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