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= Thermodynamics =


{{Status
|status=Draft
|owner=Knowledge Agent
|last_update=2026-07-15
|review=Pending
}}


== Heat transfer and heat dissipation ==
{{TOC}}
Heat can be transferred through objects and spaces. Transfer of heat means that the thermal energy is transferred from one place to another.


Generated heat is dissipated to the ambient air via various paths through the conduction, radiation, and convection.
== Overview ==


[[File:Heat dissipation path.png|center|thumb|433x433px|<ref>https://fscdn.rohm.com/en/products/databook/applinote/common/basics_of_thermal_resistance_and_heat_dissipation_an-e.pdf</ref>]]
열역학(Thermodynamics)은 열, 일, 에너지의 변환과 전달을 연구하는 물리학 분야입니다. 데이터센터 냉각 시스템 설계에서 열역학은 냉각 효율 계산, 열 부하 분석, 에너지 소비 최적화의 기초가 됩니다.


=== Thermal conduction ===
=== Summary ===
Heat is transferred from a high temperature point to a low temperature point within an identical object due to movement of molecules composing the material. No movement of the material is involved


=== Convection (heat transmission): ===
* 무엇인가? — 열, 일, 에너지의 변환과 전달 연구
Heat is transferred by flow of a fluid when there is a temperature difference between the surface of a solid and a fluid, such as air or water, that is in [[contact]] with the surfaces.
* 왜 필요한가? — 데이터센터 냉각 시스템 설계, 열 부하 분석
* 언제 사용하는가? — 수냉식 냉각 시스템, CDU 설계, 열 교환기 분석


==== Types of convection ====
---


* Fluid  : Material that flows, such as gas or liquid
== Purpose ==
* Convection : Heat transfer phenomenon where heat is transferred by a fluid that receives the heat. Note: No heat transfer through convection is expected to occur without any fluid (in a vacuum).
* Natural convection : Upward flow generated by temperature difference in fluid
* Forced convection  :  Flow generated by an external factor, such as a fan or pump


=== Heat radiation: ===
이 문서가 존재하는 이유
From the surface of an object, an electromagnetic wave is emitted with a wavelength corresponding to the surface temperature.


The electromagnetic wave is transmitted through a space and hits the destination object. The vibration energy of the electromagnetic wave causes vibration of molecules on the surface of the destination object, transferring heat and changing the temperature of the destination object. Through the heat radiation, heat may be transferred without any medium between objects (even in a vacuum)
* Goal: 열역학 기본 법칙, 열 전달 방식, 데이터센터 냉각 적용 제공
* Scope: 열역학 법칙, 전도/대류/복사, 엔탈피, 냉각 효율 계산
* Non-goals: 복잡한 유체 역학 시뮬레이션, 상세 재료 과학


== Heat Flux ==
---
Heat flux is the amount of heat energy transferred through a surface in a unit area in unit time. The heat flux can be the amount of heat transferred from or dissipated on the surface of consideration. 


== Key Concepts ==


{| class="wikitable"
! Concept
! Description
! Related
|-
| 열역학 제1법칙
| 에너지 보존 법칙
| [[Thermodynamics]]
|-
| 열역학 제2법칙
| 엔트로피 증가 법칙
| [[Thermodynamics]]
|-
| 전도 (Conduction)
| 고체 내 열 전달
| [[Thermodynamics]]
|-
| 대류 (Convection)
| 유체 내 열 전달
| [[Thermodynamics]]
|-
| 복사 (Radiation)
| 전자기파 열 전달
| [[Thermodynamics]]
|-
| 엔탈피 (Enthalpy)
| 시스템의 총 열 에너지
| [[Thermodynamics]]
|-
| CDU
| Cooling Distribution Unit
| [[CDU]]
|-
| 열 부하 (Heat Load)
| 데이터센터의 총 발열량
| [[Thermodynamics]]
|}


Heat flux is also known as thermal flux, heat flow density, heat flux density, or heat flow rate intensity. Its SI units are watts per square metre (W/m<sup>2</sup>)<ref>https://en.wikipedia.org/wiki/Heat_flux</ref>
---
 
heat flux(q) is based on these two quantities : q = Q / A


# The amount of heat transfer per unit area (Q)
== Architecture ==
# The area where the heat transfer takes place (A)


Heat Flux is dependent on,
데이터센터 열 전달 경로:


# Temperature difference '''-''' The temperature difference or gradient is necessary for any heat transfer to take place. The heat flux shares a direct relationship with the temperature gradient. As the temperature gradient increases, the heat flux magnitude increases.
<syntaxhighlight lang="mermaid">
# Thermal transfer coefficient or heat transfer coefficient '''-''' The thermal transfer coefficient is introduced through Newton’s law of cooling, the heat flux associated with a surface is linearly related to the temperature gradient. The proportionality constant linking heat flux and temperature gradient is called the heat transfer coefficient.
graph TD
    A[CPU/GPU Chip] -->|전도| B[Heat Spreader]
    B -->|전도| C[Cold Plate]
    C -->|대류| D[냉각수]
    D -->|대류| E[CDU]
    E -->|복사/대류| F[외부 공기]
    G[공기 냉각] -->|대류| F
</syntaxhighlight>


[https://www.youtube.com/watch?v=6jQsLAqrZGQ This Youtube video] explains the equation for better understanding
---


== Workflow ==


Mathematically, the heat flux equation on one dimension can be expressed as (According to Fourier’s law, the heat flux is directly proportional to the thermal or temperature gradient):
{| class="wikitable"
{| class="wikitable"
|+
! Stage
!
! Input
!
! Output
|-
|-
|heat transfer rate in Watts
| 열 부하 계산
|q = -K x A x (∆T / ∆x ) = K x A x (T2 - T1 / L)  
| 서버 사양, TDP
| 총 열 부하 (kW)
|-
|-
|heat flux in Watts per square meter
| 냉각수 유량 계산
|q<nowiki>''</nowiki> = - K x (∆T / ∆x )
| 열 부하, ΔT
| 유량 (L/min)
|-
|-
|
| CDU 용량 결정
|q is the heat flux in Watts
| 총 열 부하
K is the heat transfer coefficient
| CDU 용량 (kW)
|-
| 효율 분석
| COP, PUE
| 냉각 효율
|}


A is the area of the cross-section of the surface
---


∆T / ∆x is the temperature gradient
== Detailed Explanation ==


T2 is higher temperature
=== 열역학 제1법칙 (에너지 보존) ===


T1 is lower temperature
에너지는 생성되거나 소멸되지 않고, 형태만 변환됩니다.


L is length of one dimensional distance
Q = ΔU + W
|}


== Thermal conductivity<ref>https://en.wikipedia.org/wiki/Thermal_conductivity_and_resistivity</ref> ==
* Q: 시스템에 공급된 열
Thermal conductivity is a fundamental concept in heat transfer and is crucial in multiple industries and scientific disciplines. It refers to the ability of a material to conduct heat or the rate at which heat transfers through a substance. Understanding heat and its relationship to thermal conductivity is essential for designing efficient thermal systems, optimizing energy usage, and ensuring the safety and performance of various materials and products. Thermal conductivity is determined by various physical factors that govern the flow of heat energy.
* ΔU: 내부 에너지 변화
* W: 시스템이 한 일


데이터센터 적용:
* 서버 전력 → 열 에너지 (거의 100% 열로 변환)
* 냉각 시스템 → 열을 외부로 배출


=== 열역학 제2법칙 (엔트로피) ===


The '''thermal conductivity''' is also called the '''lambda (λ)''' '''value''', or k value.  
열은 항상 고온에서 저온으로 흐릅니다. 자연스러운 과정은 엔트로피를 증가시킵니다.


<u>Thermal conductivity is a property of the material and does not take into account thickness. Two different thicknesses of the same material still have the same λ-value.</u>
이 법칙이 데이터센터 냉각의 기본 원리입니다:
* CPU (고온) → 냉각수 → CDU → 외부 공기 (저온)
* 열 펌프(냉동기) 없이는 저온으로 열 이동 불가


The '''thermal conductivity''' of a material is a measure of its ability to conduct heat. It is commonly measured in <big>W·m<sup>−1</sup>·K<sup>−1</sup>'''(W/mK)'''</big>'''.'''
=== 열 전달 3가지 방식 ===


The defining equation for thermal conductivity is calculated by known as Fourier's Law for heat conduction.
==== 전도 (Conduction) ====


== Thermal resistance ==
고체 내에서 분자 간 충돌로 열이 전달됩니다.
Thermal resistance is a quantification of how difficult it is for heat to be conduct. The higher the thermal resistance, the more difficult it is for heat to be conducted, and vice vers. 


Thermal resistance is calculated by dividing the thickness of the material by its thermal conductivity, giving an '''R-value''' specific to that thickness
Q = k × A × ΔT / d


<u>To compare the relative performance of different <big>'''thicknesses of materials'''</big> means working out their '''thermal resistance <big>(units: m2K/W)</big>'''.</u> 
* k: 열전도율 (W/m·K)
* A: 단면적 (m²)
* ΔT: 온도차 (K)
* d: 두께 (m)


== U-value ==
**주요 재료 열전도율:**
A U-value is a measure of '''thermal transmittance''', or the amount of heat energy that moves through a floor, wall or roof, from the warm (heated) side to the cold side. It is the number of Watts per square metre of the construction, per degree of temperature difference between one side and the other <big>'''(W/m2K)'''</big>. 


The thermal resistance can be considered in the same way as the electric resistance. The basic formulas of thermal calculation can be treated in the same way as Ohm's law.  R is used as the symbol for the electric resistance, while θ (theta) is used for the thermal resistance.
{| class="wikitable"
{| class="wikitable"
|+
! Material
! colspan="2" |Electric
! Thermal Conductivity (W/m·K)
! colspan="2" |Thermal
|-
| 구리 (Copper)
| 401
|-
| 알루미늄 (Aluminum)
| 237
|-
| 철 (Steel)
| 80
|-
| 스테인리스강
| 16
|-
|-
|Voltage
| 실리콘
difference
| 149
|}
 
==== 대류 (Convection) ====
 
유체(액체/기체)의 운동으로 열이 전달됩니다.
 
Q = h × A × ΔT
 
* h: 대류 열전달 계수 (W/m²·K)
* A: 표면적 (m²)
* ΔT: 표면-유체 온도차 (K)
 
**자연 대류 vs 강제 대류:**
* 자연 대류: 밀도 차이에 의한 유체 운동 (느림)
* 강제 대류: 팬/펌프에 의한 유체 운동 (빠름)
 
==== 복사 (Radiation) ====
 
전자기파(적외선)로 열이 전달됩니다. 매개체 불필요.
 
Q = ε × σ × A × (T₁⁴ - T₂⁴)
 
* ε: 방사율 (0~1)
* σ: 스테판-볼츠만 상수 (5.67 × 10⁻⁸ W/m²·K⁴)
* A: 표면적 (m²)
* T₁, T₂: 절대온도 (K)
 
=== 엔탈피 (Enthalpy) ===
 
시스템의 총 열 에너지. 냉각 시스템 설계에서 핵심 개념입니다.
 
H = U + PV
 
* H: 엔탈피
* U: 내부 에너지
* P: 압력
* V: 부피
 
냉각수 엔탈피 변화로 열 전달량 계산:
 
Q = m × Δh
 
* m: 냉각수 질량 유량 (kg/s)
* Δh: 엔탈피 변화 (kJ/kg)


ΔV (V)
=== 데이터센터 열 부하 계산 ===
|∆𝑉 = 𝑅 × 𝐼
|Temperature
difference


ΔT (°C)
데이터센터의 총 열 부하는 서버 TDP(Thermal Design Power)의 합과 같습니다.
|∆𝑇
= 𝑅𝑡ℎ × 𝑃
|-
|Electric
resistance


R (Ω)
Q_total = Σ TDP_i + Q_other
|𝑅 = ∆𝑉 / 𝐼
|Thermal
resistance


Rth (°C/W)
* Q_total: 총 열 부하 (kW)
|𝑅𝑡ℎ = ∆𝑇 / 𝑃
* TDP_i: 각 서버의 열 설계 전력
|-
* Q_other: 네트워크, 스토리지, 조명 등 기타 발열
|Current
I (A)
|𝐼 = ∆𝑉 / 𝑅
|Heat flow
P (W)
|𝑃 = ∆𝑇 / 𝑅𝑡ℎ
|}


{| class="wikitable sortable"
**냉각수 유량 계산:**
|+The radiation heat transfer emissivity coefficients for some common materials <ref>https://www.engineeringtoolbox.com/emissivity-coefficients-d_447.html</ref>
!Surface Material
!Emissivity Coefficient
- ''ε -''
|-
|Alloy 24ST Polished
|0.09
|-
|Alumina, Flame sprayed
|0.8
|-
|Aluminum Commercial sheet
|0.09
|-
|Aluminum Foil
|0.04
|-
|Aluminum Commercial Sheet
|0.09
|-
|Aluminum Heavily Oxidized
|0.2 - 0.31
|-
|Aluminum Highly Polished
|0.039 - 0.057
|-
|Aluminum Anodized
|0.77
|-
|Aluminum Rough
|0.07
|-
|Aluminum paint
|0.27 - 0.67
|-
|Anodize black
|0.88
|-
|Antimony, polished
|0.28 - 0.31
|-
|Asbestos board
|0.96
|-
|Asbestos paper
|0.93 - 0.945
|-
|Asphalt
|0.93
|-
|Basalt
|0.72
|-
|Beryllium
|0.18
|-
|Beryllium, Anodized
|0.9
|-
|Bismuth, bright
|0.34
|-
|Black Body Matt
|1.00
|-
|Black lacquer on iron
|0.875
|-
|Black Parson Optical
|0.95
|-
|Black Silicone Paint
|0.93
|-
|Black Epoxy Paint
|0.89
|-
|Black Enamel Paint
|0.80
|-
|Brass Dull Plate
|0.22
|-
|Brass Rolled Plate Natural Surface
|0.06
|-
|Brass Polished
|0.03
|-
|Brass Oxidized 600<sup>o</sup>C
|0.6
|-
|Brick, red rough
|0.93
|-
|Brick, fire-clay
|0.75
|-
|Cadmium
|0.02
|-
|Carbon, not oxidized
|0.81
|-
|Carbon filament
|0.77
|-
|Carbon pressed filled surface
|0.98
|-
|Cast Iron, newly turned
|0.44
|-
|Cast Iron, turned and heated
|0.60 - 0.70
|-
|Cement
|0.54
|-
|Cromium polished
|0.058
|-
|Clay
|0.91
|-
|Coal
|0.80
|-
|Concrete
|0.85
|-
|Concrete, rough
|0.94
|-
|Concrete tiles
|0.63
|-
|Cotton cloth
|0.77
|-
|Copper electroplated
|0.03
|-
|Copper heated and covered with thick oxide layer
|0.78
|-
|Copper Polished
|0.023 - 0.052
|-
|Copper Nickel Alloy, polished
|0.059
|-
|Glass smooth
|0.92 - 0.94
|-
|Glass, pyrex
|0.85 - 0.95
|-
|Glass, opal
|0.87
|-
|Gold not polished
|0.47
|-
|Gold highly polished
|0.02 - 0.04
|-
|Granite, natural surface
|0.96
|-
|Gravel
|0.28
|-
|Gypsum
|0.85
|-
|Ice smooth
|0.966
|-
|Ice rough
|0.985
|-
|Inconel X Oxidized
|0.71
|-
|Iron polished
|0.14 - 0.38
|-
|Iron, plate rusted red
|0.61
|-
|Iron, dark gray surface
|0.31
|-
|Iron, rough ingot
|0.87 - 0.95
|-
|Lampblack paint
|0.96
|-
|Lead pure unoxidized
|0.057 - 0.075
|-
|Lead Oxidized
|0.43
|-
|Limestone
|0.90 - 0.93
|-
|Lime wash
|0.91
|-
|Magnesia
|0.72
|-
|Magnesite
|0.38
|-
|Magnesium Oxide
|0.20 - 0.55
|-
|Magnesium Polished
|0.07 - 0.13
|-
|Marble White
|0.95
|-
|Masonry Plastered
|0.93
|-
|Mercury liquid
|0.1
|-
|Mild Steel
|0.20 - 0.32
|-
|Molybdenum polished
|0.05 - 0.18
|-
|Mortar
|0.87
|-
|Nickel, elctroplated
|0.03
|-
|Nickel, polished
|0.072
|-
|Nickel, oxidized
|0.59 - 0.86
|-
|Nichrome wire, bright
|0.65 - 0.79
|-
|Oak, planed
|0.89
|-
|Oil paints, all colors
|0.92 - 0.96
|-
|Paper offset
|0.55
|-
|Plaster
|0.98
|-
|Platinum, polished plate
|0.054 - 0.104
|-
|Pine
|0.84
|-
|Plaster board
|0.91
|-
|Porcelain, glazed
|0.92
|-
|Paint
|0.96
|-
|Paper
|0.93
|-
|Plaster, rough
|0.91
|-
|Plastics
|0.90 - 0.97
|-
|Polypropylene
|0.97
|-
|Polytetrafluoroethylene (PTFE)
|0.92
|-
|Polyethylene, black plastic
|0.92
|-
|Porcelain glazed
|0.93
|-
|Pyrex
|0.92
|-
|PVC
|0.91 - 0.93
|-
|Quartz glass
|0.93
|-
|Roofing paper
|0.91
|-
|Rubber, foam
|0.90
|-
|Rubber, hard glossy plate
|0.94
|-
|Rubber, natural hard
|0.91
|-
|Rubber, natural oft
|0.86
|-
|Salt
|0.34
|-
|Sand
|0.9
|-
|Sandstone
|0.59
|-
|Sapphire
|0.48
|-
|Sawdust
|0.75
|-
|Silica
|0.79
|-
|Silicon Carbide
|0.83 - 0.96
|-
|Silver Polished
|0.02 - 0.03
|-
|Snow
|0.96 - 0.98
|-
|Soil
|0.90 - 0.95
|-
|Steel Oxidized
|0.79
|-
|Steel Polished
|0.07
|-
|Stainless Steel, weathered
|0.85
|-
|Stainless Steel, polished
|0.075
|-
|Stainless Steel, type 301
|0.54 - 0.63
|-
|Steel Galvanized Old
|0.88
|-
|Steel Galvanized New
|0.23
|-
|Thoria
|0.28
|-
|Tile
|0.97
|-
|Tin unoxidized
|0.04
|-
|Titanium polished
|0.19
|-
|Tungsten polished
|0.04
|-
|Tungsten aged filament
|0.032 - 0.35
|-
|Water (0 - 100<sup>o</sup>C)
|0.95 - 0.963
|-
|Wood Beech, planned
|0.935
|-
|Wood Oak, planned
|0.885
|-
|Wood, Pine
|0.95
|-
|Wrought Iron
|0.94
|-
|Zinc Tarnished
|0.25
|-
|Zinc polished
|0.045
|}
[[File:Thermal resistance formula.png|center|thumb|837x837px|https://fscdn.rohm.com/en/products/databook/applinote/common/basics_of_thermal_resistance_and_heat_dissipation_an-e.pdf]]


== Specifici heat capacity (symbol c) ==
Q = m × Cp × ΔT
It is also referred to as '''massic heat capacity''' or as the '''specific heat. The SI unit of specific heat capacity is joule per kelvin per kilogram, J⋅kg<sup>−1</sup>⋅K<sup>−1</sup>.''' <ref>https://en.wikipedia.org/wiki/Specific_heat_capacity</ref> Specific heat capacity often varies with temperature, and is different for each state of matter.


For example, the heat required to raise the temperature of 1 kg of water by 1 K is 4184 joules, so the specific heat capacity of water is 4184 J⋅kg<sup>−1</sup>⋅K<sup>−1</sup>
* Q: 열 부하 (kW)
* m: 질량 유량 (kg/s)
* Cp: 비열 (물: 4.186 kJ/kg·K)
* ΔT: 공급-반환 온도차 (K)


**예시:** 100kW 열 부하, ΔT=5°C일 때
* m = 100 / (4.186 × 5) = 4.78 kg/s ≈ 287 L/min


So, '''a high value of specific heat means that it takes MORE energy to raise (or lower) its temperature.''' '''A low value means that it does not take very much energy to heat or cool it'''. Adding heat to a “low specific heat” compound will increase its temperature much more quickly than adding heat to a high specific heat compound.
=== 냉각 효율 지표 ===


{| class="wikitable sortable"
{| class="wikitable"
|+Table of specific heat capacities at 25 °C (298 K) unless otherwise noted<ref>https://en.wikipedia.org/wiki/Table_of_specific_heat_capacities</ref>
! 지표
! rowspan="2" |Substance
! Formula
! rowspan="2" |Phase
! Description
! rowspan="2" |Isobaric mass
! Target
heat capacity
''c<sub>P</sub>''J⋅g<sup>−1</sup>⋅K<sup>−1</sup>
! colspan="2" |Molar heat capacity,
''C<sub>P,m</sub>'' and ''C<sub>V,m</sub>''
J⋅mol<sup>−1</sup>⋅K<sup>−1</sup>
! rowspan="2" |Isobaric
volumetric
heat capacity
''C<sub>P,v</sub>''
J⋅cm<sup>−3</sup>⋅K<sup>−1</sup>
! rowspan="2" |Isochoric
molar by atom
heat capacity
''C<sub>V,am</sub>''
mol-atom<sup>−1</sup>
|-
!Isobaric
!Isochoric
|-
|Air (Sea level, dry,
0 °C (273.15 K))
|gas
|1.0035
|29.07
|20.7643
|0.001297
|
|-
|Air (typical
room conditions = 20 °C (68 °F) in Oxford English Dictionary)
|gas
|1.012
|29.19
|20.85
|0.00121
|
|-
|Aluminium
|solid
|0.897
|24.2
|
|2.422
|2.91 ''R''
|-
|Ammonia
|liquid
|'''4.700'''
|'''80.08'''
|
|3.263
|3.21 ''R''
|-
|Animal tissue
(incl. human)
|mixed
|3.5
|
|
|3.7
|
|-
|Antimony
|solid
|0.207
|25.2
|
|1.386
|3.03 ''R''
|-
|Argon
|gas
|0.5203
|20.7862
|12.4717
|
|
|-
|Arsenic
|solid
|0.328
|24.6
|
|1.878
|2.96 ''R''
|-
|Beryllium
|solid
|1.82
|16.4
|
|3.367
|1.97 ''R''
|-
|Bismuth
|solid
|0.123
|25.7
|
|1.20
|3.09 ''R''
|-
|Cadmium
|solid
|0.231
|26.02
|
|2.00
|3.13 ''R''
|-
|Carbon dioxide CO<sub>2</sub>
|gas
|0.839
|36.94
|28.46
|
|
|-
|Chromium
|solid
|0.449
|23.35
|
|3.21
|2.81 ''R''
|-
|Copper
|solid
|0.385
|24.47
|
|3.45
|2.94 ''R''
|-
|Diamond
|solid
|0.5091
|'''6.115'''
|
|1.782
|0.74 ''R''
|-
|Ethanol
|liquid
|2.44
|112
|
|1.925
|
|-
|Gasoline (octane)
|liquid
|2.22
|228
|
|1.640
|
|-
|Glass
|solid
|0.84
|
|
|2.1
|
|-
|Gold
|solid
|0.129
|25.42
|
|2.492
|3.05 ''R''
|-
|Granite
|solid
|0.790
|
|
|2.17
|
|-
|Graphite
|solid
|0.710
|8.53
|
|1.534
|1.03 ''R''
|-
|Helium
|gas
|5.1932
|20.7862
|12.4717
|
|
|-
|-
|Hydrogen
| COP
|gas
| Cooling Output / Electrical Input
|'''14.30'''
| 냉동기 효율
|28.82
| 3.0+
|
|
|
|-
|-
|Hydrogen sulfide H<sub>2</sub>S
| PUE
|gas
| Total Facility Power / IT Equipment Power
|1.015
| 데이터센터 에너지 효율
|34.60
| 1.1~1.3
|
|
|
|-
|-
|Iron
| WUE
|solid
| Water Usage (L) / IT Energy (kWh)
|0.449
| 물 사용 효율
|25.09
| 최소화
|
|3.537
|3.02 ''R''
|-
|Lead
|solid
|0.129
|26.4
|
|1.440
|3.18 ''R''
|-
|Lithium
|solid
|3.58
|24.8
|
|1.912
|2.98 ''R''
|-
|Lithium at 181 °C
|solid(?)
|'''4.233'''
|
|
|
|
|-
|Lithium at 181 °C
|liquid
|'''4.379'''
|30.33
|
|2.242
|3.65 ''R''
|-
|Magnesium
|solid
|1.02
|24.9
|
|1.773
|2.99 ''R''
|-
|Mercury
|liquid
|0.1395
|27.98
|
|1.888
|3.36 ''R''
|-
|Methane at 2 °C
|gas
|2.191
|35.69
|
|
|
|-
|Methanol
|liquid
|2.14
|
|68.62
|1.695
|
|-
|Molten salt (142–540 °C)
|liquid
|1.56
|
|
|2.62
|
|-
|Neon
|gas
|1.0301
|20.7862
|12.4717
|
|
|-
|Nitrogen
|gas
|1.040
|29.12
|20.8
|
|
|-
|Oxygen
|gas
|0.918
|29.38
|21.0
|
|
|-
|Paraffin wax
C<sub>25</sub>H<sub>52</sub>
|solid
|2.5 (avg)
|'''900'''
|
|2.325
|
|-
|Polyethylene
(rotomolding grade)
|solid
|2.3027
|
|
|2.15
|
|-
|Silica (fused)
|solid
|0.703
|42.2
|
|1.547
|
|-
|Silver
|solid
|0.233
|24.9
|
|2.44
|2.99 ''R''
|-
|Sodium
|solid
|1.230
|28.23
|
|1.19
|3.39 ''R''
|-
|Steel
|solid
|0.466
|
|
|3.756
|
|-
|Tin
|solid
|0.227
|27.112
|
|1.659
|3.26 ''R''
|-
|Titanium
|solid
|0.523
|26.060
|
|2.6384
|3.13 ''R''
|-
|Tungsten
|solid
|0.134
|24.8
|
|2.58
|2.98 ''R''
|-
|Uranium
|solid
|'''0.116'''
|27.7
|
|2.216
|3.33 ''R''
|-
|Water at −10 °C (ice)
|solid
|'''2.05'''
|'''38.09'''
|
|'''1.938'''
|
|-
|Water at 25 °C
|liquid
|'''4.1816'''
|'''75.34'''
|'''74.55'''
|'''4.138'''
|
|-
|Water at 100 °C
|liquid
|'''4.216'''
|'''75.95'''
|'''67.9'''
|'''3.77'''
|
|-
|Water at 100 °C (steam)
|gas
|'''2.03'''
|'''36.5'''
|'''27.5'''
|'''1.53'''
|
|-
|Zinc
|solid
|0.387
|25.2
|
|2.76
|3.03 ''R''
|}
|}


== Volumetric heat capacity ==
---
The '''volumetric heat capacity''' of a material is the heat capacity of a sample of the substance divided by the volume of the sample.  It is the amount of energy that must be added, in the form of heat, to one unit of volume of the material in order to cause an increase of one unit in its temperature.  The SI unit of volumetric heat capacity is joule per kelvin per cubic meter, J⋅K<sup>−1</sup>⋅m<sup>−3</sup>.<ref>https://en.wikipedia.org/wiki/Volumetric_heat_capacity</ref>


The volumetric heat capacity can also be expressed as the specific heat capacity (heat capacity per unit of mass, in J⋅K<sup>−1</sup>⋅kg<sup>−1</sup>) times the density of the substance (in kg/L, or g/mL).
== Configuration ==


== Thermodynamic Process (Type of transition) ==
<syntaxhighlight lang="bash">
A Thermodynamic process is a process in which the thermodynamic state of a system is changed. A change in a system is defined by a passage from an initial to a final state of thermodynamic equilibrium.<ref>https://en.wikipedia.org/wiki/Thermodynamic_process</ref>
# 서버 TDP 확인
$ cat /proc/cpuinfo | grep "Model name"
$ lspci | grep -i vga


=== Kinds of process ===
# 열 부하 계산 (예시)
# 서버 10대 × 500W TDP = 5kW
# 냉각수 유량: 5 / (4.186 × 5) = 0.24 kg/s = 14.3 L/min


* Cyclic process
# CDU 모니터링
** Defined by a cycle of transfers into and out of a system. A cycle is a sequence of a small number of thermodynamic processes that indefinitely often, repeatedly returns the system to its original state
# CDU 제어 패널에서 공급/반환 온도, 유량 확인
* Flow process
</syntaxhighlight>
** Defined by flows through a system, a flow process is a steady state of flow into and out of a vessel with definite wall properties. especially the states of the inflow and the outflow materials, and, on the side, the transfers of heat, work, and kinetic and potential energies for the vessel
 
=== Kinds of transition ===
{| class="wikitable"
|+Thermodynamic Process, condition and work done
!Type of transition
!Condition
!Work <ref>https://www.youtube.com/watch?v=AzmXVvxXN70</ref>
1st law of thermodynamics, Q = ΔU + W
!Meaning<ref>https://pressbooks.online.ucf.edu/osuniversityphysics2/chapter/thermodynamic-processes/</ref>
|-
|Isochoric (Isovolumetric)
|dV = 0,
|So, W = 0 then


ΔU = Q = n x Cv x ΔT
---
|volume of the system does not change
|-
|Isobaric
|dP = 0,
|So,


ΔU = Q - W
== Examples ==


ΔU = n x Cv x ΔT
=== Example 1: 열 부하 계산 ===


W = P x ΔV
<syntaxhighlight lang="bash">
# 서버 10대 × 500W TDP
# 총 열 부하: 5kW


Q = n x Cp x ΔT
# 냉각수 유량 계산 (ΔT=5°C)
|pressure of the system does not change
# m = 5000 / (4186 × 5) = 0.239 kg/s
|-
# = 14.3 L/min
|Isothermal
|dT = 0,
|So, ΔU = 0 then


0 = Q - W
# CDU 용량: 5kW 이상 선택
</syntaxhighlight>


eg, Q = W
=== Example 2: 냉각수 유량 계산 ===


<syntaxhighlight lang="bash">
# 100kW 열 부하, ΔT=10°C
# m = 100000 / (4186 × 10) = 2.39 kg/s
# = 143 L/min


Where W,
# ΔT=5°C일 때
# m = 100000 / (4186 × 5) = 4.78 kg/s
# = 287 L/min
</syntaxhighlight>


P1V1 ln(V2/V1) or
---


P2V2 ln(V2/v1)
== Best Practices ==
|system at a constant temperature
|-
|Adiabatic
|Q = 0
|So, ΔU = -W


* 열 부하는 서버 TDP 합계为基础로 계산
* ΔT를 높일수록 유량 감소 (에너지 효율 ↑)
* 냉각수 품질 관리 (순도, pH, 전도도)
* 정기적인 열 교환기 청소
* COP 최적화를 위한 냉동기 설정
* PUE 모니터링으로 전체 효율 추적


Where W,
---


W = -Cv/R (P2V2 - P1V1) or
== Limitations ==


W = - n x Cv x ΔT
* 열역학 계산은 이상적인 조건 가정
|no heat is allowed to enter or leave the system by insulation
* 실제 데이터센터는 국소적 핫스팟 존재
|-
* 냉각수 누출, 펌프 고장 등 변수 다수
|cyclic
* 복잡한 유체 역학은 CFD 시뮬레이션 필요
|dE = 0, dH = 0, dP = 0, dV = 0
ΔEint=0
|
|if the state of the system at the end is same as the state at the beginning, state properties such as temperature, pressure, volume, and internal energy of the system do not change over a complete cycle Q=W(cyclic process)
|}


== Measurement thermal conductivity ==
---


* '''Experimental methods'''
== References ==
** Steady-State Heat Flow
** Transient Hot Wire Method
** Laser Flash Analysis


* '''Non-Destructive methods'''
* https://en.wikipedia.org/wiki/Thermodynamics
** infrared thermography, ultrasound, and thermal wave analysis
* https://en.wikipedia.org/wiki/Heat_transfer


== Temperature gradient ==
---
A temperature gradient refers to the difference in temperature between two points in a material or between two adjacent materials. Heat transfer occurs when there is a temperature gradient, with heat flowing from regions of higher temperature to regions of lower temperature. When there is a temperature difference, the system will naturally attempt to balance the temperatures, leading to heat transfer and thermal conductivity


== Related Pages ==


* [[CDU]]
* [[Liquid Cooling]]
* [[Cold Plate]]
* [[Heat Exchanger]]
* [[PUE]]


== References ==
---
<references />
[[Category:Linux]]


[[Category:Cooling]]
[[Category:Reference]]
[[Category:Reference]]

Revision as of 13:27, 15 July 2026

Thermodynamics

Template:Status

Template:TOC

Overview

열역학(Thermodynamics)은 열, 일, 에너지의 변환과 전달을 연구하는 물리학 분야입니다. 데이터센터 냉각 시스템 설계에서 열역학은 냉각 효율 계산, 열 부하 분석, 에너지 소비 최적화의 기초가 됩니다.

Summary

  • 무엇인가? — 열, 일, 에너지의 변환과 전달 연구
  • 왜 필요한가? — 데이터센터 냉각 시스템 설계, 열 부하 분석
  • 언제 사용하는가? — 수냉식 냉각 시스템, CDU 설계, 열 교환기 분석

---

Purpose

이 문서가 존재하는 이유

  • Goal: 열역학 기본 법칙, 열 전달 방식, 데이터센터 냉각 적용 제공
  • Scope: 열역학 법칙, 전도/대류/복사, 엔탈피, 냉각 효율 계산
  • Non-goals: 복잡한 유체 역학 시뮬레이션, 상세 재료 과학

---

Key Concepts

Concept Description Related
열역학 제1법칙 에너지 보존 법칙 Thermodynamics
열역학 제2법칙 엔트로피 증가 법칙 Thermodynamics
전도 (Conduction) 고체 내 열 전달 Thermodynamics
대류 (Convection) 유체 내 열 전달 Thermodynamics
복사 (Radiation) 전자기파 열 전달 Thermodynamics
엔탈피 (Enthalpy) 시스템의 총 열 에너지 Thermodynamics
CDU Cooling Distribution Unit CDU
열 부하 (Heat Load) 데이터센터의 총 발열량 Thermodynamics

---

Architecture

데이터센터 열 전달 경로: 

graph TD
    A[CPU/GPU Chip] -->|전도| B[Heat Spreader]
    B -->|전도| C[Cold Plate]
    C -->|대류| D[냉각수]
    D -->|대류| E[CDU]
    E -->|복사/대류| F[외부 공기]
    G[공기 냉각] -->|대류| F

---

Workflow

Stage Input Output
열 부하 계산 서버 사양, TDP 총 열 부하 (kW)
냉각수 유량 계산 열 부하, ΔT 유량 (L/min)
CDU 용량 결정 총 열 부하 CDU 용량 (kW)
효율 분석 COP, PUE 냉각 효율

---

Detailed Explanation

열역학 제1법칙 (에너지 보존)

에너지는 생성되거나 소멸되지 않고, 형태만 변환됩니다.

Q = ΔU + W

  • Q: 시스템에 공급된 열
  • ΔU: 내부 에너지 변화
  • W: 시스템이 한 일

데이터센터 적용:

  • 서버 전력 → 열 에너지 (거의 100% 열로 변환)
  • 냉각 시스템 → 열을 외부로 배출

열역학 제2법칙 (엔트로피)

열은 항상 고온에서 저온으로 흐릅니다. 자연스러운 과정은 엔트로피를 증가시킵니다.

이 법칙이 데이터센터 냉각의 기본 원리입니다:

  • CPU (고온) → 냉각수 → CDU → 외부 공기 (저온)
  • 열 펌프(냉동기) 없이는 저온으로 열 이동 불가

열 전달 3가지 방식

전도 (Conduction)

고체 내에서 분자 간 충돌로 열이 전달됩니다.

Q = k × A × ΔT / d

  • k: 열전도율 (W/m·K)
  • A: 단면적 (m²)
  • ΔT: 온도차 (K)
  • d: 두께 (m)
    • 주요 재료 열전도율:**
Material Thermal Conductivity (W/m·K)
구리 (Copper) 401
알루미늄 (Aluminum) 237
철 (Steel) 80
스테인리스강 16
실리콘 149

대류 (Convection)

유체(액체/기체)의 운동으로 열이 전달됩니다.

Q = h × A × ΔT

  • h: 대류 열전달 계수 (W/m²·K)
  • A: 표면적 (m²)
  • ΔT: 표면-유체 온도차 (K)
    • 자연 대류 vs 강제 대류:**
  • 자연 대류: 밀도 차이에 의한 유체 운동 (느림)
  • 강제 대류: 팬/펌프에 의한 유체 운동 (빠름)

복사 (Radiation)

전자기파(적외선)로 열이 전달됩니다. 매개체 불필요.

Q = ε × σ × A × (T₁⁴ - T₂⁴)

  • ε: 방사율 (0~1)
  • σ: 스테판-볼츠만 상수 (5.67 × 10⁻⁸ W/m²·K⁴)
  • A: 표면적 (m²)
  • T₁, T₂: 절대온도 (K)

엔탈피 (Enthalpy)

시스템의 총 열 에너지. 냉각 시스템 설계에서 핵심 개념입니다.

H = U + PV

  • H: 엔탈피
  • U: 내부 에너지
  • P: 압력
  • V: 부피

냉각수 엔탈피 변화로 열 전달량 계산:

Q = m × Δh

  • m: 냉각수 질량 유량 (kg/s)
  • Δh: 엔탈피 변화 (kJ/kg)

데이터센터 열 부하 계산

데이터센터의 총 열 부하는 서버 TDP(Thermal Design Power)의 합과 같습니다.

Q_total = Σ TDP_i + Q_other

  • Q_total: 총 열 부하 (kW)
  • TDP_i: 각 서버의 열 설계 전력
  • Q_other: 네트워크, 스토리지, 조명 등 기타 발열
    • 냉각수 유량 계산:**

Q = m × Cp × ΔT

  • Q: 열 부하 (kW)
  • m: 질량 유량 (kg/s)
  • Cp: 비열 (물: 4.186 kJ/kg·K)
  • ΔT: 공급-반환 온도차 (K)
    • 예시:** 100kW 열 부하, ΔT=5°C일 때
  • m = 100 / (4.186 × 5) = 4.78 kg/s ≈ 287 L/min

냉각 효율 지표

지표 Formula Description Target
COP Cooling Output / Electrical Input 냉동기 효율 3.0+
PUE Total Facility Power / IT Equipment Power 데이터센터 에너지 효율 1.1~1.3
WUE Water Usage (L) / IT Energy (kWh) 물 사용 효율 최소화

---

Configuration

# 서버 TDP 확인
$ cat /proc/cpuinfo | grep "Model name"
$ lspci | grep -i vga

# 열 부하 계산 (예시)
# 서버 10대 × 500W TDP = 5kW
# 냉각수 유량: 5 / (4.186 × 5) = 0.24 kg/s = 14.3 L/min

# CDU 모니터링
# CDU 제어 패널에서 공급/반환 온도, 유량 확인

---

Examples

Example 1: 열 부하 계산

# 서버 10대 × 500W TDP
# 총 열 부하: 5kW

# 냉각수 유량 계산 (ΔT=5°C)
# m = 5000 / (4186 × 5) = 0.239 kg/s
# = 14.3 L/min

# CDU 용량: 5kW 이상 선택

Example 2: 냉각수 유량 계산

# 100kW 열 부하, ΔT=10°C
# m = 100000 / (4186 × 10) = 2.39 kg/s
# = 143 L/min

# ΔT=5°C일 때
# m = 100000 / (4186 × 5) = 4.78 kg/s
# = 287 L/min

---

Best Practices

  • 열 부하는 서버 TDP 합계为基础로 계산
  • ΔT를 높일수록 유량 감소 (에너지 효율 ↑)
  • 냉각수 품질 관리 (순도, pH, 전도도)
  • 정기적인 열 교환기 청소
  • COP 최적화를 위한 냉동기 설정
  • PUE 모니터링으로 전체 효율 추적

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Limitations

  • 열역학 계산은 이상적인 조건 가정
  • 실제 데이터센터는 국소적 핫스팟 존재
  • 냉각수 누출, 펌프 고장 등 변수 다수
  • 복잡한 유체 역학은 CFD 시뮬레이션 필요

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References

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Related Pages

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