- 1. What did Nernst's early non-quantitative description state about the specific heat of a material at very low temperatures?
A) It diverges to infinity as absolute zero is approached.
B) It can always be made zero by cooling it down far enough.
C) It approaches a positive constant value asymptotically.
D) It remains strictly constant regardless of cooling.
- 2. What type of function is assumed for the heat capacity of a sample in the low temperature region in the text's quantitative analysis?
A) A power law
B) A logarithmic function
C) A linear function with a positive intercept
D) An exponential function
- 3. For a power-law heat capacity to be compatible with the third law, what condition must the exponent alpha satisfy?
A) Alpha must be greater than zero
B) Alpha must be equal to zero
C) Alpha must be less than zero
D) Alpha must be equal to one
- 4. What must happen to the heat capacity at absolute zero if it follows a power law?
A) It must equal the molar ideal gas constant
B) It must remain at a constant positive value
C) It must go to zero
D) It must approach infinity
- 5. Can the heat capacity be bounded below by a positive constant according to the third law?
A) Yes, for monatomic classical ideal gases
B) No, even without the power-law assumption
C) Only if Fermi-Dirac statistics apply
D) Yes, provided the temperature is strictly above zero
- 6. What is the molar specific heat at constant volume of a monatomic classical ideal gas at room temperature?
A) Five-halves times R
B) R
C) Zero
D) Three-halves times R
- 7. Does a constant heat capacity all the way to absolute zero satisfy the third law of thermodynamics?
A) Only for Fermi gases
B) No, it violates the third law
C) Yes, perfectly
D) Only for Bose gases
- 8. What happens in the limit as T0 approaches zero for an expression using a constant heat capacity?
A) It becomes undefined due to quantum effects
B) It equals the Fermi temperature
C) It converges to zero
D) It diverges
- 9. What physical property of matter starts to dominate behavior at a certain low temperature to resolve the conflict with the third law?
A) The macroscopic pressure gradient
B) The classical trajectory of particles
C) The gravitational constant
D) The quantum nature of matter
- 10. Which statistics do Fermi particles follow?
A) Quantum-Planck statistics
B) Fermi-Dirac statistics
C) Bose-Einstein statistics
D) Classical Maxwell-Boltzmann statistics
- 11. Which statistics do Bose particles follow?
A) Newtonian statistics
B) Fermi-Dirac statistics
C) Maxwell-Boltzmann statistics
D) Bose-Einstein statistics
- 12. What is true about the heat capacity of ideal gases at low temperatures under quantum statistics?
A) It remains strictly constant
B) It drops immediately to zero at room temperature
C) It is no longer temperature independent
D) It becomes independent of the molar volume
- 13. What is the value of alpha for the low-temperature power-law specific heat of Fermi gases?
A) Three-halves
B) Two
C) Zero
D) One
- 14. What is the value of alpha for the low-temperature power-law specific heat of Bose gases?
A) One-half
B) One
C) Three-halves
D) Zero
- 15. What variable represents the Avogadro constant in the Fermi temperature equation?
A) R
B) Vm
C) TF
D) NA
- 16. What does Vm represent in the context of the Fermi temperature equation?
A) Velocity maximum
B) Volume multiplier
C) Vapor mass
D) Molar volume
- 17. What does M represent in the formula for the Fermi temperature?
A) Magnetic field
B) Momentum
C) Molar mass
D) Molality
- 18. What happens to the density of a classical ideal gas at fixed particle number as T goes to zero within a purely classical setting?
A) It oscillates infinitely
B) It remains constant
C) It drops to zero
D) It becomes arbitrarily high
- 19. What happens to the interparticle spacing of a classical ideal gas as T goes to zero?
A) It goes to zero
B) It becomes independent of the volume
C) It goes to infinity
D) It equals the Avogadro constant
- 20. What assumption presumably breaks down when particles are sufficiently close together at very low temperatures?
A) The assumption of quantum dominance
B) The assumption of constant molar mass
C) The assumption of non-interacting particles
D) The assumption of Fermi-Dirac statistics
- 21. What does the entropy of a closed system at thermodynamic equilibrium approach as its temperature approaches absolute zero?
A) Zero
B) Infinity
C) Maximum pressure
D) A constant value
- 22. Parameters such as pressure or applied magnetic field cannot affect what aspect of a system at absolute zero?
A) The volume
B) The mass
C) The constant entropy value
D) The internal energy
- 23. In what state must a system be at absolute zero (zero kelvin)?
A) Maximum possible energy
B) Minimum possible energy
C) Glassy order state
D) High entropy state
- 24. Entropy is related to the number of accessible what?
A) Macrostates
B) Dimensions
C) Molecules
D) Microstates
- 25. What is the unique state with minimum energy typically called?
A) Zero state
B) Ground state
C) Excited state
D) Glassy state
- 26. What might remain if a system does not have a well-defined order, such as a glassy order, as it is brought to very low temperatures?
A) Zero energy
B) Finite entropy
C) Zero entropy
D) Infinite temperature
- 27. What is the constant entropy value remaining at absolute zero called when the minimum energy state is non-unique?
A) Ground entropy
B) Thermal entropy
C) Zero-point heat
D) Residual entropy
- 28. Which statement applies only to perfect crystalline substances?
A) Nernst statement
B) Planck statement
C) Einstein statement
D) Unattainability principle
- 29. According to the Planck statement, as temperature falls to zero, the entropy of any pure crystalline substance tends to what?
A) A variable pressure
B) A universal constant
C) Infinity
D) Zero-point heat capacity
- 30. Which of the following are considered condensed systems in the context of the Nernst statement?
A) Photons and waves
B) Gases and plasma
C) Vapors and vacuum
D) Liquids and solids
- 31. According to the Einstein statement, the entropy of any substance approaches what as temperature approaches absolute zero?
A) Zero
B) A finite value
C) Infinity
D) A negative value
- 32. What term is used for the finite-valued entropy at absolute zero in the Einstein statement?
A) Zero-point entropy
B) Ground energy
C) Thermal capacity
D) Residual pressure
- 33. Why must the heat capacity vanish at absolute zero according to the text?
A) Otherwise the entropy integral would diverge
B) Otherwise the pressure would drop to zero
C) Otherwise the system would melt
D) Otherwise the temperature would become negative
- 34. Who developed the third law of thermodynamics between the years 1906 and 1912?
A) Francis Simon
B) Walther Nernst
C) Gilbert N. Lewis
D) Merle Randall
- 35. What is another name for the third law of thermodynamics based on its developer?
A) Lewis-Randall theorem
B) Carnot theorem
C) Boltzmann principle
D) Nernst heat theorem
- 36. Who contributed to the theorem alongside Nernst, leading to the name Nernst-Simon heat theorem?
A) Merle Randall
B) Ludwig Boltzmann
C) Gilbert N. Lewis
D) Francis Simon
- 37. What kind of crystal leaves no ambiguity as to the location and orientation of each part?
A) An amorphous crystal
B) A fractured crystal
C) A perfect crystal
D) A liquid crystal
- 38. What mathematical function is used with the number of ground states to find absolute entropy at zero temperature?
A) Exponential
B) Square root
C) Sine
D) Natural log
- 39. How many unique atoms interact and absorb the incoming photon?
A) Half of the atoms
B) A unique single atom
C) All atoms
D) Two atoms
- 40. What is the formula used for entropy change based on the number of microstates Ω?
A) k_B ln(Ω)
B) k_B / ln(Ω)
C) Ω / k_B
D) ln(k_B Ω)
- 41. According to the second law of thermodynamics, ΔS equals which of the following ratios?
A) δQ / T
B) ε / N
C) h c / λ
D) T / δQ
- 42. What characterizes the temperature and entropy change calculated in the example?
A) Only the incoming photon
B) The surrounding environment
C) The entire system
D) Only the single excited atom
- 43. What is the state of ground-state helium under normal conditions?
A) Solid
B) Liquid
C) Gas
D) Glass
- 44. Which solid is mentioned as having 'proton disorder' and many nearly-degenerate ground states?
A) Solid helium
B) Ice Ih
C) Spin glass
D) Paramagnetic salt
- 45. In magnetic refrigeration, what does the parameter X represent?
A) External magnetic field
B) Entropy
C) Temperature
D) Mass of the system
- 46. At what temperature below which is the vapor pressure so low that no gas exists above the liquid?
A) 100 mK
B) 273 K
C) 0.9 K
D) 0 K
- 47. What is the vapor pressure below 100 mK according to the text?
A) 1×10−3 mmHg
B) 0 mmHg
C) 1013 mmHg
D) 10×10−31 mmHg
- 48. What does the upper layer become when a 3He and 4He solution is cooled to absolute zero?
A) Purely 4He
B) Purely 3He
C) A mixed solution
D) A solid phase
- 49. What does the lower layer become when a 3He and 4He solution is cooled to absolute zero?
A) Purely 4He
B) A supercritical fluid
C) Purely 3He
D) A gaseous phase
- 50. If sigma represents surface tension, what is the entropy per area?
A) dσ/dT
B) -dσ/dT
C) σ/T
D) -T/σ
- 51. According to the third law, what are the entropies of the solid and liquid at T = 0?
A) Equal
B) Zero
C) Infinite
D) Different
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