73 Summer 1st LE Set a With Answers

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University of the PhilippinesCollege of Science

PHYSICS 731st Long Exam

Summer 2010-11Set A

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/molK = 0.08206 Latm/molKBoltzmann constant: k = 1.38110-23 J/moleculeKStefan-Boltzmann constant: = 5.6710-8 W/m2K4

1 atmosphere = 1.013105 Pascal1000 liter = 1 m3

Avogadro’s number: NA = 6.022 x 1023 molecules/mol

INFORMATION ABOUT WATER:normal freezing point = 273.15 K = 0.00oCnormal boiling point = 373.15 K = 100.00oCtriple-point temperature = 273.16 K = 0.01oCspecific heat (liquid water) = 4.19103 J/kgKspecific heat (ice) = 2.10103 J/kgKlatent heat of fusion = 3.34105 J/kglatent heat of vaporization = 2.256106 J/kg

Hour 2

1. The triple point of water occurs at T = 273.16 K. What is this in Fahrenheit?A. 32.018 ˚FB. -17.772 ˚FC. 523.69 ˚F

D. 133.98 ˚FE. 212.02 ˚F

2. A constant-volume gas thermometer is used to measure the temperature of an object. When the thermometer is in contact with water at its triple point (273.16 K) the pressure in the thermometer is 8.500 × 104 Pa. When it is in contact with the object the pressure is 9.650 × 104 Pa. The temperature of the object is:A. 314KB. 37.0KC. 241K

D. 2020KE. 310K

3. A thermometer is placed in a beaker of ice water. Which of the following statements can be inferred? Make an exhaustive list of answers.i. The thermometer will measure its own temperature.ii. Thermal equilibrium must be achieved for the thermometer to record the ice-water temperature. iii. Using the thermometer demonstrates the zeroth law of thermodynamics

A. i onlyB. i, ii, and iiiC. ii only

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D. ii, and iii onlyE. iii only

Hour 3

4. The coefficient of linear expansion of steel is 11 × 10−6 per C°. A steel ball has a volume of exactly 100 cm3 at 0º C. When heated to 100° C, its volume increases by:A. 0.0033 cm3

B. 0.0011 cm3

C. 0.000011 cm3

D. 0.33 cm3

E. 1.23 cm3

5. A steel ball with a radius of 3.50 cm undergoes expansion after its temperature increased by 27.3 C˚. What is its final volume? Coefficient of linear expansion of steel, = 1.20x10-5 K-1

A. 0.177 cm3

B. 3.68 cm3

C. 3.56 cm3

D. 5.88x10-2 cm3

E. 3.54 cm3

6. What temperature change would require a 0.101% increase in length of a copper wire with initial length 1.25 m? Coefficient of linear expansion of copper, = 1.70x10-5 K-1

A. 215 K B. 32.5 KC. 752 K

D. 47.5 KE. 4750 K

Hour 4

7. 10 kg of ice at 0 °C is mixed with 4 kg of steam at 100 °C in a thermally isolated container and allowed to reach thermal equilibrium. What is the final temperature of the resulting mixture?A. 0.00° CB. 167 °CC. 689 ºC D. 100 ºCE. 7.14 ºC

8. What is the minimum amount of iron is needed to melt 1.45 kg of ice initially at -2.35 ˚C if the iron is initially heated to a temperature of 75.0 ˚C?specific heat of iron= 470 J/(kg·K)specific heat of ice (near 0 °C) = 2100 J/kg·KA. 13.7 kgB. 14.1 kgC. 0.203 kg

D. 0.404 kgE. 13.9 kg

9. Which of the following processes will require the greatest amount of heat?

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Csteam= 1.860x103 J/(kg·K)A. Raising the temperature of 1.0 kg steam by 10 ˚CB. Melting of 1.0 kg ice at 0 ˚CC. Raising the temperature of 1.0 kg water by 10 ˚CD. Vaporizing 1.0 kg water at 100 ˚CE. All of the above will require the same amount of heat.

Hour 5

10. A cubical Styrofoam box used to keep drinks cold at a picnic has total wall area (including the lid) of 0.80 m 2 and wall thickness 2.0 cm. It is filled with ice, water, and cans of cola at 0°C. What is the rate of heat flow into the box if the temperature of the outside wall is 30.0 °C? The coefficient of thermal conductivity of Styrofoam is k=0.010 W/(m·K)A. 0.12 WB. 120 WC. 12 W

D. 1.2 WE. 0.020 W

11. The total surface area of a human body is 1.20 x 104 cm2 and the surface temperature is 30.0 °C = 303 K. What is the total rate of radiation? The emissivity of the body is very close to unity, irrespective of skin pigmentation.A. 0.055 WB. 5.74 x 106 W C. 574 WD. 5.51 x 106 WE. 551 W

12. Heat is being transferred at a rate of 521 W through a metal slab of cross-sectional area 3.25 cm2 and length 13.1 cm from a heat source at T = 1250 K to a heat sink at T = 242 K. What is the thermal conductivity of the metal?A. 3.22 W/cmKB. 0.128 W/cmKC. 2.03x10-9 W/cmKD. 5.91x10-3 W/cmKE. 2.08 W/cmK

Hour 6

13. A hot-air balloon initially at the top of the mountain experiences an atmospheric pressure of 0.972 atm having a volume of 355 L. If the air inside the balloon is assumed to be ideal, what is the volume of the balloon after it descended to the ground where the pressure is 1.00 atm, and its temperature is constant?A. 365 L B. 355 L

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C. 345 LD. 335 L

E. 325 L

14. Which of the following statements is false about an ideal gas?A. A gas can be considered ideal when it is maintained at high temperature and low pressure.B. Isotherms of ideal gases have parabolic profiles in a PV diagram.C. An ideal gas molecule can be modeled as a point particle.D. The ideal gas condition fails when the density and pressure is large. E. The ideal gas equation is an equation only for equilibrium states.

15. An ideal gas with Cp/Cv = γ = 1. 667 is inside a piston of volume V = 0.10 m3 and pressure p = 1.0 x 104 Pa. Let the piston be compressed in such a way that the temperature remains constant, and the final pressure is double the initial pressure. What is the final volume of the gas?A. 0.031 m3

B. 0.050 m3

C. 0.10 m3

D. 0.20 m3

E. 0.17 m3

Hour 7

16. What is the root-mean-square speed of an Oxygen gas (molar mass = 32.0 g/mol) maintained at a temperature of 544 K. A. 376 m/sB. 20.6 m/sC. 752 m/sD. 651 m/sE. 1.42x103 m/s

The following table gives the fraction of molecules with v/vrms below a given value.V/Vrms fraction0.20 0.0110.40 0.0770.60 0.2180.80 0.4111.00 0.6081.20 0.7711.40 0.882

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1.60 0.9471.80 0.9792.00 0.993

17. A gas made of He molecules satisfies the Maxwell-Boltzmann distribution. The temperature of the gas is 500 K. The molar mass of He is 4.003 g/mole. What is the probability that a randomly chosen molecule has a speed less than 1.059 x 103 m/s?A. 0.011B. 0.077C. 0.218

D. 0.411E. 0.608

18. Oxygen, a diatomic ideal gas, is placed in a cylinder with a piston, with temperature 27 °C and pressure 1.0 atm. If we model an oxygen molecule as a sphere with radius r=2.0 x 10-

10 m, what is the mean free path of oxygen?A. 5.2 x 10-9 mB. 5.2 x 10-4 mC. 5.8 x 10-3 m

D. 8.2 x 10-8 m E. 5.8 x 10-8 m

Hour 8

19. Which of the following statements is false?A. At very high temperatures, all solids have the same heat capacity.B. Rotational motion contributes additional degrees of freedom for diatomic molecules even at low temperatures.C. Quantization of energy results to the failure of the equipartition theorem.D. Additional degrees of freedom are “frozen out” resulting to lower heat capacities than predicted by equipartition theorem.E. In general, polyatomic molecules have higher heat capacities compared to diatomic molecules.

20. Which of the following statements best describes the triple point?A. It is the temperature in which all three phases coexist.B. It is the point at the center of the phase diagram.C. It is the point where thermal equilibrium is achieved by the three phases.D. It is the pressure and temperature in which all three phases coexist.E. None of the above.

21. 4.6 moles of Oxygen, a diatomic gas, are kept in a closed cylinder of constant volume 2.0 m3. The initial pressure is 1.0 x 104 Pa, and the initial temperature is 523 K. If 1000 J of heat is absorbed by the gas, what is the final temperature of the gas?A. 540 KB. 1.58 x 103 KC. 2.29 x 103 K

D. 533 KE. 530 K

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Hour 9

22. 2.0 moles of Helium (an ideal monatomic gas) inside a cylinder with a piston expand from an initial pressure of 1.00 x 104 Pa, volume of 1.00 m3, and temperature 601 K. The expansion occurs so that it traces a straight line on a pV diagram, and the final state has temperature 601 K, volume 2.00 m3, and pressure 0.500 x 104 Pa. What is the work done by the gas? (Hint: Draw a pV diagram before you compute!)A. 7.50 x 103 JB. 5.00 x 103 JC. 6.93 x 103 J

D. 1.00 x 104 JE. 0.00 J

23. 4.79 moles of a polyatomic ideal gas (γ= 1.127) is allowed to expand at a constant temperature T=900 K from a volume of 2.50 m3 to a final volume of 10.0 m3. The initial pressure is 1.43 x 104 Pa. What is the work done by the gas?A.1.07 x 105 JB. 4.97 x 104 JC. 4.54 x 104 J

D. 3.23 x 104 JE. 1.43 x 105 J

24. What statement can be directly concluded from the figure above?

A. The system does a positive amount of work in going from A to B.B. Point A has a higher amount of heat compared to point B.C. The system absorbs heat in going from A to B.D. Point A has a higher amount of work compared to point B.E. No conclusion can be made.

Hour 10

25. Calculate the change in internal energy of 7.25 moles of an ideal gas undergoing isothermal compression at a temperature of 344 K.A. 31.1 kJ B. 205 J

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C. 20.7 kJ D. 307 JE. 0 J

26. What can be said about the figure given above if the process from point A to B is an isothermal expansion of an ideal gas?A. Q = 0B. U = WC. U = 0D. W is negative. E. Q = W

27. The internal energy of an ideal gas depends on:A. the pressure onlyB. the volume onlyC. the temperature onlyD. temperature, pressure, and volumeE. the temperature and pressure only

Hour 11

28. Monatomic, diatomic, and polyatomic ideal gases each undergo slow adiabatic expansions from the same initial volume and the same initial pressure to the same final volume. The magnitude of the work done by the environment on the gas:A. is greatest for the monatomic gasB. is greatest for the diatomic gasC. is greatest for the polyatomic gasD. is the same for all three gasesE. is the same only for the diatomic and polyatomic gases

29. An ideal gas has the adiabatic constant γ=1.127. What is the value of the specific heat at constant pressure?A. 8.87 R B. 1.50 R

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C. 7.87 RD. 2.50 R

E. 3.50 R

30. Initially, a monatomic ideal gas is stored at a volume of 5.00 L at a temperature of 145 ˚C. The gas expands adiabatically to a volume of 6.25 L. What is its final temperature?A. 288 ˚CB. 373 ˚CC. 100 ˚C

D. 15.1 ˚CE. 61.4 ˚C

Hour 12

31. A heat engine takes in 5.0 x 105 J , does 1.5 x 105 J of work, and discards 3.5 x 105 J of heat into the environment every cycle. The efficiency of the engine is ________.A. 0.30B. 3.3C. 0.70

D. 1.4E. 0.43

32. Calculate the efficiency of an Otto engine which uses a diatomic ideal gas and has a compression ratio of 2.25.A. 0.418B. 0.582C. 0.277

D. 0.723E. 0.679

33. What is the compression ratio of an Otto engine that uses a monatomic ideal gas as working substance while expelling 2.89 kJ for every 7.45 kJ that it absorbs?A. 2.09B. 3.41C. 1.77

D. 4.14E. 10.7

Hour 13

34. A refrigerator removes 1.00 kJ of heat from its interior, consumes 0.54 kJ of energy, and discards 1.54 kJ of heat into the heat sink. The interior of the refrigerator has a temperature of -5.0 ° C while the environment has a temperature of 30 °C. The coefficient of performance of the refrigerator is__________A. 0.54B. -0.14C. 2.85

D. 1.85 E. 7.66

35. A refrigerator consumes electrical power at the rate of 100 W. The coefficient of performance is 2.96. What is the rate at which the refrigerator dumps heat into the environment?A. 296 WB.196 W

C. 33.8 WD. 51.0 W

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E. 396 W

36. An aircon extracts 655 J of heat inside a room and rejects 925 J outside. What is its coefficient of performance?A. 4.52B. 2.43C. 3.43

D. 1.41E. 0.708

Hour 14

37. Which of the following best describes the 2nd Law of Thermodynamics?A. The refrigerator statement is not a form of the 2nd Law of Thermodynamics.B. The conversion from work to heat are reversible processes.C. Heat can be transferred from cooler object to hotter object.D. Heat is neither created nor destroyed. E. Heat can never be converted completely into mechanical work.

38. Which of the following processes violates the 2nd Law of Thermodynamics?A. Doing work using heat of combustion changing the state of the system.B. A refrigerator expelling a larger amount of heat than it has absorbed.C. An engine absorbing a larger amount of heat than it has absorbed.D. Spontaneous transfer of heat from cold to hot environment.E. A heat engine being used in reverse as a refrigerator.

39.An inventor suggests that a house might be heated by using a refrigerator to draw energy as heat from the ground and reject energy as heat into the house. He claims that the energy supplied to the house as heat can exceed the work required to run the refrigerator. This:

A. is possibleB. is impossible by first lawC. is impossible by second lawD. is impossible since heat energy flows from the (hot) house to the (cold) groundE. would only work if the ground and the house were at the same temperature

Hour 15

40. A Carnot heat engine using ideal gas as working substance has a Carnot efficiency of 0.565. If a water vapor (a real gas) was used instead, what can be said about the new Carnot efficiency of this engine?A. It will violate the Carnot condition in using the real gas.B. It is greater than 0.565.C. It is less than 0.565.D. It is exactly 0.565.E. It cannot be determined

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41. A Carnot refrigerator is known to operate between the temperatures -10 ° C and 30° C. It uses a polyatomic gas (γ=1.127) as its working substance. The minimum volume of the working substance of this Carnot refrigerator is 2.0 liters, while the maximum volume is 10 liters. The coefficient of performance of this refrigerator is ______________.A. 1.33B. 0.184C. 6.58

D. -0.25E. 0.132

Hour 16

42. A clay ball of mass 0.056 kg was dropped from a height of 2.1 m. Upon striking the ground, it sticks to the pavement converting its energy completely into heat. What is the change in entropy of the system assuming the system is at standard room temperature T = 298 K?A. 0.67 J/K B. 3.9x10-3 J/KC. 0.98 J/KD. 1.2 J/KE. Not enough information

43. What is the entropy change of 1.0 kg of ice heated so that it starts at 0.00 ° C, melts, and then ends up as liquid water at 30.0° C.Lf(water) = 3.34 x 105 J/kgLv(water) = 2256 x 103 J/kgcwater= 4190 J/kg K

A. 437 J/KB. 1.22 x 103 J/KC. 1659 J/KD. 8.70 x 103 J/KE. 8.26 x 103 J/K

Hour 17

44. What is the ratio of the final to initial number of microstates of 6.5 moles of a gas given a change in entropy of 4.5x10-23 J/K?A. 1B. 1.6x109

C. 170

D. 26E. 3.4x108

45. Let k be the Boltzmann constant. If the configuration of the molecules in a gas changes so that the multiplicity is reduced to one-third its previous value, the entropy of the gas changes by:

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A. ∆S = 3k ln 2B. ∆S = −3k ln 2C. ∆S = 0D. ∆S = k ln 3E. ∆S = −k ln 3

END OF EXAM

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