- 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) An exponential function
B) A power law
C) A logarithmic function
D) A linear function with a positive intercept
- 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 less than zero
C) Alpha must be equal to one
D) Alpha must be equal to 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 approach infinity
D) It must go to zero
- 5. Can the heat capacity be bounded below by a positive constant according to the third law?
A) No, even without the power-law assumption
B) Yes, provided the temperature is strictly above zero
C) Only if Fermi-Dirac statistics apply
D) Yes, for monatomic classical ideal gases
- 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) Three-halves times R
D) Zero
- 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 diverges
B) It becomes undefined due to quantum effects
C) It equals the Fermi temperature
D) It converges to zero
- 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 quantum nature of matter
B) The macroscopic pressure gradient
C) The gravitational constant
D) The classical trajectory of particles
- 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) Bose-Einstein statistics
B) Newtonian statistics
C) Maxwell-Boltzmann statistics
D) Fermi-Dirac statistics
- 12. What is true about the heat capacity of ideal gases at low temperatures under quantum statistics?
A) It becomes independent of the molar volume
B) It drops immediately to zero at room temperature
C) It is no longer temperature independent
D) It remains strictly constant
- 13. What is the value of alpha for the low-temperature power-law specific heat of Fermi gases?
A) Two
B) Zero
C) One
D) Three-halves
- 14. What is the value of alpha for the low-temperature power-law specific heat of Bose gases?
A) Three-halves
B) Zero
C) One
D) One-half
- 15. What variable represents the Avogadro constant in the Fermi temperature equation?
A) R
B) NA
C) Vm
D) TF
- 16. What does Vm represent in the context of the Fermi temperature equation?
A) Molar volume
B) Vapor mass
C) Velocity maximum
D) Volume multiplier
- 17. What does M represent in the formula for the Fermi temperature?
A) Molar mass
B) Molality
C) Magnetic field
D) Momentum
- 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 becomes arbitrarily high
B) It drops to zero
C) It oscillates infinitely
D) It remains constant
- 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 infinity
C) It goes to zero
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 non-interacting particles
C) The assumption of Fermi-Dirac statistics
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) A constant value
B) Infinity
C) Zero
D) Maximum pressure
- 22. Parameters such as pressure or applied magnetic field cannot affect what aspect of a system at absolute zero?
A) The volume
B) The internal energy
C) The mass
D) The constant entropy value
- 23. In what state must a system be at absolute zero (zero kelvin)?
A) Maximum possible energy
B) Glassy order state
C) High entropy state
D) Minimum possible energy
- 24. Entropy is related to the number of accessible what?
A) Dimensions
B) Microstates
C) Molecules
D) Macrostates
- 25. What is the unique state with minimum energy typically called?
A) Glassy state
B) Zero state
C) Excited state
D) Ground 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) Infinite temperature
D) Zero entropy
- 27. What is the constant entropy value remaining at absolute zero called when the minimum energy state is non-unique?
A) Ground entropy
B) Residual entropy
C) Zero-point heat
D) Thermal entropy
- 28. Which statement applies only to perfect crystalline substances?
A) Nernst statement
B) Planck statement
C) Unattainability principle
D) Einstein 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) Zero-point heat capacity
D) Infinity
- 30. Which of the following are considered condensed systems in the context of the Nernst statement?
A) Vapors and vacuum
B) Gases and plasma
C) Liquids and solids
D) Photons and waves
- 31. According to the Einstein statement, the entropy of any substance approaches what as temperature approaches absolute zero?
A) A negative value
B) A finite value
C) Zero
D) Infinity
- 32. What term is used for the finite-valued entropy at absolute zero in the Einstein statement?
A) Ground energy
B) Residual pressure
C) Thermal capacity
D) Zero-point entropy
- 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) Gilbert N. Lewis
B) Merle Randall
C) Francis Simon
D) Walther Nernst
- 35. What is another name for the third law of thermodynamics based on its developer?
A) Lewis-Randall theorem
B) Boltzmann principle
C) Nernst heat theorem
D) Carnot theorem
- 36. Who contributed to the theorem alongside Nernst, leading to the name Nernst-Simon heat theorem?
A) Ludwig Boltzmann
B) Merle Randall
C) Francis Simon
D) Gilbert N. Lewis
- 37. What kind of crystal leaves no ambiguity as to the location and orientation of each part?
A) A perfect crystal
B) An amorphous crystal
C) A liquid crystal
D) A fractured crystal
- 38. What mathematical function is used with the number of ground states to find absolute entropy at zero temperature?
A) Natural log
B) Square root
C) Exponential
D) Sine
- 39. How many unique atoms interact and absorb the incoming photon?
A) Half of the atoms
B) All atoms
C) Two atoms
D) A unique single atom
- 40. What is the formula used for entropy change based on the number of microstates Ω?
A) ln(k_B Ω)
B) k_B / ln(Ω)
C) Ω / k_B
D) k_B ln(Ω)
- 41. According to the second law of thermodynamics, ΔS equals which of the following ratios?
A) T / δQ
B) h c / λ
C) δQ / T
D) ε / N
- 42. What characterizes the temperature and entropy change calculated in the example?
A) The entire system
B) Only the single excited atom
C) The surrounding environment
D) Only the incoming photon
- 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) Ice Ih
B) Solid helium
C) Spin glass
D) Paramagnetic salt
- 45. In magnetic refrigeration, what does the parameter X represent?
A) External magnetic field
B) Temperature
C) Mass of the system
D) Entropy
- 46. At what temperature below which is the vapor pressure so low that no gas exists above the liquid?
A) 0 K
B) 100 mK
C) 273 K
D) 0.9 K
- 47. What is the vapor pressure below 100 mK according to the text?
A) 0 mmHg
B) 1013 mmHg
C) 1×10−3 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 solid phase
B) Purely 3He
C) A mixed solution
D) Purely 4He
- 49. What does the lower layer become when a 3He and 4He solution is cooled to absolute zero?
A) A supercritical fluid
B) Purely 3He
C) A gaseous phase
D) Purely 4He
- 50. If sigma represents surface tension, what is the entropy per area?
A) -T/σ
B) σ/T
C) -dσ/dT
D) dσ/dT
- 51. According to the third law, what are the entropies of the solid and liquid at T = 0?
A) Different
B) Infinite
C) Zero
D) Equal
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