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University of the Philippines College of Science

Physics 73

1st Long Problem Set B 1st Semester 2012-2013

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INSTRUCTIONS: Choose the best answer and shade the corresponding circle in your answer sheet. To change your answer, cross-out and sign your original answer and then shade your new answer. USEFUL CONSTANTS: ideal gas constant: R = 8.314 J/mol K = 0.08206 L atm/mol K Boltzmann constant: k = 1.381 x 10-23 J/molecule K Stefan-Boltzmann constant: σ = 5.67 x 10-8 W/m2 K4 1 atmosphere = 1.013 x 105 Pascal 1000 liter = 1 m3 Avogadro’s number: NA = 6.022 x 1023 molecules/mol INFORMATION ABOUT WATER: normal freezing point = 273.15 K = 0.00°C normal boiling point = 373.15 K = 100.00°C triple-point temperature = 273.16 K = 0.01°C specific heat (liquid water) = 4.19 x 103 J/kg K specific heat (ice) = 2.10 x 103 J/kg K latent heat of fusion = 3.34 x 105 J/kg latent heat of vaporization = 2.256 x 106 J/kg Hour 2 1. Normal human body temperature is 98.6 °F. What is the corresponding Celsius temperature? A. 54.8 °C B. 72.6 °C C. 40.0 °C

D. 37.0 °C E. 35.5 °C

2. The length of the column of mercury in a thermometer is 4.00cm when the thermometer is immersed in ice water and 24.0cm when the thermometer is immersed in boiling water. What should the length be at 22.0 °C? A. 4.00 cm B. 8.40 cm C. 4.40 cm

D. 5.00 cm E. 5.28 cm

3. When we measure the temperature of an object using a properly calibrated gas thermometer, we place the gas thermometer in thermal contact with the object. To infer the temperature, we must measure____________

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A. the pressure exerted by the gas B. the volume of the gas C. the number of moles of gas D. the number of molecules of gas E. the density of the gas. Hour 3 4. The coefficient of linear expansion of a certain steel-alloy bridge is 1.10 x 10-5 oC-1. If at a minimum winter temperature of minus 30 oC the bridge is 30.5 meters long, at the summer maximum of 40 oC its length is increased by A. 2.35 cm B. 2.35 mm C. 0.235 mm

D. 23.5 micrometers E. 2.35 micrometers

5. Consider the setup below. The ball is 3.00cm in diameter and is made of copper. The ring is 2.99cm in diameter and is made of steel. By how many degrees must the temperature of the copper ball be decreased so that it fits into the steel ring? The temperature of the steel ring is unchanged. αCu = 1.70 x 10-5 K-1. αSteel = 1.20 x 10-5 K-1.

A. 196K B. 277K C. 586K

D. 19 400K E. 392 K

6. Thin strips of iron and zinc are riveted together to form a bimetallic strip that bends when heated. The iron is on the inside of the bend because: A. it has a higher coefficient of linear expansion B. it has a lower coefficient of linear expansion

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C. it has a higher specific heat D. it has a lower specific heat E. it conducts energy better Hour 4 7. Body A has twice the mass and three times the specific heat of the body B. They are supplied with equal amounts of heat. Body A experiences a temperature change of ΔT. What change in temperature is experienced by body B? A. ΔT B. 3ΔT/2 C. 2ΔT/3

D. 6ΔT E. ΔT/2

8. For constant-volume processes the heat capacity of ideal gas A is greater than the heat capacity of ideal gas B. We conclude that when they both absorb the same thermal energy at constant volume: A. the temperature of A increases more than the temperature of B B. the temperature of B increases more than the temperature of A C. the internal energy of A increases more than the internal energy of B D. the internal energy of B increases more than the internal energy of A E. A does more positive work than B 9. To raise the temperature of a 2.0 kg piece of metal from 20 oC to 100 oC 61.8 kilojoules of heat is added. What is the specific heat of the metal? A. 0.39 kJ/kg K B. 0.31 kJ/kg K C. 1.6 kJ/kg K

D. 1.2 kJ/kg K. E. 0.77 kJ/kg K

Hour 5 10. The total energy of a blackbody radiation source is collected for one minute and used to heat water. The temperature of the water increases from 20.0 C to 20.5 C. If the absolute temperature of the blackbody were doubled and the experiment repeated, the temperature of the water will increase from 20.0 C to ___________ A. 21.0 C B. 25.0 C C. 28.0 C

D. 8.00 C E. 32.0 C

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11. If the thickness of a uniform wall is doubled, the rate at which heat is conducted through the wall is A. doubled B. increased by a factor of 4 C. decreased by a factor of 4

D. cut in half E. unchanged

12. You are asked to design a cylindrical steel rod 50.0 cm long with a circular cross section that will conduct 150 J/s from a furnace at 400°C to a container of ice under 1 atmosphere. What must the rod’s cross-sectional area be (assume that there is no heat loss through the sides)? ksteel = 50.2 W/(m K), kice = 1.60 W/(m K) A. 0.373 m2

B. 11.7 m2

C. 0.117 m2

D. 4.7 x 10-3 m2

E. 3.73 x 10-3 m2

Hour 7 The following table gives the fraction of molecules with v/vrms below a given value.

v/vrms fraction 0.20 0.011 0.40 0.077 0.60 0.218 0.80 0.411 1.00 0.608 1.20 0.771 1.40 0.882 1.60 0.947 1.80 0.979 2.00 0.993

13. The atomic radius of Helium is 0.490 angstroms or 0.490 x 10-10 m. A box of Helium gas has approximately 1.40 x 1027 molecules per cubic meter. What is the mean free path of the gas molecules? A. 8.33 x 10-9 m B. 4.90 x 10-10 m C. 4.19 x 10-9 m

D. 1.67 x 10-8 m E. 2.21 x 10-8 m

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14. A volume of an ideal gas goes through a temperature change from 20 oC to 60 oC. The relation between the average molecular kinetic energy K1at 20 oC and average molecular kinetic energy K2 at 60 oC is ____________________. A. K1 = K2 B. K1 = 0.33 K2 C. K1 = 3 K2

D. K1 = 0.88 K2 E. K1 = 1.14 K2

15. The speed of sound vsound through an ideal gas is directly proportional to the rms speed of the gas molecules. The ratio of the speed of sound (vsound in Helium)/(vsound in Oxygen) through helium gas (He) with molecular weight of 4, and oxygen (O2) with molecular weight of 32 when both are assumed to be ideal at the same temperature would be ___________________. A. 1.41 B. 2.08 C. 2.38

D. 2.83 E. 4.00

16. A gas made of oxygen molecules (a diatomic gas) satisfies the Maxwell-Boltzmann distribution. The temperature of the gas is 500 K. The molar mass of O2 is 32.0 g/mole. What is the probability that a randomly chosen molecule has a speed less than 500 m/s? A. 0.218 B. 0.411 C. greater than 0.993

D. 0.80 E. 0.60

Hour 8 17. An ideal monatomic gas has a molar heat capacity at constant pressure Cmp. What is the molar heat capacity at constant volume of an ideal diatomic gas in terms of Cmp? A. Cmp B. Cmp + R C. Cmp - R

D. Cmp + 3R/2 E. Cmp - 3R/2

18. Given 1 kg of oxygen gas (O2) at 20 °C, what fraction of the internal energy is rotational? A. 0.1 B. 0.2 C. 0.25

D. 0.4 E. 0.5

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Hour 9 19. Assume that all of the following processes have the same initial pressure P1, initial volume V1, and final volume V2. All of the gases involved have the same number of moles n. Which of the following processes will produce the largest magnitude of work done by an ideal gas? A. adiabatic expansion of a monatomic ideal gas. B. isobaric expansion C. isothermal expansion D. adiabatic expansion of a diatomic ideal gas E. free expansion 20. 2.0 Joules of work is done on an ideal while it is maintained in thermal isolation. How much has the internal energy changed? A. 2.0 J B. -2.0 J C. 4.0 J

D. -4.0 J E. 0.0 J

21. 1.0 liter of Helium gas (assumed as an ideal gas) at room temperature (20 oC) and 1 atmosphere of pressure is compressed isothermally to a volume of 100 milliliters. How much work is done on the gas? A. 5.6 kJ B. 0.47 kJ C. 47 kJ

D. 230 kJ E. 0.23 kJ

Hour 10 22. An ideal gas undergoes a cyclic process in which the net work W is done by the gas. What is the net amount of heat added to the gas in one cycle? A. W B. -W C. zero

D. 2W E. W/2

23. In a certain thermodynamic process, a system absorbs heat 100kJ and has an equal amount of positive work done on it. What is the change in the internal energy of the system? A. 100kJ B. 200kJ C. -200kJ

D. 0.00 J E. 50.0 kJ

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24. 3.98 moles of a diatomic ideal gas is compressed isobarically from 4.75 L to 2.13 L. The gas was initially at 253 K. What is the work done on the gas? A. -6.71 x 103 J B. -6.63 x 101 J C. 6.71 x 103 J

D. -6.63 x 101 J E. 4.62 x 103 J

Hour 11 25. An ideal gas expands while the pressure is constant. Which of the following is/are true? A. Heat flows into the system B. Work is negative C. Internal energy increases

D. A and B E. A and C

26. A cylinder contains 20 liters of air at 1.00 atm (treated as an ideal gas). Suppose the ratio of Cp to CV for air is 1.41. If this sample of air is compressed adiabatically to a volume of 5 liters, the pressure after compression is A. 2.7 atm B. 7.1 atm C. 8.4 atm

D. 4.0 atm E. 9.7 atm

27. A polyatomic ideal gas (ɣ = 1.30), initially at 10.1 m3 and 2.67 atm undergoes adiabatic expansion to a final volume of 12.4 m3. What is the work done by the gas? A. 3.12 MJ B. 13.9 J C. 564 kJ

D. -2.87 J E. 5.57 J

Hour 12 For the next two questions, consider an engine which absorbs 100 J and rejects 60 J in each cycle. 28. What is its efficiency? A. 0.40 B. 0.60 C. 0.75

D. 0.25 E. 0.50

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29. If each cycle takes 0.50 s, find the power output of this engine in watts. A. 80 Watts B. 200 Watts C. 120 Watts

D. 40 Watts E. 500 Watts

30. An Otto engine uses diatomic gas for fuel. Its cylinder has a maximum and minimum volume of 1.25 L and 0.250 L, respectively. What is its efficiency? A. 0.535 B. 0.927 C. 0.660

D. 0.475 E. 0.200

Hour 13 31. A refrigerator absorbs thermal energy of magnitude |QC| from a low temperature reservoir and rejects thermal energy of magnitude |QH| to a high temperature reservoir. Work W is done on the working substance. The coefficient of performance is given by: A. |QC|/W B. |QH|/W C. (|QC| + |QH|)/W

D. W/|QC| E. W/|QH|

32. A refrigerator expels 800 kJ into the environment in order to remove an amount of 130 kJ every cycle from the interior of the refrigerator and. What is the coefficient of performance of the refrigerator? A. 0.163 B. 6.15 C. 0.194

D. 5.15 E. 0.662

33. A refrigerator uses 30.0kJ of work per minute and dumps 80.0kJ of heat per minute into a hot reservoir. How long will it take for this refrigerator to freeze 1.00kg of water initially at 25.0°C? A. 8.78 minutes B. 2.10 minutes C. 6.68 minutes

D. 47.2 minutes E. 78.7 minutes

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Hour 14 34. Which of the following is true? A. The second law of thermodynamics is a generalized energy conservation statement. B. Heat can never be used to do work. C. All natural processes are reversible. D. The engine and refrigerator statements describe the same principle. E. Heat transfer from a cold to a hot reservoir can be done with no work. 35. Which of the following statements is true? A. The second law applies to heat engines while the third law applies to refrigerators. B. The second law applies only to Carnot engines. C. The Carnot engine is only possible if we assume that the second law is not true. D. The second law only applies to ideal gases. E. The second law prohibits the spontaneous transfer of heat from a cooler to a hotter object. 36. An engine operating in a cycle would violate the second law of thermodynamics if it ________________. A. changed all the heat from a source to mechanical work B. changed all of its mechanical work to heat C. were irreversible D. operated as a Carnot cycle E. was less efficient than a Carnot cycle Hour 15 37. A refrigerator is run by a motor with 500 W of output power, and the refrigerator removes heat at the rate of 2 x106 J/hr . If the temperature outside of the fridge is 30 C, what is the lowest possible temperature inside the refrigerator? A. 303 K B. 159 K C. 289 K

D. 200 K E. None of the above

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38. The temperatures TC of the cold reservoirs and the temperatures TH of the hot reservoirs for four Carnot engines are: engine 1: TC = 400K and TH = 500K engine 2: TC = 500K and TH = 600K engine 3: TC = 400K and TH = 600K engine 4: TC = 600K and TH = 800K Rank these engines according to their efficiencies, least to greatest A. 1, 2, 3, 4 B. 1 and 2 tie, then 3 and 4 tie C. 2, 1, 3, 4 D. 1, 2, 4, 3 E. 2, 1, 4, 3 39. Which of the following statements related to the Carnot theorem is false? A. Adiabatic processes eliminate heat transfer involved in mechanical processes. B. Isobaric processes allow reversible heat transfers. C. A Carnot engine is easily run backwards as a refrigerator. D. Carnot cycle steps require the system to always be in equilibrium states. E. Irreversibility of thermodynamic processes limits engine efficiency. Hour 16 40. Let ΔSirrev denote the change in entropy of a sample for an irreversible process from state A to state B. Let ΔSrev denote the change in entropy of the same sample for a reversible process from state A to state B. Then: A. ΔSirrev > ΔSrev B. ΔSirrev = ΔSrev C. ΔSirrev < ΔSrev

D. ΔSirrev = 0 E. ΔSrev = 0

41. 6.21 kg of water absorb heat to raise its temperature from 20.1 °C to 37.8 °C. What is the change in entropy of the water? A. 1.52 kJ/K B. 16.4 kJ/K C. 27.6 kJ/K

D. 0.662 kJ/K E. 12.2 kJ/K

42. If a 2.00-kg piece of lead at 100°C is dropped into a lake at 10.0°C, find the entropy change of the universe. cPb = 130 J/kg K

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A. 2270 J/K B. 2410 J/K C. 10.9 J/K

D. 1741 J/K E. 2310 J/K

Hour 17 43. If 500J of heat is conducted from a reservoir at 400K to one at 300K, what is the maximum amount of work that you can extract from this amount of heat. A. 125J B. 0.00139J C. 0.417

D. 167J E. 500J

44. Which of the following statements is false? A. A thermodynamic system always tends to the most probable state. B. The most probable state corresponds to the macroscopic state with most number of microscopic states. C. A high disorder is measured for a state having a large number of possible configurations. D. An increase in the number of microscopic states is seen for a system undergoing a reversible adiabatic expansion. E. Multiple microscopic states can correspond to the same macroscopic state. 45. Given a system with 1015 possible microstates. Which of the following is its entropy? A. 4.77 x 10-22 J/K B. 1.38 x 10-13 J/K C. 1.38 x 10-23 J/K

D. 3.18 x 10-22 J/K E. 23.0 J/K

END OF EXAM