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Chapter 2: Review Lecture 05: Chapter 2 Review Quiz Today?

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Main Concepts of Chap 2. Work done by compressed gas system: Heat Transfer ▫Conduction ▫Convection ▫Radiation 1 st law of Thermodynamics: Power cycle, Refrigeration cycle, Heat Pump cycle Thermal Efficiency and Coefficient of Performance. Reading Assignment: Homework Assignment: Read Chap 3: Sections 1-5 From Chap 2: 46, 59, 82,97

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Recall Chapter 2 concepts: 3 1 st Law of Thermodynamics: Q in W out system ΔEΔE for most Thermodynamics applications: ΔKE = ΔPE = 0 then

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Work done by Gas System 4 W > 0 : Expansion of Gas W < 0 : Compression of Gas Run Animation = Area under the p-V graph over process

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Heat Transfer Radiation: 5 where A is area κ is thermal conductivity dT/dx is temperature gradient Conduction: Convection: where A is area h c is the convection coefficient T b -T f is the difference between the body and free steam fluid temp. where T b is absolute surface temperature ε is emissivity of the surface σ is Stefan-Boltzmann constant A is surface area

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Thermodynamic Cycle: S4S4 S2S2 S1S1 S3S3 P v Clockwise around the cycle: Work is done by the system. Power Cycle: Counter clockwise around the cycle: Work is done on the system. Refrigeration Cycle:

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7 Sec 2.6: Energy Analysis of Cycles Heat Pump Cycle Power cycle: Refrigeration cycle: Cycle Models:

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8 Concept Questions: True or False: a) In principle, expansion work can be evaluated using ∫pdV for both actual and quasi-equilibrium expansion processes. False b) The change in the internal energy of a system between two states is the change in the total energy of the system between the two states less the change of the system’s kinetic and gravitation potential energies between these states. True c) The change in gravitational potential energy of a 2 lb mass whose elevation decreases by 40 ft where g = 32.2 ft/s 2 is -2576 ft-lb f. True d) The rate of heat transfer from a hot baked potato to the ambient air is greater with forced convection than natural convection. True

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9 Example 3 (Problem 2.91): A heat pump maintains a dwelling at 68 o F. When operating steadily, the power input to the heat pump is 5 hp, and the heat pump receives energy by heat transfer from 55 o F well water at a rate of 500 BTU/min. a) Determine the COP. b) Evaluating electricity at $0.10 per kW-hr, determine the cost of electricity in a month when the heat pump operates for 300 hr.

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11 Example (2.70): A gas is contained in a vertical piston-cylinder assembly by a piston weighing 1000 lb f and having a face area of 12 in 2. The atmosphere exerts a pressure of 14.7 psi on the top of the piston. An electrical resistor transfers energy to the gas in the amount of 5 BTU as the elevation of the piston increases by 2 ft. The piston and cylinder are poor thermal conductors and friction can be neglected. Determine the change in internal energy of the gas, in BTU, assuming it is the only significant internal energy change of any component present. P atm =14.7 psi h = 2 ft A piston = 12 in 2 W piston = 1000 lb f W elec = - 5 BTU

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Example (2.83): A power cycle has a thermal efficiency of 40% and generates electricity at a rate of 100 MW. The electricity is valued at $0.08 per kW h. Based on the cost of fuel, the cost to supply Q in is $4.50 per GJ. For 8000 hours of operation annually, determine, in $ (a)the value of electricity generated per year (b)the waste heat returned to the environment (c)the annual fuel cost (d)Is operation profitable? 13 Fuel Air W out =100 MW Q in Q out

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Example Problem (2.63) A gas is compressed in a piston cylinder assembly form p 1 = 2 bar to p 2 = 8 bar, V 2 = 0.02 m 3 in a process during which the relation between pressure and volume is pV 1.3 = constant. The mass of the gas is 0.2 kg. If the specific internal energy of the gas increase by 50 kJ/kg during the process, deter the heat transfer in kJ. KE and PE changes are negligible. 15

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End of Lecture 05: Solutions to example problems follow 17

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18 Example 3 (Problem 2.91) Page 1 of 2: A heat pump maintains a dwelling at 68 o F. When operating steadily, the power input to the heat pump is 5 hp, and the heat pump receives energy by heat transfer from 55 o F well water at a rate of 500 BTU/min. a) Determine the COP. b) Evaluating electricity at $0.10 per kW-hr, determine the cost of electricity in a month when the heat pump operates for 300 hr. where: and Principle: COP for heat pump (written in terms of power) therefore:

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19 Example 3 (Problem 2.91)…page 2 of 2: A heat pump maintains a dwelling at 68 o F. When operating steadily, the power input to the heat pump is 5 hp, and the heat pump receives energy by heat transfer from 55 o F well water at a rate of 500 BTU/min. a) Determine the COP. b) Evaluating electricity at $0.10 per kW-hr, determine the cost of electricity in a month when the heat pump operate for 300 hr. where: Principle: Cost = Cost of energy * Power * time therefore:

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20 Example (2.70): Page 1 of 4 A gas is contained in a vertical piston-cylinder assembly by a piston weighing 1000 lb f and having a face area of 12 in 2. The atmosphere exerts a pressure of 14.7 psi on the top of the piston. An electrical resistor transfers energy to the gas in the amount of 5 BTU as the elevation of the piston increases by 2 ft. The piston and cylinder are poor thermal conductors and friction can be neglected. Determine the change in internal energy of the gas, in BTU, assuming it is the only significant internal energy change of any component present. P atm =14.7 psi h = 2 ft A piston = 12 in 2 W piston = 1000 lb f W elec = - 5 BTU Solution: Apply the 1 st law of thermodynamics

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21 where mg = 1000 lb f A = 12 in 2 Δh = 2 ft W elec_in = 5 BTU Because of the statement “poor thermal conductors”, it can be assumed that this is an adiabatic process (Q = 0) and we will also assume that the process occurs as a slow quasi-equilibrium process in which case the kinetic energy terms will also be small (ΔKE = 0). Finally, since the piston floats on the contained gas, the outside atmospheric pressure maintains a constant pressure on the cylinder…so this is a constant pressure process (isobaric) therefore: (for constant pressure) (neg. since its put into the system) Example Problem (2.70) …page 2 of 4

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22 For equilibrium: F top =p atm A W=1000lb f F bottom =p A and the increase in Volume: therefore the work done by the gas was positive work by the system Example Problem (2.70) …page 3 of 4

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23 Returning to the 1 st law: Example Problem (2.70) …page 4 of 4

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24 Example (2.70): A gas is contained in a vertical piston-cylinder assembly by a piston weighing 1000 lb f and having a face area of 12 in 2. The atmosphere exerts a pressure of 14.7 psi on the top of the piston. An electrical resistor transfers energy to the gas in the amount of 5 BTU as the elevation of the piston increases by 2 ft. The piston and cylinder are poor thermal conductors and friction can be neglected. Determine the change in internal energy of the gas, in BTU, assuming it is the only significant internal energy change of any component present. P atm =14.7 psi h = 2 ft A piston = 12 in 2 W piston = 1000 lb f W elec = - 5 BTU

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Example (2.83): Page 1 of 3 A power cycle has a thermal efficiency of 40% and generates electricity at a rate of 100 MW. The electricity is valued at $0.08 per kW h. Based on the cost of fuel, the cost to supply Q in is $4.50 per GJ. For 8000 hours of operation annually, determine, in $ (a)the value of electricity generated per year (b)the waste heat returned to the environment (c)the annual fuel cost (d)Is operation profitable? 25 Fuel Air W out =100 MW Q in Q out

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Example (2.83): Page 2 of 3 A power cycle has a thermal efficiency of 40% and generates electricity at a rate of 100 MW. The electricity is valued at $0.08 per kW h. Based on the cost of fuel, the cost to supply Q in is $4.50 per GJ. For 8000 hours of operation annually, determine, in $ (a)the value of electricity generated per year and (b)next find the heat generated 26 and the heat returned to the environment

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Example (2.83): page 3 of 3 A power cycle has a thermal efficiency of 40% and generates electricity at a rate of 100 MW. The electricity is valued at $0.08 per kW h. Based on the cost of fuel, the cost to supply Q in is $4.50 per GJ. For 8000 hours of operation annually, determine, in $ (c)Cost of fuel? (d)Is operation profitable? 27 Profit = Revenue – Costs So, this could be profitable, but the calculation ignore other costs such as capital and labor.

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Example Problem (2.63) page 1 of 4 A gas is compressed in a piston cylinder assembly form p 1 = 2 bar to p 2 = 8 bar, V 2 = 0.02 m 3 in a process during which the relation between pressure and volume is pV 1.3 = constant. The mass of the gas is 0.2 kg. If the specific internal energy of the gas increase by 50 kJ/kg during the process, deter the heat transfer in kJ. KE and PE changes are negligible. 28 Solution: starting with the 1 st Law of Thermodynamics where: ΔKE=0 ΔPE = 0 ΔU/m = 50 kJ/kg m = 0.2 kg p 1 = 2 bar p 2 = 8 bar V 1 = ? V 2 = 0.02 m 3 also: pV 1.3 = constant therefore:

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Example Problem (2.63)…page 2 of 4 A gas is compressed in a piston cylinder assembly form p 1 = 2 bar to p 2 = 8 bar, V 2 = 0.02 m 3 in a process during which the relation between pressure and volume is pV 1.3 = constant. The mass of the gas is 0.2 kg. If the specific internal energy of the gas increase by 50 kJ/kg during the process, deter the heat transfer in kJ. KE and PE changes are negligible. 29 Solution continued: also: therefore:

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30 so work done is: Example Problem (2.63)…page 3 of 4

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31 Internal Energy is given as Finally back at the 1 st Law: gives Example Problem (2.63)…page 4 of 4

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