University of the PhilippinesCollege of Science

PHYSICS 731st Long Problem Set

1st semesterAY 2010 - 2011

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 = 1.01105 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

Lecture Hour 2

1. Which of the following principles justifies the use of thermometers?a. zeroth law of thermodynamicsb. first law of thermodynamicsc. second law of thermodynamicsd. third law of thermodynamicse. fourth law of thermodynamics

2. 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____________

A. the pressure exerted by the gasB. the volume of the gasC. the number of moles of gasD. the number of molecules of gasE. the density of the gas.

3. The Rankine temperature scale has the same zero as the Kelvin scale but the divisions are the same as the Fahrenheit scale. If the temperature change between morning and noon is 5.0°C, what is the temperature change in degrees Rankine?A. 9.0B. 2.8C. 500.D. 494E. none of the above

Lecture Hour 3

4. The coefficient of linear expansion of a solid material is found to be 2.4 x 10-5 K-1. If the temperature of this material is raised by 47C0, what is the change in its volume if it initially has a volume of 17 cubic centimetres?a. 0.019 ccb. 0.058 ccc. 0.000072 ccd. 0.0034 cce. not enough information

5. A 1000.00 cm3 glass container is completely filled with mercury at 273.15 K. The system is then heated to 328.15 K and 8.95 cm3 of mercury overflow. Given that the coefficient of volume expansion of mercury is 18.0 x 10-5 K-1, find the coefficient of volume expansion of glass.a. 1.7 x 10-5 K-1

b. 2.7 x 10-5 K-1

c. 3.7 x 10-5 K-1

d. 4.7 x 10-5 K-1

e. 5.7 x 10-5 K-1

6. It is known that the fractional changes in length, area and volume are proportional to the change in temperature; that is ΔL/L=α ΔT, ΔA/A= η ΔT, ΔV/V = βΔT. Which of the following is true(i) α = 2 η(ii) 2α = η(iii) 1.5 α = β(iv) β = 2α(v) β = 3α(vi) 3α = η

A. (i) and (iv)B. (i) and (v)C. (ii) and (vi)D. (ii) and (v)E. (i) and (vi)

Lecture Hour 4

7. 10 kg of ice at 0 °C is mixed with 15 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? Lv(water)=2256 x 103 J/(kg K)A. 689 ºCB. 100 ºCC. 167 °C D. 7.14 ºCE. 0.00° C

8. Silver has a melting point of 1234 K, a specific heat of 234 J/kg K and a heat of fusion 88.3 x 103 J/K, while Gold has a melting point of 1336 K, a specific heat of 126 J/kg K and a heat of fusion 64.5 x 103 J/K. If 3.0 kg of gold and silver are initially at a temperature of 298.15 K, which metal will require more heat to melt, and how much heat is required to melt that metal?

a. Gold, with an amount of heat of 9.21 x 105 Jb. Silver, with an amount of heat of 9.21 x 105 Jc. Both will require an equal amount of heat of 3.92 x 105 Jd. Gold, with an amount of heat of 5.86 x 105 J

e. Silver, with an amount of heat of 5.86 x 105 J

Lecture Hour 5

9. Consider heat conducted through two different types of materials. Which of the following statements is true?a. If heat flows through the materials in series, then the total heat current is additive.b. Heat transfer via radiation always takes place through some medium.c. The heat current is the same regardless if the materials are connected in series or not.d. A good absorber of radiation must also be a good emitter of radiation.e. No actual motion of fluid is involved in convection.

10. One end of an insulated metal rod is maintained at 1000C, and the other end is maintained at 00C by an ice-water mixture. The rod is 60.0 cm long and has a cross-sectional area of 1.25 cm2. The heat conducted by the rod melts 8.50g of ice in 10min. Find the thermal conductivity k of the metal. a. 227 W/m Kb.158 W/m Kc. 349 W/m Kd. 251 W/m Ke. 0.0227 W/(m K)

Lecture Hour 6

11. It was experimentally determined that the pressure of system is directly proportional to its volume and inversely proportional to the square of its temperature. Which of the following is a possible equation of state for the system?a. pV = cTb. pV = cT2

c. pT2 = cVd. p/T2 = cVe. p = cV/T

12. Which of the following is NOT a state variable?A. WorkB. Internal energyC. EntropyD. TemperatureE. Pressure

Lecture Hour 7

13. A room with dimensions 7.00 m X 8.00 m X 2.50 m is filled with pure oxygen at 22.0 °C and pressure 1.00 atm. How many moles of oxygen is in the room?

A. 5.78 x 103 molesB. 7.75 x 104 molesC. 5.71 x 102 molesD. 0.765 molesE. 765 moles

14. A welder using a tank of 0.750 m3 fills it with oxygen gas (molar mass=32.0 g/mol) at a gauge pressure of 3.00 x 105 Pa and temperature of 37.0 °C. What is the mass of the oxygen in the tank?

1 atmosphere = 1.01105 PascalA. 2.34 x 104 gB. 2.79 x 103 gC. 3.13 x 104 gD. 57.9 gE. 3.73 x 103 g

15. An ideal gas has a temperature of 383.15 K, while its pressure is 2.02 x 105 Pa. If the molecules of this ideal gas are spheres with a radius of 5.0 x 10-12 m, what would be the mean free path of the molecules of this ideal gas?

a. 16.4 mb. 8.34 x 10-5 mc. 5.90 x 10-5 md. 2.95 x 10-16 me. 1.85 x 104 m

Lecture Hour 8

16. According to the kinetic theory of gases, which of the following assumptions is not valid?

a. The gas contains a very large number of molecules N inside a container of volume V.b. The molecules are assumed to have a finite dimension, with a finite radius.c. The molecules are governed by Newton's laws of motion.d. Any collisions made by the molecule with the container walls is perfectly elastic.e. The container walls are infinitely massive, perfectly rigid and do not move.

17. A gas made of He molecules satisfies the Maxwell-Boltzmann distribution. The temperature of the gas is 500 K; and the molar mass of He is 4.003 g/mole. What is the root-mean-square speed?A. 5.55 m/sB. 2.50 m/sC. 55.8 m/sD. 1.77 x 103 m/sE. 175 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 0.8821.60 0.9471.80 0.9792.00 0.993

18. A gas made of He molecules (a monatomic gas) 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 1.062 x 103 m/s?A. 0.011

B. 0.077C. 0.218D. 0.411E. 0.608

Lecture Hour 9

19. Consider the phase diagram of water. At the triple point of the phase diagram, which of the following phases of water will exist?

a. Liquid Waterb. Icec. Water Vapord. Ice and Liquid Watere. Ice, Water Vapor and Liquid Water

20. Assume that a molecule of an ideal gas has three translational, three rotational and two vibrational degrees of freedom. If the equipartition law is valid for this molecule, what would be the specific heat capacity at constant volume of this ideal gas?

a. 8.314 J/mol Kb. 12.47 J/mol Kc. 20.79 J/mol Kd. 33.26 J/mol Ke. 24.94 J/mol K

21. Heating at constant pressure. How much heat in Joules is needed to heat 2.00 moles of hydrogen gas (a diatomic gas) so that its temperature is increased from 20 to 100 C, while keeping the pressure constant? Assume that the heat capacity at constant volume of hydrogen is well-approximated by the equipartition theorem.A. 2.00 kJB. 19.7 JC. 4.66 kJD. 2.49 kJE. 9.31 kJ

Lecture Hour 10

22. Consider 7.25 mol of an ideal gas which is expanding isothermally, causing its pressure to drop by half. If the temperature of the ideal gas during the expansion is 300.15 K, how much work is done by the ideal gas as it expands?

a. 1.25 x 104 Jb. -1.25 x 104 Jc. 2.50 x 104 Jd. -2.50 x 104 Je. 0 J

23. 2.00 moles of an ideal diatomic gas (γ=1.40) undergoes a constant pressure expansion. Its initial volume, pressure and temperature is 1.0 m3, 4.99 kPa and 300 K respectively. If its final volume is 3.0 m3, what is the work done by the gas? A. 9.98 kJB. 24.9 kJ

C. 6.88 kJD. 5.48 kJE. 0.18 J

24. 2.0 moles of an ideal diatomic gas (γ=1.40) undergoes a constant temperature expansion. Its initial volume, pressure and temperature is 1.0 m3, 4.99 kPa and 300 K respectively. If its final volume is 3.0 m3, what is the work done by the gas? A. 9.98 kJB. 24.9 kJC. 6.88 kJD. 5.48 kJE. 0.18 J

Lecture Hour 11

25. Which of the following relations will hold for an ideal gas undergoing an adiabatic process?

a. ΔU = 0b. W = 0c. Q = 0d. ΔU = Q > 0e. W = P(V2-V1)

26. Thermodynamic Processes. In an isobaric process, which of the following quantities remains constant in value?

a. Volumeb. Temperaturec. Internal Energyd. Pressuree. Entropy

27. In a certain chemical process, a lab technician supplies 254 kJ of heat to a system, and at the same time, the system does 73 kJ of work on the surroundings. What is the change in internal energy of the system?A. 181 kJB. 327 kJC. -181 kJD. -327 kJE. none of the above

Lecture Hour 12

28. Consider 6.75 mol of a diatomic ideal gas whose temperature increases from 298.15 K to 323.15 K. If the volume of this ideal gas remains constant, what would be the change in its internal energy?

a. 0 Jb. 1403.0 Jc. 4209.0 Jd. 2014.5 Je. 3507.5 J

29. 9.50 mol of a monatomic ideal gas expands adiabatically, in the process causing its temperature to drop from 450.5 K to 380.5 K. What would be the change in internal energy of this ideal gas?

a. -8293 Jb. 8293 Jc. 13820 Jd. -13820 Je. 5529 J

30. Change in Internal Energy for an Ideal Gas. What is the change in the internal energy of 30.0 mol of Oxygen (a diatomic gas) if its temperature changes from 290.15 K to 360.15 K?

a. 4.80 x 103 Jb. 5.24 x 104 Jc. 1.75 x 104 Jd. 2.62 x 104 Je. 4.36 x 104 J

Lecture Hour 13

31. What is the efficiency of an engine that discards 5500 J of heat per cycle to perform 2600 J of work?a. 32%b. 47%c. 68%d. 3.1%e. None of the above

32. How much heat does an internal combustion engine discard if it takes in 10 kJ of heat from burning its fuel and if it has r =9.50 and γ = 1.40?a. 4063.6 Jb. 133 kJc. 1052.6 Jd. 5936.4 Je. not enough information

33. Engine Cycles. What would be the efficiency of a heat engine which obeys the Otto cycle (r = 9) and uses as its working substance Helium (γ = 1.67)?

a. 97%b. 77%c. 57%d. 87%e. 67%

Lecture Hour 14

34. What is the coefficient of performance of a refrigerator operating as a Carnot engine between 5.0 oC and 25oC?

a. 0.25b. 0.068c. 15

d. 14e. 5

35. A refrigerator absorbs 5.00 kJ of energy from a freezer and rejects 8.00 kJ into the environment. Find the coefficient of performance of the refrigerator.

a. 1.67b. 0.6c. 0.375d. 2.67e. 0.63

36. REFRIGERATOR. Due to the summer heat, you want to make your room as cool as possible. You don’t own an air conditioning unit but an “ingenious” idea pops on your head: keep all doors and windows closed, set your refrigerator at the lowest temperature setting and keep its door open. Recalling your Physics 73 lessons you realize that this won’t work because:

a. Your refrigerator cannot generate enough coolness.b. The temperature difference between your room and refrigerator is very large.c. The refrigerator takes heat from the room but throws a larger amount right back at the room.d. The power needed to cool your way through this method is very large.e. The temperature difference between your room and refrigerator is not large enough.

Lecture Hour 1637. A Carnot heat engine's heat reservoir is at a temperature of 501°C, while its cold reservoir is at a temperature of 25.0 °C. What is the thermal efficiency of this engine?

a. 0.655b. 1.60c. 19.04d. 0.950e. 0.615

38. A Carnot engine works between two heat reservoirs at temperatures TH = 300 K and TC = 77 K. If it absorbs 150 J of energy from the hot reservoir for each cycle, how much work does it do?a. 38.5 Jb. 111.5 Jc. 74.3 Jd. 25.7 Je. 51.8 J

39. A Carnot engine takes in steam at 2700C and discharges condensed steam at 500C. If the useful power output of the engine is 100 kW, how much heat does it release to the surroundings in 1h?a. 8.89 x 109 Jb. 3.60 x 108 Jc. 3.31 x 107 Jd. 2.19 x 106 Je. not enough information

40. An engine operates between 200K and 100 K. In each cycle it takes 100 J from the hot reservoir, loses 25 J to the cold reservoir, and does 75 J of work. This engine violates:A. both the first and second laws of thermodynamicsB. the first law but not the second law of thermodynamics

C. the second law but not the first law of thermodynamicsD. neither the first law nor the second law of thermodynamicsE. cannot answer without knowing the mechanical equivalent of heat

Lecture Hour 17

41. Rank, from smallest to largest, the changes in entropy of a pan of water on a hot plate, as the tem-perature of the water

1. goes from 20◦ C to 30◦ C2. goes from 30◦ C to 40◦ C3. goes from 40◦ C to 45◦ C4. goes from 80◦ C to 85◦ C

A. 1, 2, 3, 4B. 4, 3, 2, 1C. 1 and 2 tie, then 3 and 4 tieD. 3 and 4 tie, then 1 and 2 tieE. 4, 3, 2, 1

Lecture Hour18

42. Three moles of an ideal gas occupy a volume V. The gas undergoes a free expansion to a volume 6V. What is the change in entropy of the gas? A. 17.3 J/KB. 27.4 J/KC. 44.7 J/KD. 100.1 J/KE. 149.6 J/K

43. Consider N molecules of an ideal gas which occupies a volume V. The gas then expands to a volume 2V. Suppose there are three possible ways for this expansion to occur:(i) adiabatic reversible(ii) adiabatic irreversible(iii) isothermal reversible(iv) isobaric reversibleWhich of the above processes will yield the largest change in entropy?a. (iv)b. (iii)c. (ii)d. (i)e. all of the above have the same change in entropy

44. Let k be the Boltzmann constant. If the thermodynamic state of a gas at temperature Tchanges isothermally and reversibly to a state with three times the number of microstates asinitially, the heat input to the gas is:A. Q = 0B. Q = 3kTC. Q = −3kTD. kT ln 3E. −kT ln 3

45. An isothermal process for an ideal gas is represented on a P-V diagram by:A. a horizontal lineB. a vertical lineC. a portion of an ellipseD. a portion of a parabolaE. a portion of a hyperbola

END OF EXAM