Cryogenic Engineering

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2017 Fall Semester

Cryogenic Engineering

Kim, Min Soo

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Chapter 2.

LOW TEMPERATURE PROPERTIES OF

ENGINEEING MATERIALS

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2.1 Introduction

Stress-strain curve at room temperature Stress-strain curve for cooper alloy at low temperature

Extrapolation for material properties at very low temperature is not exact !!

 Vanishing of specific heat

 Superconductivity phenomenon

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2.2 Ultimate and yield strength

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2.2 Ultimate and yield strength

Torpid vibration at low temperature Diatomic molecule

Diatomic molecule

Vigorous vibration at room temperature

As temperature is lowered, atoms of the material vibrate less rigorously,

a larger applied stress is required to tear

dislocations from their atmosphere of

alloying atoms.

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2.3 Impact Strength

The Charpy and the Izod impact tests

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2.3.1 Lattice Structure

(1) 2024-T4 aluminum; (2) beryllium copper; (3) K Monel; (4) titanium;

(5) 304 stainless steel; (6) C1020 carbon steel; (7) 9 percent Ni steel (Durham et al. 1962)

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2.3.1 Lattice Structure

BCC (Body-Centered Cubic) vs FCC (Face-Centered Cubic)

Copper-Nickel alloy Aluminum alloy Stainless steel Zirconium Titanium

Ductile Iron Carbon alloy

Molybdenum Zinc Most plastics

Brittle

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2.4 Hardness and ductility

Hardness is a measure of how resistant solid matter is to various kinds of

permanent shape change when a compressive force is applied. Some materials, such as metal, are harder than others. Macroscopic hardness is generally

characterized by strong intermolecular bonds, but the behavior of solid materials under force is complex; therefore, there are different measurements of hardness:

scratch hardness, indentation hardness, and rebound hardness.

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2.4 Hardness and ductility

 Scratch hardness

Scratch hardness tests are used to determine the hardness of a material to scratches and abrasion.

Pencil scratch hardness tester Scratch test

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 Indentation hardness

Indentation hardness tests are used in mechanical engineering to determine the hardness of a material to deformation.

Two types of indentation

Indentation hardness tester

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2.4 Hardness and ductility

 Rebound hardness

The Leeb rebound hardness test is one of the four most used methods for testing metal hardness.

Portable rebound hardness

testing machine. Procedure of rebound hardness test

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In materials science, ductility is a solid material's ability to deform under tensile stress; this is often characterized by the material's ability to be stretched into a wire. Malleability , a similar property, is a material's ability to deform under

compressive stress; this is often characterized by the material's ability to form a thin sheet by hammering or rolling.

Ductility test and measurement

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2.4 Hardness and ductility

Tensile test of an AlMgSi alloy. The local necking and the cup and cone fracture surfaces are typical for ductile metals.

This tensile test of a nodular cast iron

demonstrates low ductility.

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Gold leaf can be produced owing to gold's malleability.

Schematic appearance of round metal bars after tensile testing.

(a) Brittle fracture (b) Ductile fracture

(c) Completely ductile fracture

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2.4 Hardness and ductility

 Ductile–brittle transition temperature

At low temperatures some metals that would be ductile at room temperature become brittle. This is known as a ductile to brittle transition.

Brittle and ductile failure of steel, at low and high temperature respectively.

Brittle and ductile failure mechanisms, for silica and aluminium respectively. Image credits

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2.4 Hardness and ductility

 Stress-strain diagrams for typical brittle and ductile materials

Brittle materials Ductile materials

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2.5 Elastic modulus

"Young's modulus" or modulus of elasticity, is a number that measures an

object or substance's resistance to being deformed elastically (i.e., non-

permanently) when a force is applied to it.

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2.5 Elastic modulus

 Young’s modulus, E

Young's modulus

(slope of a stress-strain curve)

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2.5 Elastic modulus

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2.5 Elastic modulus

Young’s Modulus - Density Materials Selection

Chart, showing the classes of materials

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2.5 Elastic modulus

 Shear modulus, G

In materials science, shear modulus or modulus of rigidity, denoted by G, or

sometimes S or μ, is defined as the ratio of shear stress to the shear strain.

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2.5 Elastic modulus

 Shear modulus, G

Shear frame for evaluation of the in-plane

shear modulus and strength of FRP

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2.5 Elastic modulus

 Bulk modulus, B

The bulk modulus (K or B) of a substance measures the substance's resistance to uniform compression. It is defined as the ratio of the infinitesimal pressure increase to the resulting relative decrease of the volume.

where ρ is density and dP/dρ denotes the derivative of pressure with respect to

density. The inverse of the bulk modulus gives a substance's compressibility.

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2.5 Elastic modulus

 Bulk modulus, B

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Refrigeration System & Control Laboratory , Seoul National University

2.5 Elastic modulus

 Relations between elastic modulus

For homogeneous isotropic materials simple relations exist between elastic constants (Young's modulus E, shear modulus G, bulk modulus K, and

Poisson's ratio ν) that allow calculating them all as long as two are known

𝑬𝑬 = 𝟐𝟐𝟐𝟐 𝟏𝟏 + 𝝂𝝂 = 𝟑𝟑𝟑𝟑(𝟏𝟏 − 𝟐𝟐𝝂𝝂)

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2.6 Thermal conductivity

k

_𝑡𝑡

: Heat-transfer rate per unit area divided by the temperature gradient

𝑞𝑞 = −k 𝑡𝑡 𝐴𝐴 𝑑𝑑𝑇𝑇

<Fourier’s law> 𝑑𝑑𝑑𝑑 k 𝑡𝑡 = 𝑊𝑊

𝑚𝑚 · 𝐾𝐾

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Refrigeration System & Control Laboratory , Seoul National University

2.6 Thermal conductivity

𝛿𝛿𝑄𝑄 = 𝑑𝑑𝑑𝑑 + 𝛿𝛿𝑊𝑊

<1

^st

law of thermodynamics>

𝛿𝛿𝑄𝑄

Control Volume

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 Internal energy ( 𝒖𝒖 )

𝛿𝛿𝑄𝑄 = 𝑑𝑑𝑑𝑑 + 𝛿𝛿𝑊𝑊

1

2 𝑚𝑚(𝑣𝑣

_𝑥𝑥²

+ 𝑣𝑣

_𝑦𝑦²

+ 𝑣𝑣

_𝑧𝑧²

) 1

2 𝐼𝐼(𝑤𝑤

_𝑥𝑥²

+ 𝑤𝑤

_𝑦𝑦²

+ 𝑤𝑤

_𝑧𝑧²

) 1

2 ( 𝑚𝑚 ̇𝑑𝑑

²

+ 𝑘𝑘𝑑𝑑

²

)

1

2 ( 𝑚𝑚( ̇𝑑𝑑

²

+ ̇𝑦𝑦

²

+ ̇𝑧𝑧

²

) + 𝑘𝑘(𝑑𝑑

²

+𝑦𝑦

²

+ 𝑧𝑧

²

))

Translational energy Rotational energy Vibrational energy

: 1

^st

law of thermodynamics

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Refrigeration System & Control Laboratory , Seoul National University

2.6 Thermal conductivity

 Three different mechanisms for conduction in materials

<A> : Electron motion (metallic conductor)

<B> : Lattice vibration-energy transport (phonon motion; only have energy)

<C> : Molecular motion (gases)

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 Gases thermal conductivity

𝑘𝑘 𝑡𝑡 = 1 8 9𝛾𝛾 − 5 𝜌𝜌𝑐𝑐 𝑣𝑣 ̅𝑣𝑣𝜆𝜆 𝐸𝐸𝑑𝑑𝑐𝑐𝑘𝑘𝐸𝐸𝐸𝐸, 1913

𝛾𝛾: specific heat ratio 𝜌𝜌: density of material

𝑐𝑐

_𝑣𝑣

: specific heat at constant volume

̅𝑣𝑣: average particle velocity

𝜆𝜆: mean free path of particles

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Refrigeration System & Control Laboratory , Seoul National University

2.6 Thermal conductivity

 Gases thermal conductivity

̅𝑣𝑣 = 8𝑔𝑔 𝑐𝑐 𝑅𝑅𝑇𝑇 𝜋𝜋

2

(𝑃𝑃𝑃𝑃𝐸𝐸𝑃𝑃𝐸𝐸𝐸𝐸𝑡𝑡, 1958)

𝑔𝑔

_𝑐𝑐

: 1 𝑘𝑘𝑔𝑔 � 𝑚𝑚/𝑁𝑁 � 𝑃𝑃

²

𝑅𝑅 : 𝑅𝑅

_𝑢𝑢

/𝑀𝑀 , 𝑅𝑅

_𝑢𝑢

= 8.31434

_{𝑚𝑚𝑚𝑚𝑚𝑚}^𝐽𝐽

� 𝐾𝐾

𝑀𝑀: molecular weight of the gas

𝑇𝑇: absolute temperature of the gas

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 Solids thermal conductivity

𝑘𝑘 𝑡𝑡 = 1 3 𝜌𝜌𝑐𝑐 𝑣𝑣 ̅𝑣𝑣𝜆𝜆

𝜌𝜌: density of material

𝑐𝑐

_𝑣𝑣

: specific heat at constant volume

̅𝑣𝑣: average particle velocity

𝜆𝜆: mean free path of particles

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Refrigeration System & Control Laboratory , Seoul National University

2.6 Thermal conductivity

Thermal conductivity of copper alloys Graphite Thermal Conductivity vs Al and Cu Straps

 Solids thermal conductivity

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2.7 Specific heats of solids

 Specific heat

The energy required to change the temperature of the substance by one degree!

• 𝑪𝑪

_𝒑𝒑

When constant pressure

• 𝑪𝑪

_𝒗𝒗

When constant volume

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Refrigeration System & Control Laboratory , Seoul National University

Debye specific heat function

 Debye model

For solids, “Debye model” represents how the specific heats change under the temperature variation

𝐶𝐶 𝑣𝑣 = 9𝑅𝑅𝑇𝑇𝑅 𝜃𝜃 𝐷𝐷 3 �

0

𝜃𝜃

_𝐷𝐷

/𝑇𝑇 𝑑𝑑 4 𝐸𝐸 𝑥𝑥 𝑑𝑑𝑑𝑑

(𝐸𝐸 𝑥𝑥 − 1) 2 = 3R 𝑇𝑇 𝜃𝜃 𝐷𝐷

3

𝐷𝐷( 𝑇𝑇 𝜃𝜃 𝐷𝐷 )

𝜃𝜃

_𝐷𝐷

: Debye Characteristic temperature 𝐷𝐷(T/𝜃𝜃

_𝐷𝐷

) : Debye function

where, 𝜃𝜃

_𝐷𝐷

=

^ℎ𝑣𝑣_𝑘𝑘^𝑎𝑎

(

_{4𝜋𝜋𝑉𝑉}^3𝑁𝑁

)

¹^⁄³

ℎ ∶ Planck^′s constant

𝑣𝑣_𝑎𝑎 ∶ Speed of sound in the solid 𝑘𝑘 ∶ 𝐵𝐵𝐵𝐵𝐵𝐵𝑡𝑡𝑧𝑧𝑚𝑚𝐵𝐵𝐸𝐸𝐸𝐸^′𝑃𝑃 𝑐𝑐𝐵𝐵𝐸𝐸𝑃𝑃𝑡𝑡𝐵𝐵𝐸𝐸𝑡𝑡

⁄

𝑁𝑁 𝑉𝑉 ∶ 𝑁𝑁𝑑𝑑𝑚𝑚𝑁𝑁𝐸𝐸𝑃𝑃 𝐵𝐵𝑜𝑜 𝐵𝐵𝑡𝑡𝐵𝐵𝑚𝑚𝑃𝑃 𝑝𝑝𝐸𝐸𝑃𝑃 𝑑𝑑𝐸𝐸𝑢𝑢𝑡𝑡 𝑣𝑣𝐵𝐵𝐵𝐵𝑑𝑑𝑚𝑚𝐸𝐸 𝑜𝑜𝐵𝐵𝑃𝑃 𝑡𝑡ℎ𝐸𝐸 𝑃𝑃𝐵𝐵𝐵𝐵𝑢𝑢𝑑𝑑

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Debye specific heat function

•

𝑇𝑇

𝜃𝜃

_𝐷𝐷 > 3 ,

𝐶𝐶

_𝑣𝑣

𝑅𝑅 ≈

3

(Dulong-Petit value)

•

𝑇𝑇

𝜃𝜃

_𝐷𝐷 < 1

12 ,

𝐶𝐶

_𝑣𝑣

𝑅𝑅 ∝ 𝑇𝑇

³

The Debye specific heat function

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Refrigeration System & Control Laboratory , Seoul National University

Specific heat affected by electrons

According to quantum theory,

𝐶𝐶 𝑣𝑣,𝑒𝑒 = 4𝜋𝜋 4 𝐵𝐵𝑚𝑚 𝑒𝑒 𝑀𝑀𝑅𝑅 2 𝑇𝑇

ℎ 2 𝑁𝑁 0 (3𝜋𝜋 2 𝑁𝑁 𝑉𝑉) ⁄ 2 3 ⁄ = 𝛾𝛾 𝑒𝑒 𝑇𝑇

𝐵𝐵

=

𝑁𝑁𝑑𝑑𝑚𝑚𝑁𝑁𝐸𝐸𝑃𝑃 𝐵𝐵𝑜𝑜 𝑜𝑜𝑃𝑃𝐸𝐸𝐸𝐸 𝐸𝐸𝐵𝐵𝐸𝐸𝑐𝑐𝑡𝑡𝑃𝑃𝐵𝐵𝐸𝐸𝑃𝑃 𝑝𝑝𝐸𝐸𝑃𝑃 𝐵𝐵𝑡𝑡𝐵𝐵𝑚𝑚 𝑚𝑚

_𝑒𝑒 =

𝐸𝐸𝐵𝐵𝐸𝐸𝑐𝑐𝑡𝑡𝑃𝑃𝐵𝐵𝐸𝐸 𝐸𝐸𝑜𝑜𝑜𝑜𝐸𝐸𝑐𝑐𝑡𝑡𝑢𝑢𝑣𝑣𝐸𝐸 𝑚𝑚𝐵𝐵𝑃𝑃𝑃𝑃

𝑀𝑀

=

𝐵𝐵𝑡𝑡𝐵𝐵𝑚𝑚𝑢𝑢𝑐𝑐 𝑤𝑤𝐸𝐸𝑢𝑢𝑔𝑔ℎ𝑡𝑡 𝐵𝐵𝑜𝑜 𝑚𝑚𝐵𝐵𝑡𝑡𝐸𝐸𝑃𝑃𝑢𝑢𝐵𝐵𝐵𝐵

𝑅𝑅

=

𝑆𝑆𝑝𝑝𝐸𝐸𝑐𝑐𝑢𝑢𝑜𝑜𝑢𝑢𝑐𝑐 𝑔𝑔𝐵𝐵𝑃𝑃 𝑐𝑐𝐵𝐵𝐸𝐸𝑃𝑃𝑡𝑡𝐵𝐵𝐸𝐸𝑡𝑡 𝑜𝑜𝐵𝐵𝑃𝑃 𝑚𝑚𝐵𝐵𝑡𝑡𝐸𝐸𝑃𝑃𝑢𝑢𝐵𝐵𝐵𝐵 𝑇𝑇

=

𝐴𝐴𝑁𝑁𝑃𝑃𝐵𝐵𝐵𝐵𝑑𝑑𝑡𝑡𝐸𝐸 𝑡𝑡𝐸𝐸𝑚𝑚𝑝𝑝𝐸𝐸𝑃𝑃𝐵𝐵𝑡𝑡𝑑𝑑𝑃𝑃𝐸𝐸

ℎ

=

𝑃𝑃𝐵𝐵𝐵𝐵𝐸𝐸𝑐𝑐𝑘𝑘

^′

𝑃𝑃 𝑐𝑐𝐵𝐵𝐸𝐸𝑃𝑃𝑡𝑡𝐵𝐵𝐸𝐸𝑡𝑡 𝑁𝑁

₀ =

𝐴𝐴𝑣𝑣𝐵𝐵𝑔𝑔𝐵𝐵𝑑𝑑𝑃𝑃𝐵𝐵

^′

𝑃𝑃 𝐸𝐸𝑑𝑑𝑚𝑚𝑁𝑁𝐸𝐸𝑃𝑃

𝑁𝑁 𝑉𝑉 ⁄

=

𝑁𝑁𝑑𝑑𝑚𝑚𝑁𝑁𝐸𝐸𝑃𝑃 𝐵𝐵𝑜𝑜 𝑜𝑜𝑃𝑃𝐸𝐸𝐸𝐸 𝐸𝐸𝐵𝐵𝐸𝐸𝑐𝑐𝑡𝑡𝑃𝑃𝐵𝐵𝐸𝐸𝑃𝑃 𝑝𝑝𝐸𝐸𝑃𝑃 𝑑𝑑𝐸𝐸𝑢𝑢𝑡𝑡 𝑣𝑣𝐵𝐵𝐵𝐵𝑑𝑑𝑚𝑚𝐸𝐸

𝛾𝛾

_𝑒𝑒 =

𝐸𝐸𝐵𝐵𝐸𝐸𝑐𝑐𝑡𝑡𝑃𝑃𝐵𝐵𝐸𝐸𝑢𝑢𝑐𝑐 𝑃𝑃𝑝𝑝𝐸𝐸𝑐𝑐𝑢𝑢𝑜𝑜𝑢𝑢𝑐𝑐 − ℎ𝐸𝐸𝐵𝐵𝑡𝑡 𝑐𝑐𝐵𝐵𝐸𝐸𝑜𝑜𝑜𝑜𝑢𝑢𝑐𝑐𝑢𝑢𝐸𝐸𝐸𝐸𝑡𝑡

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Specific heat affected by electrons

Table. Electronic specific heat coefficients

Ordinary temperature  𝛾𝛾

_𝑒𝑒

is small (ignorable)

Low Temperature  𝛾𝛾

_𝑒𝑒

becomes important!

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Refrigeration System & Control Laboratory , Seoul National University

2.8 Specific heat of liquids and gases

 Specific heat of a material (equipartition theorem)

𝐶𝐶 𝑣𝑣 = 1 2 𝑅𝑅𝑜𝑜

( 𝑜𝑜 : number of degrees of freedom)

① Monatomic gas

- Translational motion : 3 - Rotational motion : 0

- Vibrational motion : 0 ∴ 𝐶𝐶

_𝑣𝑣

= 3 2 𝑅𝑅

• Degree of freedom

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2.8 Specific heat of liquids and gases

② Diatomic gas

- Translational motion : 3 - Rotational motion : 2 - Vibrational motion : 2

• Degree of freedom

∴ 𝐶𝐶

_𝑣𝑣

= 7 2 𝑅𝑅

(according to the classical theory)

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Refrigeration System & Control Laboratory , Seoul National University

2.8 Specific heat of liquids and gases

In the actual case, rotational, vibrational modes are quantized!

<Variation of the specific heat 𝑪𝑪_𝒗𝒗 for hydrogen gas>

0~10K Translational motion only (

^𝐶𝐶_𝑅𝑅^𝑣𝑣

=

³₂

)

10~1000K Translational+Rotational motion (

=

⁵₂

)

1000K~ Translational+Rotational+Vibrational motion (

=

⁷₂

)

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2.9 Coefficient of thermal expansion

 Coefficient of thermal expansion

3

t

β = λ

𝛽𝛽 is fractional change in volume per unit change in temperature is the linear coefficient of thermal expansion

λ

t

- For isotropic materials

p

1 v v T

 ∂ 

β =   ∂   (in the vicinity of the critical point)

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Refrigeration System & Control Laboratory , Seoul National University

2.9 Coefficient of thermal expansion

Linear coefficient of thermal expansion for several materials at low temperature:

(1) 2024-T4 aluminum (2) beryllium copper (3) K Monel (2) (4) titanium (5) 304 stainless steel (6) C1020 carbon steel

 The temperature variation of the linear coefficient for thermal expansion for

several materials

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2.9 Coefficient of thermal expansion

Variation of the intermolecular potential energy for a pair of molecules

 The intermolecular potential-energy curve

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Refrigeration System & Control Laboratory , Seoul National University

2.9 Coefficient of thermal expansion

 The intermolecular forces

- The intermolecular potential-energy curve is not symmetrical. Therefore, as the molecule acquires more energy, its mean position relative to its neighbors becomes larger, that is, the material expands.

- The coefficient of thermal expansion increases as temperature is

increased.

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2.9 Coefficient of thermal expansion

 Coefficient of thermal expansion

G

c

v

B γ ρ β =

𝜌𝜌 is the density of the material 𝐵𝐵 is the bulk modulus 𝛾𝛾

_𝐺𝐺

is the Gruneisen constant

- For crystalline solids, the Gruneisen relation

Values of the Gruneisen constant

for selected solids

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Refrigeration System & Control Laboratory , Seoul National University

2.10 Electrical conductivity

𝑘𝑘

_𝑒𝑒

= 𝐼𝐼 �

𝐴𝐴𝑃𝑃𝐸𝐸𝐵𝐵 𝑑𝑑𝑉𝑉 �

𝑑𝑑𝑑𝑑 = 𝐼𝐼 �

� 𝐴𝐴

𝑉𝑉 𝐿𝐿 = 𝐿𝐿 𝑅𝑅𝐴𝐴

𝑞𝑞 = 𝑘𝑘𝐴𝐴 𝑑𝑑𝑇𝑇 𝑑𝑑𝑑𝑑

Electrical resistivity, 𝜌𝜌 =

_𝑘𝑘¹

𝑒𝑒

As T ↓, Vibrational E ↓

𝐼𝐼 = 𝑘𝑘

_𝑒𝑒

𝐴𝐴 𝑑𝑑𝑉𝑉

𝑑𝑑𝑑𝑑

(49)

2.11 Superconductivity

• Only at very low T

• Disappearance of all electric resistance

• Appearance of perfect diamagnetism

Paramagnetism ∼ magnet

Diamagnetism ∼ repel

Ferromagnetism ∼ stick

(50)

Refrigeration System & Control Laboratory , Seoul National University

2.11 Superconductivity

Superconductivity levitation

(51)

(52)

Refrigeration System & Control Laboratory , Seoul National University

2.11 Superconductivity

𝑇𝑇 ∶ 𝑇𝑇 < 𝑇𝑇

_𝑚𝑚

ℋ ∶ ℋ

_𝑚𝑚

(Critical field)

└ magnetic field strength required to destroy superconductivity 𝐼𝐼 ∶ 𝐼𝐼

_𝑐𝑐

(Critical current)

└ upper limit to the electric current without destroying superconductivity

Normal Superconducting

(53)

(54)

Refrigeration System & Control Laboratory , Seoul National University

2.11 Superconductivity

(55)

 Applications

MRI (Magnetic Resonance Imaging)

High magnetic field stability

(56)

Refrigeration System & Control Laboratory , Seoul National University

2.12 Cryogenic fluid property

LN

₂

(𝐵𝐵𝑢𝑢𝑞𝑞𝑑𝑑𝑢𝑢𝑑𝑑 N

₂

)

→ Clear, Colorless

→ N.B.P. (Normal Boiling Point) : 77 K

→ Produced by the distillation of air

→ Small heat of vaporization

(57)

2.12 Cryogenic fluid property

Usage of LN

₂

(𝐵𝐵𝑢𝑢𝑞𝑞𝑑𝑑𝑢𝑢𝑑𝑑 N

₂

)

Quick freezing of food, Drying etc.

(58)

Refrigeration System & Control Laboratory , Seoul National University

2.12 Cryogenic fluid property

Liquid nitrogen

(59)

→ Slightly magnetic (paramagnetic)

→ N.B.P. (Normal Boiling Point) : 90 K

→ Produced by the distillation of air

→ Slightly magnetic (paramagnetic)

LO

₂

(𝐵𝐵𝑢𝑢𝑞𝑞𝑑𝑑𝑢𝑢𝑑𝑑 O

₂

)

(60)

Refrigeration System & Control Laboratory , Seoul National University

2.12 Cryogenic fluid property

Usage of LO

₂

(𝐵𝐵𝑢𝑢𝑞𝑞𝑑𝑑𝑢𝑢𝑑𝑑 O

₂

)

Fuel of rocket, welding etc.

(61)

(62)

Refrigeration System & Control Laboratory , Seoul National University

2.13 𝐇𝐇 𝟐𝟐

N.B.P. = 20.3 K

𝐻𝐻 − 𝐻𝐻 𝐻𝐻 − 𝐷𝐷 𝐷𝐷 − 𝐷𝐷 𝑇𝑇 − 𝑇𝑇

hydrogen

𝑯𝑯 𝑫𝑫

deuterium

𝑻𝑻

tritium

𝒑𝒑𝒑𝒑𝒑𝒑𝒑𝒑𝒑𝒑𝒑𝒑 𝟏𝟏 𝟏𝟏 𝟏𝟏

𝒑𝒑𝒏𝒏𝒖𝒖𝒑𝒑𝒑𝒑𝒑𝒑𝒑𝒑 𝟎𝟎 𝟏𝟏 𝟐𝟐

𝒏𝒏𝒆𝒆𝒏𝒏𝒆𝒆𝒑𝒑𝒑𝒑𝒑𝒑𝒑𝒑 𝟏𝟏 𝟏𝟏 𝟏𝟏

Types of hydrogen atom

D T

(63)

2.13 𝐇𝐇 𝟐𝟐

Tritium production

(64)

Refrigeration System & Control Laboratory , Seoul National University

2.13 𝐇𝐇 𝟐𝟐

Fusion reaction

(65)

2.13 𝐇𝐇 𝟐𝟐

N.B.P. = 20.3 K

𝐵𝐵𝑃𝑃𝑡𝑡ℎ𝐵𝐵 − H

₂

(Spins aligned, high energy) 𝑝𝑝𝐵𝐵𝑃𝑃𝐵𝐵 − H

₂

(Spins opposite direction, low energy)

Types of hydrogen molecules

(66)

Refrigeration System & Control Laboratory , Seoul National University

2.13 𝐇𝐇 𝟐𝟐

(67)

2.13 𝐇𝐇 𝟐𝟐

₂

→ 𝑝𝑝𝐵𝐵𝑃𝑃𝐵𝐵 − H

₂

+ Δ𝛼𝛼 (ℎ𝐸𝐸𝐵𝐵𝑡𝑡 𝐵𝐵𝑜𝑜 𝑐𝑐𝐵𝐵𝐸𝐸𝑣𝑣𝐸𝐸𝑃𝑃𝑃𝑃𝑢𝑢𝐵𝐵𝐸𝐸) 70.3 kJ/kg

Latent heat 44.3 kJ/kg

At high temperature is a mixture of 75% 𝐵𝐵𝑃𝑃𝑡𝑡ℎ𝐵𝐵 − H

₂

and 25% 𝑝𝑝𝐵𝐵𝑃𝑃𝐵𝐵 − H

₂

As temperature is cooled to the normal boiling point of hydrogen, the

₂

concentration decreases from 75 𝑡𝑡𝐵𝐵 0.2%

(68)

Refrigeration System & Control Laboratory , Seoul National University

2.13 𝐇𝐇 𝟐𝟐

(69)

2.13 𝐇𝐇 𝟐𝟐

300 K

Gas H

₂

20 K

Liq H

₂

Latent heat + Sensible latent + Heat of conversion

Gas Liq

Ortho → Para

Storage

Catalyst

(Speed up conversion)

(70)

Refrigeration System & Control Laboratory , Seoul National University

2.13 𝐇𝐇𝐇𝐇 𝟒𝟒

• Difficult to liquefy

• N.B.P. = 4.2 K

• No triple point

(71)

2.13 𝐇𝐇𝐇𝐇 𝟒𝟒

He − Ⅰ : Normal fluid He − Ⅱ : Super fluid

└ act as if it has zero viscosity 𝑣𝑣𝑢𝑢𝑃𝑃𝑐𝑐𝐵𝐵𝑃𝑃𝑢𝑢𝑡𝑡𝑦𝑦, 𝜏𝜏 = 𝜇𝜇

^{𝑑𝑑𝑉𝑉}_{𝑑𝑑𝑑𝑑}

Behavior of superfluid

(72)

Refrigeration System & Control Laboratory , Seoul National University

2.13 𝐇𝐇𝐇𝐇 𝟒𝟒

Superfluid helium

(73)

2.14 𝐇𝐇𝐇𝐇 𝟑𝟑

• N.B.P. = 3.19 K

• Super fluid transition = 3.5 mK

2.9𝑀𝑀𝑃𝑃𝐵𝐵

(74)

Refrigeration System & Control Laboratory , Seoul National University

2.14 𝐇𝐇𝐇𝐇 𝟑𝟑

He

³

: $200,000/12grams

resource : Physics Projects Deflate for Lack of Helium-3.

Spectrum.ieee.org. Retrieved on 2011-11-08.

Price of He

³

and He

⁴