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Review Exam3

Review Exam3. Overview. Exam 2 on Wednesday December 02 nd in BPS 1410 Section 001 from 8am to 8:50am Section 002 from 9:10 to 10am Section 003 from 10:20 to 11:10am Exam 3 focuses on Solids and fluids Thermal physics Energy in thermal processes. Solids and fluids. Review.

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Review Exam3

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  1. Review Exam3 PHY231

  2. Overview • Exam 2 on Wednesday December 02nd in BPS 1410 • Section 001 from 8am to 8:50am • Section 002 from 9:10 to 10am • Section 003 from 10:20 to 11:10am • Exam 3 focuses on • Solids and fluids • Thermal physics • Energy in thermal processes PHY231

  3. Solids and fluids Review PHY231

  4. Elastic deformation of solids – Basic concept: Stress = Force per unit area , causes the deformation Strain = Measure of the deformation Elastic modulus = The larger it is the harder to deform • We’ve seen three different types of deformation: • Young’s modulus (Y): Elasticity in length • Shear modulus (S): Elasticity of shape • Bulk modulus (B): Elasticity of Volume

  5. Density = Mass / Volume • Density of an object: • Pressure : (from force perpendicular to surface) Pressure = Force / Area Pressure in Pa = N/m2 • Pressure in a static fluid Pressure increases with depth. If location 2 is deeper by a height h compare to a higher location 1 in the fluid, one has: Open tube manometer Measure P of the fluid Barometer Measure atm. pressure Gauge pressure = P-P0

  6. Pascal’s principle • Application: • Lifting of heavy objects using small forces Change in pressure is transmitted everywhere in an enclosed fluid Pressure transmitted to the right • Buoyant force B (supportive force from a fluid) Add pressure on the left A small force F1 creates a large force F2 because area A1 is much smaller than area A2 (same pressure F1/A1=F2/A2) Enclosed fluid Buoyant force is equal to the weight mfg of the fluid displaced by the object • Object denser than the fluid sinks • - Object less dense than the fluid floats: • - To float, the object must displace a mass of fluid equals to its own mass

  7. Flow rate: How much volume of fluid is transported every second in the fluid • Equations for incompressible and non-viscous fluid in motion: Continuity equation: Typically, fluid flowing in a pipe. If the cross-section of the pipe changes from A1 to A2, the velocity of the fluid must change. Pipe gets smaller, velocity increases. Bernouilli’s equation: At two different locations in the fluid. Comes from energy conservation. P is the static pressure seen before. v is the velocity of the fluid and y the height. Typically when fluid speeds up the static pressure decreases. • For viscous fluids, use Poiseuille’s law: Flow rate depends very strongly on the radius R of the pipe it is flowing through. Flow rate increases also with pressure drop DP and decreases for larger fluid viscosity h and larger pipe length L

  8. Elastic deformation • A uniform pressure of 7.0  105 N/m2 is applied to all six sides of a copper cube. What is the percentage change in volume of the cube? (for copper, B = 14  1010 N/m2) • a. 2.4  102 % • b. 0.4  102 % • c. 8.4  102 % • d. 0.5  103 % PHY231

  9. Elastic deformation • A uniform pressure of 7.0  105 N/m2 is applied to all six sides of a copper cube. What is the percentage change in volume of the cube? (for copper, B = 14  1010 N/m2) • a. 2.4  102 % • b. 0.4  102 % • c. 8.4  102 % • d. 0.5  103 % PHY231

  10. Hydrostatic pressure • How deep under the surface of a lake would the pressure be double that at the surface? (1 atm = 1.01 × 105 Pa) • a. 1.00 m • b. 9.80 m • c. 10.3 m • d. 32.2 m PHY231

  11. Hydrostatic pressure • How deep under the surface of a lake would the pressure be double that at the surface? (1 atm = 1.01 × 105 Pa) • a. 1.00 m • b. 9.80 m • c. 10.3 m • d. 32.2 m PHY231

  12. Buoyant force • A ping-pong ball has an average density of 0.0840 g/cm3 and a diameter of 3.80 cm. What force would be required to keep the ball completely submerged under water? • a. 1.000 N • b. 0.788 N • c. 0.516 N • d. 0.258 N PHY231

  13. Buoyant force • A ping-pong ball has an average density of 0.0840 g/cm3 and a diameter of 3.80 cm. What force would be required to keep the ball completely submerged under water? • a. 1.000 N • b. 0.788 N • c. 0.516 N • d. 0.258 N PHY231

  14. Continuity equation • Water is being sprayed from a nozzle at the end of a garden hose of diameter 2.0 cm. If the nozzle has an opening of diameter 0.50 cm, and if the water leaves the nozzle at a speed of 10 m/s, what is the speed of the water inside the hose? • a. 0.63 m/s • b. 0.80 m/s • c. 2.5 m/s • d. also 10 m/s PHY231

  15. Continuity equation • Water is being sprayed from a nozzle at the end of a garden hose of diameter 2.0 cm. If the nozzle has an opening of diameter 0.50 cm, and if the water leaves the nozzle at a speed of 10 m/s, what is the speed of the water inside the hose? • a. 0.63 m/s • b. 0.80 m/s • c. 2.5 m/s • d. also 10 m/s PHY231

  16. Thermal physics Review PHY231

  17. Conversion from TC inCelsius to T in Kelvin • Temperature units: • Kelvin K (SI unit), Celsius ºC, Fahrenheit ºF Conversion from TC inCelsius to TF in Fahrenheit A step of 1 ºC is the same as a step of 1 K A step of 1 ºC is equal to a step of 1.8 º F T=0 K is the absolute zero (TC=-273.15 ºC, TF=-459.67 ºC) At T=0 K, all atoms are at rest (no kinetic energy and pressure P=0) • Constants: • NA = 6.02*1023Avogadro constant • R = 8.314 J/(mol.K) Gas constant • kB= R/NA=1.38*10-23 J/KBoltzmann constant • s= 5.67*10-8 W/m2K4Stefan-Boltzmann constant

  18. SUMMARY – IDEAL GAS • Number of mols of particles • NA=6.02*1023 is the Avogadro’s number • Ideal gas law using number of moles of particles n and gas constant R= 8.31 J/(mol.K) • Temperature increases with particles’ KE • kB Boltzmann constant • Pressure increases with number of particles per unit volume (N/V) • Pressure increases with particles’ KE • Velocity of particles increases with temperature and, at a given T, larger for lighter elements. M is the molar mass (mass of one mole of a given substance)

  19. Heat: • Providing Heat Q to a substance can for example increase its temperature or change its characteristics Heat flowing in or out of a substance of mass m and specific heat c when its temperature is changed by DT (usually expressed in ºC) Heat flowing in or out of a substance of mass m during a change of phase described by latent heat L (for example: Solid-to-liquid use Lfusion) • Thermalization: • Two or more systems at different temperatures and in contact are exchanging energy through heat until they all reach the same temperature. Assuming N systems one has: • Two systems of mass m1 and m2, specific heat c1 and c2, and initial temperatures T1 and T2 Expresses conservation of energy with Qj is the heat received of lost by the jth system. (Assuming no phase change)

  20. Energy transfer between systems at different T: • Conduction: • Radiation • Thermal expansion (linear, area and volume):

  21. Ideal gas law • Two moles of nitrogen gas are contained in an enclosed cylinder with a movable piston. If the gas temperature is 298 K, and the pressure is 1.01  106 N/m2, what is the volume? (R = 8.31 J/molK) • a. 9.80  103 m3 • b. 4.90  103 m3 • c. 17.3  103 m3 • d. 8.31  103 m3 PHY231

  22. Ideal gas law • Two moles of nitrogen gas are contained in an enclosed cylinder with a movable piston. If the gas temperature is 298 K, and the pressure is 1.01  106 N/m2, what is the volume? (R = 8.31 J/molK) • a. 9.80  103 m3 • b. 4.90  103 m3 • c. 17.3  103 m3 • d. 8.31  103 m3 PHY231

  23. Volume expansion • A brass cube, 10 cm on a side, is raised in temperature by 200°C. The coefficient of volume expansion of brass is 57  106/C. By what percentage does volume increase? • a. 12% • b. 2.8% • c. 1.1% • d. 0.86% PHY231

  24. Volume expansion • A brass cube, 10 cm on a side, is raised in temperature by 200°C. The coefficient of volume expansion of brass is 57  106/C. By what percentage does volume increase? • a. 12% • b. 2.8% • c. 1.1% • d. 0.86% PHY231

  25. Calorimetry • An 80.0-g piece of copper, initially at 295°C, is dropped into 250 g of water contained in a 300-g aluminum calorimeter; the water and calorimeter are initially at 10.0°C. What is the final temperature of the system? (Specific heats of copper and aluminum are 0.092 0 and 0.215 cal/g°C, respectively. cw = 1.00 cal/g°C) • a. 12.8°C • b. 16.5°C • c. 28.4°C • d. 32.1°C PHY231

  26. Calorimetry • An 80.0-g piece of copper, initially at 295°C, is dropped into 250 g of water contained in a 300-g aluminum calorimeter; the water and calorimeter are initially at 10.0°C. What is the final temperature of the system? (Specific heats of copper and aluminum are 0.092 0 and 0.215 cal/g°C, respectively. cw = 1.00 cal/g°C) • a. 12.8°C • b. 16.5°C • c. 28.4°C • d. 32.1°C PHY231

  27. Conduction • The thermal conductivity of aluminum is 238 J/s·m·°C and of copper is 397 J/s·m·°C. A rod of each material is used as a heat conductor. If the rods have the same geometry and are used between the same temperature differences for the same time interval, what is the ratio of the heat transferred by the aluminum to the heat transferred by the copper? • a. 0.599 • b. 1.67 • c. 0.359 • d. 2.78 PHY231

  28. Conduction • The thermal conductivity of aluminum is 238 J/s·m·°C and of copper is 397 J/s·m·°C. A rod of each material is used as a heat conductor. If the rods have the same geometry and are used between the same temperature differences for the same time interval, what is the ratio of the heat transferred by the aluminum to the heat transferred by the copper? • a. 0.599 • b. 1.67 • c. 0.359 • d. 2.78 PHY231

  29. Radiated power • An object at 27°C has its temperature increased to 37°C. The power then radiated by this object increases by how many percent? • a. 3.3 • b. 15 • c. 37 • d. 253 PHY231

  30. Radiated power • An object at 27°C has its temperature increased to 37°C. The power then radiated by this object increases by how many percent? • a. 3.3 • b. 15 • c. 37 • d. 253 PHY231

  31. Energy in thermal processes Review PHY231

  32. R = 8.314 J/(mol.K) Universal gas constant • PV-diagram for ideal gases: • Ideal gas law • Processes can be conveniently visualized in a PV-diagram • Area under PV curve is the work done on the gas • <0 when gas expands (gas does work on outside) • >0 when it contracts • When P=constant: • Change of internal energy is the sum of heat + work • For all processes one also has • Isothermal curves in PV diagram show DU=0 so Q+W=0 Monoatomic gas CV=3R/2 Diatomic gas CV=5R/2

  33. P=constant Q=0 V=constant T=constant

  34. Enclosed area in PV diagram is the net work • Cycles in PV diagram: • Heat engine: Efficencye (general): Efficencye for ideal (Carnot) engine: • Refrigerat./heat pump: T in K !!!! Refrigerator - coefficient of performance Heat pump - coefficient of performance

  35. Isobaric process • A cylinder containing an ideal gas has a volume of 2.0 m3 and a pressure of 1.0  105 Pa at a temperature of 300 K. The cylinder is placed against a metal block that is maintained at 900 K and the gas expands as the pressure remains constant until the temperature of the gas reaches 900 K. The change in internal energy of the gas is +6.0  105 J. How much heat did the gas absorb? • a. 0 • b. 4.0  105 J • c. 6.0  105 J • d. 10  105 J PHY231

  36. Isobaric process • A cylinder containing an ideal gas has a volume of 2.0 m3 and a pressure of 1.0  105 Pa at a temperature of 300 K. The cylinder is placed against a metal block that is maintained at 900 K and the gas expands as the pressure remains constant until the temperature of the gas reaches 900 K. The change in internal energy of the gas is +6.0  105 J. How much heat did the gas absorb? • a. 0 • b. 4.0  105 J • c. 6.0  105 J • d. 10  105 J PHY231

  37. Ideal engine • A heat engine operating between a pair of hot and cold reservoirs with respective temperatures of 500 K and 200 K will have what maximum efficiency? • a. 60% • b. 50% • c. 40% • d. 30% T in K !!!! PHY231

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