Lecture Notes on Helium and Cryogenics

Overview of Previous Lecture

• Discussed hydrogen, ortho and para forms and conversion of hydrogen.
• Introduced helium and its phase diagram.
• Explored superfluidity of helium, particularly superfluid helium.

Today's Lecture Content

• Uses of Helium-4
• Thermal Effects of Helium Gas
  • Thermomechanical Effect
  • Mechanocaloric Effect
  • Fountain Effect
  • Rolling Film Effect
• Sound Propagation in Superfluid Helium
• Helium-3 Isotope
• Phase Diagram of Helium-3
• Summary of Cryogens

Review of Helium-4 Phase Diagram

• Phases: vapor, liquid, solid
• No triple point; phases do not coexist.
• Helium-I and Helium-II:
  • Helium-I transitions to Helium-II below lambda point (2.17 K).
  • Helium-II exhibits zero viscosity and high thermal conductivity.
• Kapitza's statement: Viscosity independent of pressure drop, function of temperature.

Utility of Helium-4

• Superconducting magnets submerged in liquid helium for NMR and MRI applications.
  • NMR: Used in pharmaceutical labs for molecular structure analysis.
  • MRI: Used for medical imaging, requires high magnetic fields.
• Cryocoolers: Close cycle coolers using helium gas to achieve low temperatures.
• Superconducting magnets at CERN (1.9 K) and ITER project (4 K) utilize helium-4 for cooling.

Other Uses of Helium

• Leak detection systems due to helium's thin gas properties.
• Shielding gas in arc welding to provide an inert atmosphere.

Properties of Superfluid Helium-II

• Exhibits unique thermal and mechanical effects.
  • Thermomechanical Effect: Heat induces flow of superfluid to equalize concentrations.
  • Mechanocaloric Effect: Mechanical action creates a temperature difference.
  • Fountain Effect: Heat application causes superfluid to flow and create a fountain effect.
  • Rolling Film Effect: Superfluid clings to walls and flows against gravity.

Sound Propagation in Helium

• First Sound: Ordinary sound in superfluid helium-I and helium-II.
• Second Sound: Oscillation of normal fluid (helium-I) and superfluid (helium-II) due to temperature gradient.
• Third Sound: Oscillation in thin films of superfluid helium-II.
• Zero Sound: Recent research indicator in superfluid helium.

Helium-3 Isotope

• Non-radioactive; boiling point: 3.19 K.
• Properties: critical pressure 0.117 MPa; very rare in nature.
• Phase diagram: No triple point; must be compressed to solidify.
• Helium-3 is utilized in dilution refrigerators for achieving low temperatures.

Phase Diagram of Helium-3

• Similar to helium-4, no coexistence of phases; must compress to solidify.
• Exhibits superfluid transition near 3.2 mK.

Mixture of Helium-3 and Helium-4

• Lambda point decreases with increased helium-3 concentration.
• Below 0.8 K: phase separation occurs; superfluid helium-II and normal helium-3 exist separately.
• Tricritical point (TCP): Intersection of lambda line with phase separation region at 0.872 K and 0.669 mole fraction of helium-3.

Summary of Cryogenics

• Discussed various cryogens, their properties, and applications.
• Emphasis on understanding T-s diagrams for problem-solving related to liquefiers and refrigeration.
• Importance of helium-4 and helium-3 in cryogenics, notably for NMR, MRI, and dilution refrigerators.

Self-Assessment Exercise

• Encouragement to assess understanding of lecture content and solve problems provided.