 V3 V1 V3 ln 4 ft 3 0.8 ft 3 144 f 2t in 2 BTU 778 ft lb f 11.9 BTU 22 Example Problem (2.37) A 10 V battery supplies a constant current of 0.5 amp to a resistance for 30 min. a) Determine the resistance, in ohms. b) For the battery., determine the amount of energy transfer to work, in kJ. Solution: Electrical Work Principle Pelec VI therefore: V = 10 V Welec Pelec t I = 0.5 A Δt=30 min Pelec VI (10V )(0.5 A) 5 W then Welec (5W )(30 min) 60 s 1 J / s 1 kJ 1 min 1 W 1000 J Welec 0.15 kJ 23 Example Problem (2.31) Air contained within a piston-cylinder assembly is slowly heated. As shown in the figure, during the process the pressure first varies linearly with volume and then remains constant. Determine the total work in kJ. P (kPa) 2 3 Solution: 150 VB 1 WA B p dV 100 VA Conceptually, this represents the area of the P-V plot underneath the process lines. W12 50 V2 p dV A PV _ trapezoid V1 0.030 0.045 W23 0.070 V (m3) V3 p dV A PV _ rectangle V2 1 (100 150)(0.045 0.030) kPa m3 2 2 1 kJ 3 1kN / m 1.875 kPa m 1.875 kJ 1kPa 1 kN m (150)(0.070 0.045) kPa m3 1kN / m 2 1 kJ 3.75 kPa m 3.75 kJ 1kPa 1 kN m 3 Wtotal W13 W12 W23 1.875 3.75 5.625 kJ