Physics73_PS1

University of the PhilippinesCollege of Science

Physics 73

First Problem SetSecond Semester, AY 20142015

First Problem Set Second Semester, AY 20142015 Physics 73

Instructions: Choose the letter of the best answer to each of the following questions. Tochange your answer, cross (X) out the shaded letter and supply your new answer with yoursignature beside the item. Any form of cheating in examinations or any act of dishonesty inrelation to studies, such as plagiarism, shall be subject to disciplinary action.

USEFUL CONSTANTSIdeal gas constant: R = 8.314 J/molK = 0.08206 Latm/molKBoltzmann constant: k = 1.381 1023 J/moleculeKStefan-Boltzmann constant: = 5.67 108 W/m2K41 atm = 1.01 105 Pa1000 L = 1 m3

Avogadros number: NA = 6.022 1023 molecules/mol

INFORMATION ABOUT WATERNormal freezing point = 273.15 K = 0.00 CNormal boiling point = 373.15 K = 100.00 CTriple-point temperature = 273.16 K = 0.01 CSpecific heat (liquid water) = 4.19 103 J/kgKSpecific heat (ice) = 2.10 103 J/kgKLatent heat of fusion = 3.34 105 J/kgLatent heat of vaporization = 2.256 106 J/kg

Hour 2

1. Feeling the... Temperature? The temperature of Room A was measured to be 30.0C.The thermometers for room B and C used other temperature scales. The temperature ofRoom B was measured to be 95.0F , while the temperature of Room C was measured tobe 298 K. Which room is the coldest?

A. Room A

B. Room B

C. Room C

D. All rooms have the same temperature.

2. Change! A piece of metal was heated from 300 K to 430 K. What is the change in temper-ature in Fahrenheit degrees?

A. 130 F

B. 72.2 F C. 234 F

D. 189 F

A 2


3. A certain thermometer. In a certain constant-volume gas thermometer, a temperature of23 K corresponds to a pressure of 5.9 104 Pa. What is the temperature corresponding toa pressure of 6.7 104 Pa?

A. T2 = 0.049 K

B. T2 = 1.7 K

C. T2 = 26 K

D. T2 = 920 K

Hour 3

For the next two numbers, consider an unknown material that expanded by 0.03% after beingheated from 300 K to 350 K.

4. Alpha ko. What is the coefficient of linear expansion of the material?A. 6.0 106 K1B. 1.5 106 K1C. 1.5 102 K1D. 1.7 103 K1

5. Volume mo! If the same material is used to create a solid cylinder initially with radius10.0 cm and height 3.00 cm, what will be the cylinders new volume if it undergoes atemperature change of 40 K?

A. 942.48 cm3

B. 942.70 cm3

C. 943.15 cm3

D. 942.64 cm3

A 3


6. Fat hamster. A copper cylinder with coefficient of linearexpansion = 1.7 105(C)1 and Youngs modulusY = 11 1010 Pa initially has a temperature of 20.C.A hamster decided to sit on the cylinder, changing itstemperature to 37C. The hamster is so fat and heavythat it prevents the copper from expanding. What is thethermal stress on the cylinder?

A. 3.2 107 PaB. 4.3 107 PaC. 1.1 107 PaD. 8.9 107 Pa

Hour 4

7. Its getting hot in here. How much energy is needed to obtain 300 g of water at 25.0 Cfrom ice initially at 0 C?

A. 1.00 105 JB. 1.32 105 JC. 3.14 104 JD. 1.15 105 J

8. Ugh. Copper. 250 g of water at 25 C is poured inside a copper (cCu = 390 J/kgK) potinitially at 70 C. What should be the mass of the copper pot if the equilibrium temperatureof the system is 45 C?

A. 2.14 kg

B. 0.0291 kg

C. 0.910 kg

D. 0.250 kg

A 4


9. Wall-E tries coffee. Wall-E, a robot with mass 20. kg, temperature 290 K and specificheat 910 J/kg K, drinks a cup of coffee with mass 2.2 kg, temperature 350 K and specificheat 4100 J/kg K. If no heat is exchanged with the surroundings, what is Wall-Es finalequilibrium temperature?

A. 290 K

B. 310 K

C. 320 K

D. 340 K

Hour 5

10. Radiate Happiness. A cube (e = 0.60) with side length 5 m has a temperature of 350 K.What is the total rate of radiation of energy of the cube?

A. 7.66 104 WB. 6.38 104 WC. 1.28 104 WD. 5.11 104 W

11. HEAT. A brass cylindrical rod of length 5 cm and diameter 6 cm has one end inside a 0 Cice bath, while the other end is attached to a steam bath at 110 C. What is the rate of heatflow within the rod? (kbrass = 109 W/mK)

A. 6.78 104 WB. 6.78 102 WC. 2.71 103 WD. 2.71 105 W

12. Whats Cooking? Which of the heat transfer mechanisms are being used when you areboiling oil inside a pan placed over a gas burner?

I conduction

II convection

III radiation

A. III only

B. I and III

C. II and III

D. I, II, and III

A 5


Hour 6

13. Lazy people beware. Which of the following statements below is/are factors consideredin the van der Waals equation?

I The forces of attraction between identical gas particles

II The electrostatic forces between electrons and nuclei of different gas molecules

III The volume of the gas molecules

A. I only

B. II only

C. I and III

D. I and II

14. You are so dense. What is the density of nitrogen gas at pressure 3.50 kPa and temperature40 C? (MNitrogen = 28 g/mol)

A. 0.162 kg/m3

B. 37.6 kg/m3

C. 0.0376 kg/m3

D. 1.46 103 kg/m315. A breather. What is the product of the volume and the pressure of 13 moles of an ideal

gas at 37C?

A. 3.4 104 JB. 4.0 103 JC. 39 J

D. 330 J

Hour 7

16. Vrms. A rigid vessel contains some amount of ideal gas. The density and pressure of thegas was determined to be = 1 kg/m3 and P = 1 Pa, respectively. What is the vrms of themolecules of the gas?

A. 1.50 m/s

B. 1.73 m/s

C. 1.41 m/s

D. 1.00 m/s

A 6


17. Kinetic Molecular Theory. Which of the following is/are part of the assumptions of theKinetic Molecular Theory of an ideal gas?

I The volume contains a large number of particles.

II The particles behave like point particles.

III The particle collisions are inelastic.

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

18. Nitro. In a nitrogen gas with temperature T, 94.7% of N2molecules have speeds less than 1000 m/s. The temperature isthen increased four-folds. What fraction of molecules now havespeeds less than 1000 m/s?

A. 1.1%

B. 41.1%

C. 88.2%

D. 99.3%

Hour 8

19. Noble Gases. Helium gas, neon gas, and argon gas were put in three separate identicalvessels. Each of these vessels contain the same amount of these monatomic gases. Whichof the gases would need to absorb the greatest amount of heat in order for their temperaturesto increase by the same amount?

A. Helium gas

B. Neon gas

C. Argon gas

D. They all need an equal amount of heat

A 7


20. Matter Phases. Which one of the following statements about the phases of matter is true?A. The liquid phase cannot exist for temperatures higher than the triple point tem-

perature for any given pressure.

B. The gas and liquid phases are indistinguishable beyond the critical point.

C. There is no combination of pressure and temperature where the three phases ofmatter are in phase equilibrium.

D. A solid can undergo sublimation by increasing its temperature at a constant pres-sure higher than the triple point pressure.

21. Graphene. Graphene is a two-dimensional solid made up of Carbon atoms. What is itsconstant-volume heat capacity according to equipartition theorem?

A. 3R

B. 32R

C. 2R

D. 52R

Hour 9

22. Compressed Gas. Some n moles of ideal gas was put inside a cylinder with a movablepiston. Initially, the temperature, pressure, and volume of the gas were determined to beT0, P0, and V0, respectively. The gas was then compressed to a final temperature, pressure,and volume of Tf , Pf , and Vf , respectively. The process traces out a straight line in thePV diagram. What is the work done by the gas? (P0 < Pf , Tf > T0, Vf < V0)

A. nRT0ln(P0/Pf)

B. nRTf ln(Vf/V0)

C. Pf(Vf V0)D. (P0 + Pf)(Vf V0)/2

23. Work Gas. What type of process involves no work done by the gas?

A. isochoric

B. isobaric

C. isothermal

D. cyclic

A 8


Hour 10

24. Isobaric Expansion. An ideal gas expands isobarically. What is true about the heat flowQ, and the work done W ?

A. Heat flows out the gas and work is done on the gas.B. Heat flows out the gas and work is done by the gas.C. Heat flows into the gas and work is done on the gas.D. Heat flows into the gas and work is done by the gas.

25. Delta U. Which of the following statements about the change in internal energy U of asystem consisting of an ideal gas is/are true? (Q = heat added to the system, W = workdone by the system)

I. For a cyclic process, U = 0 since Q = 0 and W = 0II. For an isothermal process, U = 0, and Q = W

III. For an isochoric process, U = WA. I onlyB. II onlyC. III onlyD. I and II only

Hour 11

26. Internal Energy. Some n moles of an ideal gas, initially with pressure P0 and volume V0,was allowed to undergo a thermodynamic process tracing a straight line in the PV diagramup to some final pressure 2P0 and volume V0/2. What is the change in internal energy ofthe ideal gas? Denote the molar heat capacity at constant volume of the ideal gas by CV .

A. 2CVP0V0/RB. P0V0/2C. nRln(2)D. zero

A 9


27. Ideal Gas. Which of the statements are TRUE about an ideal gas?

I The change in internal energy of an adiabatic process is always zero

II The change in internal energy of an isothermal process is zero

III If the temperature change is the same, then the change in internal energy is greater inan isochoric process than in an isobaric process.

IV For a cyclic process, the change in internal energy is always zero

A. I, II, and IV only

B. I and IV only

C. I and II only

D. II and IV only

Hour 12

28. Diesel Efficiency. A diesel engine performs 3500 J of mechanical work and discards1000 J of heat each cycle. What is the thermal efficiency of the engine?

A. 22 %

B. 28 %

C. 78 %

D. 350 %

29. Otto Efficiency. What is the theoretical efficiency for an Otto cycle engine with = 1.45and r = 9.50.

A. 36 %

B. 55 %

C. 64 %

D. 96 %

30. Eternal Flame. A perpetual engine generates enough work to power itself and provideenergy for other uses. Which of law/s of thermodynamics is/are violated?

A. 1st Law of Thermodynamics

B. 2nd Law of Thermodynamics

C. Both 1st and 2nd Law of Thermodynamics

D. No law is violated

A 10


Hour 13

31. Power Ref. A refrigerator has a coefficient of performance of 3.5. If it uses 200. W ofelectrical power, how much heat is delivered to the hot reservoir in one second?

A. 57 J

B. 200 J

C. 700 J

D. 900 J

32. Reverse Psychology. A heat engine has an efficiency of 25%. If it is to be run in reverseas a refrigerator, what is the corresponding coefficient of performance?

A. 0.75

B. 1.33

C. 3.00

D. 4.00

33. The More the Merrier. A heat engine has an efficiency of 25%. A refrigerator with coef-ficient of performance 4 is used in conjunction with this heat engine to increase efficiency.What is the resulting efficiency of the combination if 40% of the work done by the heatengine is used to power the refrigerator?

A. 0.300

B. 0.450

C. 0.500

D. 0.625

A 11


Hour 14

34. ERM. In the ERM shown, TH > TC . Which of the process shown violates the 2nd Law ofthermodynamics?

A. I only

B. II and III only

C. I and III only

D. I, II and III

Hour 15

35. No Undo. Which of the following is/are irreversible process/es?

I. Adiabatic free expansion of an ideal gas.

II. A body sliding to rest because of friction.

III. Two gases mixing in the same container.

A. I only B. II only C. III only D. I, II and III

A 12


36. The Perfect Steam. A steam engine works between a hot reservoir at 373 K and a coldreservoir at 273 K. What is the maximum possible work that it can do if 200 J of energy isextracted from the hot reservoir?

A. 53.6 J

B. 73.3 J

C. 146.4 J

D. 273.0 J

37. Tea Time. You make tea with 0.250 kg of 85.0 C water and let it to cool to 20.0 C beforedrinking it. Calculate the entropy change of the water while it cools.

A. -0.210 kJKB. -1.52 kJK

C. 1.52 kJKD. 0.210 kJK

Hour 16

38. If I Lose Myself. A glass filled with 0.500 kg ice initially at 0 C is allowed to completelymelt and reach the room temperature 20 C. Assuming during this process, the room doesnot change its temperature, what is the total change of entropy of the room and the ice?

A. 46.8 J/K

B. 463.3 J/K

C. 759.4 J/K

D. 1472 J/K

39. Clarity. Two cars weighing 2000 kg and moving at 30 m/s undergoes a head on inelasticcollision. The temperature of the cars, ground, and the environment is 293K and does notchange during the process. What is the change of entropy of the universe?

A. Zero

B. 205 J/K

C. 3072 J/K

D. 6143 J/K

Hour 17

40. Triple. The number of microstates of a gas is proportional to V3, where V is the volumethat the gas occupies. What is the change in entropy per molecule of the gas if the volumeit occupies is tripled?

A. 3k ln (2) B. 2k ln (3) C. k ln (3) D. 3k ln (3)

A 13

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Physics73_PS1