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THERMODYNAMICS ME 022 Final Exam Total Marks 45 1. You stick a spherical He balloon in the freezer. What happens to the size of the balloon? Be as quantitative as possible. 2. You have a 1.000 cm diameter steel ball which you desire to pass through a 0.999 cm inner diameter Al ring. (a) If you heat them up both together, how hot must they get before you can accomplish your task. (b) If you heat up only the ring, how hot must it get? (You may look up the coefficient of expansion.) 3. A grandfather clock’s pendulum is made from steel, and calibrated at 5 C such that one period is 1 second. How much time does it lose in a day, if the temperature increases to 35 C? (Recall that is the equation for the period of a pendulum.) 4. You have 2 gas tanks connected to each other by a valve. Tank A is twice the size of tank B. They are both initially at 20 C. (a) If tank A starts at 104 Pa and tank B starts at 105 Pa, what is the final temperature and pressure of each tank when the valve is opened? (You may assume the ideal gas law, and that no heat is added nor work done.) 5. A textbook gives the coefficient of volume expansion for air as 3.67  10-3 near room temperature. Use the ideal gas law to obtain a theoretical value for this number, and compare. 6. A dead-weight piston is set up with an ideal gas inside the chamber. The piston is made out of 50 cm thick copper. (Recall that there is atmospheric air above the piston pushing down on it.) If the system is in equilibrium with T = 1500K and contains 10 moles of gas, determine the volume of the gas. 7. You add 50 g of ice at –5 C to 200 g of water at 25 C. What is the final temperature of the mixture, assuming that no heat is lost to the outside? 8. You add 50 g of steam at 150 C to 50 g of ice at –5 C. What is the final temperature of the mixture, assuming that no heat is lost to the outside? 9. A cylindrical copper rod of length 1.2 m and cross-sectional area of 4.8 cm2 is insulated to prevent heat loss through its surface. The ends are maintained at a temperature difference of 100 C by having one end in a water-ice mixture and the other in a boiling water/steam mixture. If you initially have 10 g of ice on the one end and lots of steam on the other, how long does it take to melt the ice? 10. How long would it take to melt the ice in the previous problem if the rod were 0.6 m of Cu and 0.6 m of iron? 11. How about if the rod in problem 12 were divided in half the other way: 1.2 m of 2.4 cm2 Cu side by side with 1.2 m of 2.4 cm2 iron? 12. A “solar cooker” consists of a curved parabolic-like reflector which focuses sunlight onto the object to be heated. The solar power per unit area reaching the Earth at the location of a 0.50 m diameter solar cooker is 600 W/m2. Assuming that 50% of the incident energy is converted to heat energy, how long would it take to boil 1.0 L of water initially at 20 C? 13. A 1 kg cube of steel is heated from 20 C until the volume expands by 0.10 %. (a) What is its final temperature? (b) How much work was done in the expansion by pushing against the atmosphere? (c) How much work was done in the expansion by having to raise its center of mass? (d) How much heat was added in the process? 14. The tungsten filament of a certain 100W light bulb radiates 2W of light (the other 98 W of energy is carried away by convection and conduction). The filament has a surface area of 0.25 mm2 and an emissivity of 0.95. How hot is the filament? 15. At high noon, the Sun delivers about 1000 W/m2 of radiant energy (or perhaps a bit less, in Wisconsin!). Suppose this strikes a blacktop which is insulated from the ground below. (Or equivalently, suppose the dirt below the blacktop has a very low thermal conductivity.) Ignoring conduction and convection, what temperature would you predict the blacktop to reach? 16. A large cold object is at 273 K, and a large hot object is at 373 K. 8.00 J of heat energy is transferred from the hot to the cold object, which is not enough to substantially change their temperatures. What is the total entropy change of this process? 17. Fifteen identical particles have various speeds: one has a speed of 2.00 m/s; two have speeds of 3.00 m/s; three have speeds of 5.00 m/s; four have speeds of 7.00 m/s; three have speeds of 9.00 m/s; and two have speeds of 12.0 m/s. (a) Find the average speed, the rms speed, and the most probable speed. (b) If the particles have a molar mass of 1000 g/mole, make a reasonable guess as to the likely temperature of the particles. 18. A refrigerator with C.O.P. = 4.7, extracts heat from the inside at a rate of 250 J per cycle. (a) How much work per cycle is required to operate the refrigerator? (b) How much heat per cycle is discharged into the room? 19. An engine using a polyatomic (atoms not in a row) ideal gas is driven by this cycle: from A to B, the pressure increase to 3 times its original pressure while keeping V constant; from B to C, it expands adiabatically until it reaches 4 times the original volume; from C to D, the pressure drops at constant V; from D to A it contracts adiabatically. (a) Sketch the cycle, indicating P, V, and T, for all points. (b) What is the efficiency of this cycle? (c) What’s the maximum efficiency possible between the high and low temperatures. (Leave all answers in terms of the original P, V, and T.) 20. A monatomic ideal gas (1 mole) undergoes this cycle: starting from 1 atm, 0 C, it contracts adiabatically to P = 2 atm, then it expands isothermally, then it contracts isobarically. (a) Sketch the cycle, indicating P, V, and T, for all points. (b) What is the efficiency of this cycle? (c) What is S for each leg of the cycle? 21. A monatomic ideal gas (n moles) undergoes this cycle: (1) starting at V1, T1, it increases the temperature at constant volume to 3T1; (2) from V1, 3T1, it increases the volume at constant temperature to 2V1; (3) from 2V1, 3T1, it decreases the temperature at constant volume back to the original temperature, T1; (4) from 2V1, T1, it decreases the volume back to the original volume, V1. (a) Sketch the cycle on a P-V diagram. (b) In terms of n and T1, what is the net work done by the game per cycle? (c) What is the efficiency of the cycle? 22. What is the State Postulate?

THERMODYNAMICS
ME 022

Final Exam

Total Marks 45

 

 

  1. You stick a spherical He balloon in the freezer. What happens to the size of the balloon? Be as quantitative as possible.

 

  1. You have a 1.000 cm diameter steel ball which you desire to pass through a 0.999 cm inner diameter Al ring. (a) If you heat them up both together, how hot must they get before you can accomplish your task. (b) If you heat up only the ring, how hot must it get? (You may look up the coefficient of expansion.)

 

  1. A grandfather clock’s pendulum is made from steel, and calibrated at 5° C such that one period is 1 second. How much time does it lose in a day, if the temperature increases to 35° C? (Recall that is the equation for the period of a pendulum.)

 

  1. You have 2 gas tanks connected to each other by a valve. Tank A is twice the size of tank B. They are both initially at 20° (a) If tank A starts at 104 Pa and tank B starts at 105 Pa, what is the final temperature and pressure of each tank when the valve is opened? (You may assume the ideal gas law, and that no heat is added nor work done.)

 

  1. A textbook gives the coefficient of volume expansion for air as 3.67 ´ 10-3 near room temperature. Use the ideal gas law to obtain a theoretical value for this number, and compare.

 

  1. A dead-weight piston is set up with an ideal gas inside the chamber. The piston is made out of 50 cm thick copper. (Recall that there is atmospheric air above the piston pushing down on it.) If the system is in equilibrium with T = 1500K and contains 10 moles of gas, determine the volume of the gas.

 

  1. You add 50 g of ice at –5° C to 200 g of water at 25° What is the final temperature of the mixture, assuming that no heat is lost to the outside?

 

  1. You add 50 g of steam at 150° C to 50 g of ice at –5° What is the final temperature of the mixture, assuming that no heat is lost to the outside?

 

  1. A cylindrical copper rod of length 1.2 m and cross-sectional area of 4.8 cm2 is insulated to prevent heat loss through its surface. The ends are maintained at a temperature difference of 100° C by having one end in a water-ice mixture and the other in a boiling water/steam mixture. If you initially have 10 g of ice on the one end and lots of steam on the other, how long does it take to melt the ice?

 

  1. How long would it take to melt the ice in the previous problem if the rod were 0.6 m of Cu and 0.6 m of iron?

 

  1. How about if the rod in problem 12 were divided in half the other way: 1.2 m of 2.4 cm2 Cu side by side with 1.2 m of 2.4 cm2 iron?

 

  1. A “solar cooker” consists of a curved parabolic-like reflector which focuses sunlight onto the object to be heated. The solar power per unit area reaching the Earth at the location of a 0.50 m diameter solar cooker is 600 W/m2. Assuming that 50% of the incident energy is converted to heat energy, how long would it take to boil 1.0 L of water initially at 20° C?

 

  1. A 1 kg cube of steel is heated from 20° C until the volume expands by 0.10 %. (a) What is its final temperature? (b) How much work was done in the expansion by pushing against the atmosphere? (c) How much work was done in the expansion by having to raise its center of mass? (d) How much heat was added in the process?

 

  1. The tungsten filament of a certain 100W light bulb radiates 2W of light (the other 98 W of energy is carried away by convection and conduction). The filament has a surface area of 0.25 mm2 and an emissivity of 0.95. How hot is the filament?

 

  1. At high noon, the Sun delivers about 1000 W/m2 of radiant energy (or perhaps a bit less, in Wisconsin!). Suppose this strikes a blacktop which is insulated from the ground below. (Or equivalently, suppose the dirt below the blacktop has a very low thermal conductivity.) Ignoring conduction and convection, what temperature would you predict the blacktop to reach?

 

  1. A large cold object is at 273 K, and a large hot object is at 373 K. 8.00 J of heat energy is transferred from the hot to the cold object, which is not enough to substantially change their temperatures. What is the total entropy change of this process?

 

  1. Fifteen identical particles have various speeds: one has a speed of 2.00 m/s; two have speeds of 3.00 m/s; three have speeds of 5.00 m/s; four have speeds of 7.00 m/s; three have speeds of 9.00 m/s; and two have speeds of 12.0 m/s. (a) Find the average speed, the rms speed, and the most probable speed. (b) If the particles have a molar mass of 1000 g/mole, make a reasonable guess as to the likely temperature of the particles.

 

  1. A refrigerator with C.O.P. = 4.7, extracts heat from the inside at a rate of 250 J per cycle. (a) How much work per cycle is required to operate the refrigerator? (b) How much heat per cycle is discharged into the room?

 

  1. An engine using a polyatomic (atoms not in a row) ideal gas is driven by this cycle: from A to B, the pressure increase to 3 times its original pressure while keeping V constant; from B to C, it expands adiabatically until it reaches 4 times the original volume; from C to D, the pressure drops at constant V; from D to A it contracts adiabatically. (a) Sketch the cycle, indicating P, V, and T, for all points. (b) What is the efficiency of this cycle? (c) What’s the maximum efficiency possible between the high and low temperatures. (Leave all answers in terms of the original P, V, and T.)

 

  1. A monatomic ideal gas (1 mole) undergoes this cycle: starting from 1 atm, 0° C, it contracts adiabatically to P = 2 atm, then it expands isothermally, then it contracts isobarically. (a) Sketch the cycle, indicating P, V, and T, for all points. (b) What is the efficiency of this cycle? (c) What is DS for each leg of the cycle?

 

  1. A monatomic ideal gas (n moles) undergoes this cycle: (1) starting at V1, T1, it increases the temperature at constant volume to 3T1; (2) from V1, 3T1, it increases the volume at constant temperature to 2V1; (3) from 2V1, 3T1, it decreases the temperature at constant volume back to the original temperature, T1; (4) from 2V1, T1, it decreases the volume back to the original volume, V1. (a) Sketch the cycle on a P-V diagram. (b) In terms of n and T1, what is the net work done by the game per cycle? (c) What is the efficiency of the cycle?

 

  1. What is the State Postulate?

 

 

 

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