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Chapter 2 Lecture 02: Work and Energy

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Todays 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: Homework Assignment: Read Chap 2. Sections 1-5 From Chap 2: Problems 6, 20, 24, 32

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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 2.1: Reviewing Mechanical Concepts of Energy

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Thermodynamics Work 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. 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. 4 Sec 2.2: Broadening Our Understanding of Work

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Joules 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 familys brewery, where there was a constant ambient temperature. The friction of the water molecules rubbing together caused the temperature to increase. 5 Sec 2.2: Broadening Our Understanding of Work Joules Equipment - Manchester

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Work Sign Convention W > 0 : Work done BY the system W < 0 : Work done ON the system 6 Sec 2.2.1: Sign Convention Sign is not inherently important, but this is the convention. W < 0 : Work done ON the system (System is compressed) W > 0 : Work done BY the system (System expands)

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Power = Rate of Energy Transfer Books convention: Dot above symbol represents the rate. 7 Sec 2.2.2: Power The rate of work can be expressed as

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Work Properties Work is NOT a property of a system like V, T, or E. Work occurs when the system undergoes a process. 8 Sec 2.2 : Work A differential of a property is exact. V The differential of work depends upon the path.

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But, work depends on the process. 9 Sec 2.2 : Work For Bobby work depends on the path, since friction is a non- conservative force.

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So, we need to have a PV relationship for the process. 10 Sec 2.2 : Work 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

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11 Sec 2.2 : Work 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. Non-quasi-static Process V V V Thermodynamics Kinetics

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12 Sec 2.2 : Work Now we move the wall slowly, such that the gas is able to adjust instantly. This is a reversible quasi-static process. Quasi-static V V V V V V V V

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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 p 1 =10 psi, V 1 =4.0 ft 3 to state 2 Process 2-3: Constant volume heating to state 3, where p 3 =50 psi Process 3-1: Expansion to the initial state, during which the p-V relationship is pV = constant. 13 V

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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 15 Sec 2.3: Broadening Our Understanding of Energy Pressure can be a form of energy if P> P atm P atm P Thus, the general energy equation is

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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. 16 Solution:

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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) V (m 3 ) Solution:

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End of Lecture 02 Slides that follow show solutions to Example problems. 18

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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 ft 3 to state Process 1-2: Isobaric Process

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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 Process 2-3: Isovolumetric Process

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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 Process 3-1: Isothermic Process

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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. 22 Solution: Electrical Work Principle therefore: V = 10 V I = 0.5 A Δt=30 min then

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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) V (m 3 ) Solution: Conceptually, this represents the area of the P-V plot underneath the process lines.

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