宇 宙 航 空 研 究 開 発 機 構 研 究 開 発 資 料

JAXA Ｒesearch and Development Memorandum

ジェットエンジンサイクル検討における熱力学物性値について

二村 尚夫

宇宙航空研究開発機構研究開発資料

2011年2月

JAXA-RM-10-016宇宙航空研究開発機構研究開発資料

ੑ᧛ ዏᄦ

Thermodynamic properties of working substances on jet engine cycle studies

Hisao FUTAMURA

ABSTRACT

Thermodynamic properties of chemical equilibrium air is calculated and compared with available data. Thermodynamic functions are tabulated and partial pressures of spiecies are drawn on charts.

Keywords; thermodynamics; chemical equilibrium; sandard atmosphere; themodynamic function; equation of state; virial coefficient

᭎ ⷐ

ࠫࠚ࠶࠻ࠛࡦࠫࡦߦ߅ߌࠆᾲജቇ,ౝㇱⓨ᳇ജቇߦ㊀ⷐߣߥࠆⓨ᳇ߩᾲജቇ‛ᕈ୯ߦ㑐ߒ,ᢙ⒳㘃ߩၮ␆ᑼ,ᾲജቇ࠺

࡯࠲ࠍㆡ↪ߔࠆ႐วߦߟ޿ߡ,ታ↪▸࿐ߦ߅޿ߡ૶↪ߐࠇࠆᾲജቇ㑐ᢙࡕ࠺࡞߇߽ߚࠄߔᏅ⇣ࠍ᣿ࠄ߆ߦߔࠆߣߣ߽

ߦ,ඨℂᗐ᳇૕ߣߒߡขࠅᛒߞߚ႐วߩၮᧄ⊛ߥ࠺࡯࠲ᢙ⴫ࠍ⚫੺ߔࠆ.

⸥ภ

C_v ቯኈᾲኈ㊂(ቯኈᲧᾲ) U ౝㇱࠛࡀ࡞ࠡ࡯

Cp ቯ࿶ᾲኈ㊂(ቯ࿶Ყᾲ) Z ࿶❗ଥᢙ,㜞ᐲ G ࠡ࠶ࡉࠬߩ⥄↱ࠛࡀ࡞ࠡ࡯ f ࡈࠟࠪ࠹ࠖ

H ࠫࠝࡐ࠹ࡦࠪࡖ࡞㜞ᐲ n ࡕ࡞ᢙ

P ࿶ജ,ಽ࿶ v ᲧኈⓍ

R ৻⥸ࠟࠬቯᢙ Kp ࿶ജᐔⴧቯᢙ

S ࠛࡦ࠻ࡠࡇ࡯ Kf ↢ᚑᐔⴧቯᢙ

T ᷷ᐲ Ƕ 㔚㔌ᐲ

ߪߓ߼ߦ

JAXA⥶ⓨࡊࡠࠣ࡜ࡓࠣ࡞࡯ࡊߢߪ,ᐔᚑ15ᐕᐲࠃࠅޟࠢ࡝࡯ࡦࠛࡦࠫࡦᛛⴚߩ⎇ⓥ㐿⊒ޠ੐ᬺࠍㅴ߼ߡ޿ࠆ.ᒰ੐ᬺ

ߩ⋡⊛ߣߔࠆ⥶ⓨࠛࡦࠫࡦߩⅣႺㆡวᕈᡷༀߦ㑐ߔࠆᜰᮡ,ߔߥࠊߜ,ࠛࡦࠫࡦ㛍㖸ૐᷫ,ࠛࡦࠫࡦឃ᳇ਛߩ᦭ኂ‛⾰ૐᷫ,

ੑ㉄ൻ὇⚛ឃ಴ߩ೥ᷫߩᐲว޿ߪ,ቯ߼ࠄࠇߚࡕ࠺࡞ᄢ᳇ߦኻߒߡ,ታ㓙ߩ㘧ⴕᤨ,߽ߒߊߪ࿾਄ㆇォᤨߦ߅ߌࠆ࠺࡯࠲ࠍ

ୃᱜߔࠆᒻߢ⹏ଔߐࠇࠆߩ߇ᮡḰߢ޽ࠅ,ᒰ੐ᬺ߽ߥࠆߴߊ,ߎࠇߦᴪߞߚᒻᑼߢߩ⹏ଔࠍ⋡ᜰߒߡ޿ࠆ.ߎߩ㓙,㘧ⴕ⁁ᘒ ߣࠛࡦࠫࡦㆇォ⁁ᘒߩ⚵ߺวࠊߖߦࠃࠅ,ࠛࡦࠫࡦࠨࠗࠢ࡞ਛߩઍ⴫ὐߦ߅ߌࠆ᷷ᐲ,࿶ജ,Ά὾ࠟࠬ⚵ᚑߪᄢ߈ߊᄌൻߒ, ฦⷐ⚛ߩᕈ⢻,ో૕ᕈ⢻ߦ߽ᓇ㗀߇෸߱น⢻ᕈ߇޽ࠆ.ߎߩࠛࡦࠫࡦౝㇱߩᾲ⊛,ᵹ૕⊛⁁ᘒߩ᭎⇛ࠍᛠីߔࠆၮߦߥࠆߩ ߇ᾲജቇߦࠃࠆࠛࡦࠫࡦࠨࠗࠢ࡞⸘▚ߢ޽ࠅ,૞േᵹ૕ߩᾲ‛ᕈ࠺࡯࠲ߢ޽ࠆ.JAXA ߢߪᓥ᧪ࠃࠅ,ࠫࠚ࠶࠻ࠛࡦࠫࡦ,ࡠ ࠤ࠶࠻ࠛࡦࠫࡦߩᕈ⢻ផቯ߅ࠃ߮ᭂ⿥㖸ㅦⓨ᳇ജቇߩಽ㊁ߢൻቇᾲജቇ⸘▚ࠍ೑↪ߒߡ޿ࠆ^1-5)㧚

ᾲജቇ⊛ขࠅᛒ޿ߩ⢛᥊

19਎♿ߦቢᚑߒߚฎౖᾲജቇ,߅ࠃ߮ 20 ਎♿೨ඨߦቢᚑߒߚ㊂ሶ⛔⸘ᾲജቇߦ㑐ߒߡߪ,ℂ⺰⊛ߥขࠅᛒ޿ߪ,౉ᚻ น⢻ߥ,޿ߕࠇߩᢎ⑼ᦠߦࠃߞߡ߽,ߐ߶ߤᄢ߈ߥᏅ⇣߇ή޿ߣ⠨߃ࠄࠇࠆ.߻ߒࠈ,ߘߩᓟߩ⸘▚ᯏߩ⊒㆐ߩᕲᕺࠍฃ ߌߡ,ᣥ᧪ߩᢙ⴫ߦ㗬ࠆ೑↪ᴺ߆ࠄ,ၮ␆ᑼ,ㄭૃᑼࠍ↪޿ߚᢙ୯⸃ᨆߦㆡ↪ᣇᴺ߇⒖ߞߡ߅ࠅ,ᢙ⴫૞ᚑᤨߩ⸘▚⺋Ꮕ,

⺋ᬀࠃࠅ,ណ↪ߔࠆၮ␆ᑼ,ൻቇ⒳,ㄭૃᑼዉ಴ᤨߩ೨ឭ᧦ઙߩี๧߇ᄢಾߦߥߞߡ޿ࠆ.߹ߚ,╙㧞ߩ໧㗴ߣߒߡ㧿㧵න

૏♽ߩ਎⇇⊛ߥណ↪,㧵㨁㧼㧭㧯ߩ᷷ᐲ,࿶ജၮḰᄌᦝߩߚ߼,ᓥ᧪ߩᑼ,ᢙ⴫ߩਛߦߪ૶↪਄ߩ⠨ᘦ߇ᔅⷐߦߥߞߡ޿

ࠆ߽ߩ߇⃻ࠇߡ޿ࠆ.ᧄ␠࿑ᦠ㙚߅ࠃ߮୘ੱ෼⬿ߩෳ⠨ᢥ₂ߦ߽⋥ធᲧセ߇࿎㔍ߥ߽ߩ߇޽ࠅ,ᣂ㞲๧ߪή޿߇หߓᖠ ߺࠍᛴ߃ࠆੱߩߚ߼ߦℂ⸃ߒ߿ߔߊ,೑↪ߢ߈ࠆౠሶߣߔࠆߎߣࠍ⋡⊛ߣߒߡ޿ࠆ.ߥ߅,ࠟࠬߩ㕖ℂᗐᕈߩ߁ߜૐ᷷, 㜞࿶ߦ߅ߌࠆ࿶ജߩᓇ㗀ߦߟ޿ߡߪ,⛯ႎߦߡขࠅᛒ߁.

࿾⃿࡮ᄢ᳇

ᄢ᳇⚵ᚑߣ᭴ㅧ

ቝቮ‛ℂቇߩಽ㊁ߢߪ,⑼ቇ⊛ߥⷰኤߣࠪࡒࡘ࡟࡯࡚ࠪࡦߦࠃࠅᄥ㓁♽ౝฦᖺᤊ,ⴡᤊߩᄢ᳇ߩ⸃᣿߇ㅴࠎߢ߅ࠅ,ฦ ᖺᤊ,ⴡᤊߩᄢ᳇࠺࡯࠲ߩขᓧߣᄢ᳇ࡕ࠺࡞ߩ᭴▽߇ㅴࠎߢ޿ࠆ ⁶⁾.࿾⃿ᄢ᳇ߪઁߩᖺᤊߣ⇣ߥࠅ,ੑ㉄ൻ὇⚛߇ዋߥߊ,

㉄⚛߇⼾ንߥ․ᓽࠍ᦭ߒ,ߐࠄߦ࿾⴫㕙Ⓧߩ70%ࠍභ߼ࠆᶏ᳓ߣᄢ᳇ߩ㑆ߢ᳓߇⫳⊒ߒ,㔕ߣߥߞߡ⒖േߒ,㒠㔎,㒠㔐ߣ ߒߡ㒽᳓ߣߥࠅ,ᴡᎹࠍ⚻↱ߒߡᶏߦᚯࠆᓴⅣߦࠃࠅ,േᬀ‛ߩ↢ᕷⅣႺࠍ⛽ᜬߒߡ޿ࠆ.⥶ⓨᯏߩ㘧ⴕߔࠆ࿾⃿ᄢ᳇ߪ, ႐ᚲ,ቄ▵ߦࠃߞߡ․ᕈߣᵹേ⁁ᘒ߇⇣ߥࠅ,ᣣޘ,ᤨޘೞޘߣ⃻ࠇࠆᄌൻࠍ᳇⽎ቇߪขࠅᛒߞߡ޿ࠆ.ᄥ㓁♽ࠬࠤ࡯࡞

ߢߺࠇ߫,ᄢ᳇ߪቝቮ߹ߢㅪ⛯⊛ߦᐢ߇ߞߡ߅ࠅ,ᶏ㕙ߩࠃ߁ߦႺ⋡߇޽ࠆ⸶ߢߪߥ޿.ߚߛߒ,ߘߩᕈ⾰ߪ৻᭽ߢߪߥ ߊ,࿾⴫ㄭߊߢߪ࿾⃿ߩ⥄ォ߿ᣣᾖ,ᶏ㒽ߩᓇ㗀߇޽ࠅ,ု⋥ᣇะߦߪኻᵹ࿤,ᚑጀ࿤,ਛ㑆࿤,ᾲ࿤╬ߩ࿤⇇߇ሽ࿷ߒ,ߐࠄ ߦ⿥㜞ጀߦ߅޿ߡߪᄥ㓁߆ࠄߩ⩄㔚☸ሶ,ቝቮ✢ߩᓇ㗀ࠍฃߌߡ޿ࠆ.

⥶ⓨᯏ⸳⸘࡮⹜㛎ߩታ↪⊛ߥ࿾⃿ߩᄢ᳇ࡕ࠺࡞߇㧵㧿㧻ߩᮡḰߣߒߡ೙ቯߐࠇߡ߅ࠅ⁷⁾,໡ขᒁࠍ฽߼ᐢߊ೑↪ߐࠇ ߡ޿ࠆ.ᮡḰᄢ᳇ߩ㜞ᐲ 85㨗㨙એਅߦ߅޿ߡߪ,ߘߩൻቇ⊛⚵ᚑߪ৻ቯߣߺߥߐࠇߡ߅ࠅ,రߦߥߞߚ☨࿖ᮡḰᄢ᳇

1976ߦߪ⴫1ߦ␜ߔᢙ୯߇ቯ߼ࠄࠇߡ޿ࠆ⁸⁾.ᓥ೨ߩᮡḰᄢ᳇ߣ߽߶߷৻⥌ߒߡ߅ࠅ,1948ᐕߩ࿖㓙᳇⽎ቇળߩቯ߼ߚ

⚵ᚑߣ੐ታ਄৻⥌ߒߡ޿ࠆ.

⴫1 ࿖㓙ᮡḰᄢ᳇ߩ⚵ᚑ⁸⁾

ൻቇ⒳ ಽሶ⸥ภ ಽሶ㊂[kg/kmol] ࡕ࡞ಽ₸ ⚥Ⓧ

⓸⚛ N2 28.0134 0.78084 0.78084

㉄⚛ O2 31.9988 0.209476 0.990316

ࠕ࡞ࠧࡦ Ar 39.948 0.00934 0.999656

ੑ㉄ൻ὇⚛ CO2 44.00995 0.000314* 0.99997

ࡀࠝࡦ Ne 20.183 0.00001818 0.99998818

ࡋ࡝࠙ࡓ He 4.0026 0.00000524 0.99999342

ࠢ࡝ࡊ࠻ࡦ Kr 83.80 0.00000114 0.99999456

ࠠ࠮ࡁࡦ Xe 131.30 0.000000087 0.99999543

ࡔ࠲ࡦ CH4 16.04303 0.000002 0.99999743

᳓⚛ H2 2.01594 0.0000005 0.99999793

એਅߪJIS W 0201-1990 ߦࠃࠆ

৻㉄ൻ⓸⚛ N2O 44.0128 0.0000005* 0.99999843

ࠝ࠱ࡦ(ᄐ) O3 47.9982 0.0000007߹ߢ 0.99999913

ࠝ࠱ࡦ(౻) O3 47.9982 0.0000002߹ߢ 0.99999913

ੑ㉄ൻ⎫㤛 SO2 64.0628 0.000001߹ߢ 1.0

ੑ㉄ൻ⓸⚛ NO2 46.0055 0.0000002߹ߢ 1.0

ࠃ߁⚛ I2 253.8088 0.0000001߹ߢ 1.0

ᵈ*ࠟࠬߩ฽㊂ߪ,ᤨೞ෶ߪ႐ᚲߦࠃߞߡᄢ߈ߊᄌേߔࠆߎߣ߇޽ࠆ.

߹ߚ,ᮡḰᄢ᳇ߦ߅ߌࠆု⋥ᣇะߩ᷷ᐲߣ᷷ᐲ൨㈩ߪ⴫2ߩࠃ߁ߦቯ߼ࠄࠇߡ޿ࠆ.

⴫

ᮡḰᄢ᳇ߩ㜞ᐲᄌൻ

ࠫࠝࡐ࠹ࡦࠪࡖ࡞

㜞ᐲ

ಽሶࠬࠤ࡯࡞᷷ᐲ ൨㈩

ᄢ᳇᷷ᐲ

ᄢ᳇࿶

-2.00 -6.5 301.15

0 -6.5 288.15 101325

11 0.0 216.65 22632

20 1.0 216.65 5474.8

32 2.8 228.65 868.01

47 0.0 270.65 110.90

51 -2.8 270.65 66.938

71 -2.0 214.65 3.9564

84.8520 187.65 0.39814

ᄌേᚑಽ

⴫

ߦ␜ߐࠇࠆੑ㉄ൻ὇⚛

৻㉄ൻ⓸⚛ߪᄢ᳇⚵ᚑ਄ߩᄌേ߇⹺߼ࠄࠇߡ޿ࠆ

߹ߚ

⴫߆ࠄ㒰ᄖߐࠇߡ޿ࠆ᳓ߪ࿾⃿

ⅣႺࠍ․ᓽઃߌࠆ਄ߢᦨ߽ᓇ㗀ࠍ෸߷ߒߡ޿ࠆ‛⾰ߢ޽ࠅ

㔕

㔎

㔐

㔵

㔮

᳖ߣ࿾਄ߩ᳇⽎᧦ઙਅߢ߽࿕૕

ᶧ૕

᳇૕

ߣߘߩᕈ⁁ࠍᄌ߃ࠆ

⴫

ߩൻቇ⒳߇࿾⃿⴫㕙਄ߩ޿߆ߥࠆ႐ᚲ

ᤨ㑆ߦ߅޿ߡ߽

߶߷৻ቯߩᄢ᳇⚵ᚑࠍ␜ߔߩߦኻߒ

᳓ಽߪ႐ᚲߣᤨ㑆ߦࠃࠅ

ߐ߹ߑ߹ߦᄌൻߒ

฽᦭㊂ߪᦨᄢ

ߦ㆐ߔࠆߣ޿߁

ᮡḰᄢ᳇ߩ߽ߣߣߥߞߚ

ߩ೨ᢥᛮ☴ࠍઃ㍳ߦ⸥ߔ

ⓨ᳇ߩ‛ᕈ୯

ᮡḰᄢ᳇ߩ‛ᕈ୯

⥶ⓨᯏߩ⊓႐ߒߚ

਎♿ೋ㗡ߦߪ᳇⽎ቇߪߔߢߦ⏕┙ߐࠇߡ߅ࠅ

ฦ࿖߇᳇⽎บࠍ⸳⟎ߒߡቯᏱ⊛ߥ᷹ⷰࠍⴕߞߡ

޿ߚ

߹ߚᄢ᳇ߩ㜞ᐲᄌൻߦ㑐ߒߡ߽㜞ጊ

᳇⃿ߦࠃࠆ᷹ⷰߥߤߢ᷷ᐲ

࿶ജߩᄌൻߣᾲജቇ⊛ᕈ⾰߽ℂ⸃ߐࠇߡ޿ߚ

⧷࿖

᰷Ꮊߢߪ⥶ⓨ⸘ེߩၮḰߣᩞᱜߩᔅⷐᕈ߇޽ࠅ

╙৻ᰴᄢᚢᓟߩᣧߊ߆ࠄᮡḰᄢ᳇೙ቯߩേ߈߇޽ࠅ

ߎࠇߦ๭ᔕ ߒߡ☨࿖ߢ߽

߇

ᐕߦ

ࠍ⊒ⴕߒ

ᐕߩ

⊒⿷ߦ㓙ߒ

࿖㓙⊛ᄢ᳇⴫೙

૞ߩⷐ᳞ߦၮߠ߈

ࠍ⊒ⴕߒߡ޿

ࠆ

೨㗄ߦ߽␜ߒߚߣ߅ࠅ

ᄢ᳇ߩᕈ⁁ߪ᳓ಽࠍ㒰޿ߡߪ

᷷ᐲ

㨪

࿶ജ

㨪

᳇࿶ߩൻቇ⊛⚵ᚑ߇৻ቯߩᷙ

ว᳇૕ߣߺߥߐࠇࠆ

ߎߩ᷷ᐲ

࿶ജߩ▸࿐ߢߪ

ੇ῎ߒߚⓨ᳇ߪඨℂᗐ᳇૕ߣߒߡᛒ߁ߎߣ߇น⢻ߢ޽ࠆ

ߩቯ⟵ߔࠆਅጀᄢ᳇

એਅ

ߦ㑐ߔࠆቯᢙ⟲ߪ⴫

ߣ߅ࠅߢ޽ࠆ

⴫

‛ℂቯᢙ╬

ቯᢙ ⸥ภ ୯ න૏

ࡏ࡞࠷ࡑࡦቯᢙ

˜

ࠕࡏࠟ࠼ࡠᢙ

˜

৻⥸ࠟࠬቯᢙ

˜

㊀ജቯᢙ

ၮḰᶏ㕙਄ᄢ᳇࿶

˜

࿾⃿ඨᓘ

˜

ၮḰᶏ㕙਄ᄢ᳇᷷ᐲ

ࠨࠩ࡜ࡦ࠼ቯᢙ

ࠨࠩ࡜ࡦ࠼☼ᕈᑼਛߩቯᢙ Ǫ

˜

ⓨ᳇ߩᲧᾲᲧ ǫ

ᐔဋ᦭ലⴣ⓭ඨᓘ ǻ

˜

߹ߚ,ᐔⴧߩ઒ቯߣߒߡ,86km એਅߢߪ,ᄢ᳇ߪ㜞ᐲߦࠃࠄߕੇ῎ߒߚ⚵ᚑ৻ቯߩℂᗐ᳇૕ߢ޽ࠅ,࠳࡞࠻ࡦߩಽ࿶ߩᴺ

ೣ߇ᚑࠅ┙ߟߣߐࠇߡ޿ࠆ.

ߎߎߢ㊀ജࡐ࠹ࡦࠪࡖ࡞ߪ,ਁ᦭ᒁജࡐ࠹ࡦࠪࡖ࡞ߣ㆙ᔃജࡐ࠹ࡦࠪࡖ࡞ߩ๺ߢ޽ࠅ,ߎࠇࠍ߽ߣߦࠫࠝࡐ࠹ࡦࠪࡖ

࡞㜞ᐲ߇ቯ⟵ߐࠇߡ޿ࠆ.㊀ജቯᢙߪ✲ᐲ45qߦ߅ߌࠆᶏ㕙਄ߩᐔဋ㊀ജߣߒߡቯ߼ࠄࠇߚ߇,෩ኒߦߪ45ࠑ32̡33̢ ߩ୯ߢ޽ࠆ.

ᧄႎߢߪ,ⓨ᳇߅ࠃ߮Ά὾ࠟࠬߩ᭴ᚑಽሶࠍ㧔ඨ㧕ℂᗐ᳇૕ߩᷙวࠟࠬߣߒߡขᛒ߁ߎߣࠍᔨ㗡ߦ߅߈,㕖ℂᗐᕈࠍ

ี๧ߒߡୃᱜߔࠆߎߣࠍ⠨߃ߡ޿ࠆߩߢ,ฦಽሶߩᾲജቇ⊛․ᕈߣࡕ࡞ಽ₸߆ࠄᗐቯߐࠇࠆᓇ㗀ࠍ⠨߃ࠆ.

ℂᗐ᳇૕ߩ᧦ઙߪ೰૕ಽሶࡕ࠺࡞☸ሶߩቢోᒢᕈⴣ⓭߆ࠄዉ߆ࠇࠆCv(T)㧩ቯᢙ,߆ߟ Pv=nRT ߥࠆ⁁ᘒᣇ⒟ᑼߦᓥ ߁ߎߣߢ޽ࠆ.ߎࠇߦኻߒ,ඨℂᗐ᳇૕ߪ᳇૕᭴ᚑ☸ሶߩ࿁ォ,ᝄേ,㔚ሶബ⿠ߦࠃࠆౝㇱࠛࡀ࡞ࠡ࡯U߇U=Cv(T)Tߦ߅

޿ߡ Cv(T)ҁቯᢙߢ޽ࠅߥ߇ࠄ,Pv=nRT ߦᓥ߁ߣߺߥߔߎߣߦ޽ࠆ.ฦ᳇૕ᚑಽߪ‛⾰ߣߒߡࡋ࡝࠙ࡓࠍ㒰߈ਃᘒࠍ␜

ߒ߁ࠆߩߢ,㘻๺✢ౝ߅ࠃ߮,ߘߩㄭறߢߪ,ߎߩ᧦ઙࠍḩߚߐߥ޿.ታ࿷᳇૕ߢߪ,᭴ᚑൻቇ⒳㑆ߩൻቇ෻ᔕᐔⴧࠍ⠨ᘦ ߔࠆߎߣߣ,೰૕෻⊒ߩઍࠊࠅߦឃ㒰૕Ⓧߣಽሶ㑆ജࠍಽሶ㑆〒㔌ߩ㑐ᢙߣߒߡ,ಽሶ㑆ࡐ࠹ࡦࠪࡖ࡞ࠍቯ⟵ߒ,ਥߦ࡟

࠽࡯࠼࡚ࠫ࡯ࡦ࠭ဳࡐ࠹ࡦࠪࡖ࡞ߣᄙේሶಽሶߦ߅ߌࠆ㆙ᔃജߦࠃࠆࡐ࠹ࡦࠪࡖ࡞ߩᄌᒻߦၮߠ޿ߡ⸘▚ߐࠇࠆ࿶❗

ଥᢙZ=Pv/RTߩ୯ߦ㑐ߔࠆ1߆ࠄߩਵ㔌ߩ⒟ᐲߦࠃߞߡ,ߘߩ㕖ℂᗐᕈ߇␜ߐࠇࠆ.

ታ࿷ലᨐࠍ฽߻⁁ᘒᣇ⒟ᑼߦߪ,ࡈࠔࡦ࡮࠺࡞࡮ࡢ࡯࡞ࠬߩ⁁ᘒᣇ⒟ᑼߩઁ,ߐ߹ߑ߹ߥ⁁ᘒᣇ⒟ᑼ߇ឭ᩺ߐࠇߡ޿

ࠆ߇,ฦ᳇૕ᚑಽߦ㑐ߒ⛔৻⊛ߥ࠺࡯࠲߇↪ᗧߐࠇߡ޿ߥ޿⁁ᴫਅߢߪ,ࡆ࡝ࠕ࡞⁁ᘒᣇ⒟ᑼࠍ↪޿ࠆߩ߇ᅷᒰߢ޽ࠆ.

࿶❗ଥᢙߪૐ࿶ߢߪ⌀ⓨߦㄭߠߊߦㅪࠇℂᗐ᳇૕ߦㄭߠߊ߇,⥃⇇᷷ᐲઃㄭߩૐ᷷ߢߪ 1 એਅߦߥࠅ,ㅒߦ㜞᷷ߢߪ

୘ޘߩಽሶߩ෻⊒ജ߇ᄢ߈ߊ,1 એ਄ߣߥࠆ.ߐࠄߦ㜞᷷ߢߪಽሶߩ⸃㔌,ߐࠄߦ⿥㜞᷷ߢߪ㔚㔌ࠍ↢ߓ,ⓨ᳇ߩൻቇ⚵ᚑ ߇ᄌൻߔࠆߎߣߦߥࠆ.

෻ᔕ,⋧ᄌൻߥߤ,ㆊ⒟ߩ೨ᓟߢᷙว‛߇ᤨ㑆⊛ߦ቟ቯߒߡሽ࿷ߔࠆ⁁ᘒ,ߔߥࠊߜ♽ߩൻቇᐔⴧࠍ⠨߃ࠆ਄ߢߪ,ో ൻቇ⒳ߩࠡࡉࠬߩ⥄↱ࠛࡀ࡞ࠡ࡯Gi(P,T)ߩ✚๺߇ᦨዊߣߥࠆߎߣߦ╬ߒ޿߇,⸘▚ᣇᴺߣߒߡߪ,⥄↱ࠛࡀ࡞ࠡ࡯ᦨዊ ൻᴺߣᐔⴧቯᢙᴺߩੑߟߩታ↪⊛ߥᣇᴺ߇㐿⊒ߐࠇߡ߅ࠅ,ᓟ⠪ߦ߅޿ߡߪ,ඨℂᗐ᳇૕ߩᐔⴧቯᢙࠍታ࿷᳇૕ߦߟ޿

ߡ૶↪ߔࠆ႐ว,࿶ജPߩઍࠊࠅߦࡈࠟࠪ࠹ࠖfࠍ↪޿ࠆߎߣߢห᭽ߩ⚿ᨐࠍᓧࠆߎߣ߇ߢ߈ࠆ.

ࠛࡦࠫࡦࠨࠗࠢ࡞ਛߢߩⓨ᳇ߩ‛ᕈ୯

ਅጀᮡḰᄢ᳇ߩᾲ‛ᕈ୯ߩᅷᒰᕈߩ߽ߣߢ,ߎߩ⁁ᘒࠍⅣႺߣߔࠆ㐿᡼♽ߩᾲࠨࠗࠢ࡞ࠍ᭴ᚑߔࠆߎߣࠍ⠨߃ࠆ.ⓨ

᳇߅ࠃ߮὇ൻ᳓⚛Ά὾↢ᚑࠟࠬਛߩฦൻቇ⒳ߩ㕖ℂᗐᐲߪ࿶❗ଥᢙ߹ߚߪࡈࠟࠪ࠹ࠖߦࠃߞߡี๧น⢻ߢ޽ࠆ.߹ߚ, 㜞᷷⁁ᘒߢߪᾲ⸃㔌,ൻቇ෻ᔕ߇↢ߓ,⚵ᚑߘߩ߽ߩ߇ᄌൻߔࠆ.

㔚㔌ߩน⢻ᕈ

JANAF⴫ߦߪ,㔚ሶ,ࠗࠝࡦ߽ឝタߐࠇߡ޿ࠆ.ൻቇᐔⴧ⁁ᘒߦ޽ࠆ㔚᳇⊛ߦਛᕈߥൻቇ⒳MߣߘߩࠗࠝࡦM⁺,M-ߘࠇߙ

ࠇߩ᳇⋧✚᜝෻ᔕᑼߩ㑐ଥߪ

M = M⁺ + e^- ߅ࠃ߮

M + e^- = M^-

ߢ޽ࠅ,࿶ജᐔⴧቯᢙߪฦಽሶ,ࠗࠝࡦ,㔚ሶߩ↢ᚑᐔⴧቯᢙߣ㔚㔌ᐲǶࠍ↪޿ߡ Kp(T) = Kf(T)_M⁺ Kf(T)_e^- / Kf(T)_M =[P_M⁺][P_e^-]/[P_M] =Ƕ²/(1-Ƕ) Kp(T) = Kf(T)_M^- / Kf(T)_M Kf(T)_e^- =[P_M-]/[P_M][P_e^-] =Ƕ/(1-Ƕ)² ߣ⴫ߐࠇࠆ.ᱜ⽶ߩࠗࠝࡦỚᐲߪ╬ߒ޿ߩߢ

Kf(T)_M⁺ Kf(T)_e^- / Kf(T)_M =[P_M⁺][P_e^-]/[P_M] =[P_M⁺]²/[P_M]

Kf(T)_M^- Kf(T)_e^- / Kf(T)_M =[P_M^-][P_e^-]/[P_M] =[P_M^-]²/[P_M]

ߣߥࠆ.㔚ሶߪᮡḰ↢ᚑ‛⾰ߥߩߢlog Kf = 0ߢ޽ࠅ,ࠗࠝࡦỚᐲߪ⚿ዪ,

[P_M⁺] = л(Kf(T)_M⁺ Kf(T)_e^- / Kf(T)_M)* л[P_M]= лKf(T)_M⁺ / Kf(T)_M л[P_M]

[P_M^-] = л(Kf(T)_M^- Kf(T)_e^- / Kf(T)_M)* л[P_M]= лKf(T)_M^- / Kf(T)_M л[P_M]

ߣߥࠆ.

ᏗࠟࠬAr, Ne, Kr, XeߩࠗࠝࡦAr⁺, Ne⁺, Kr⁺, Xe⁺ߣ㔚ሶߣߩ㔚㔌෻ᔕᑼߪ,଀߃߫ࠕ࡞ࠧࡦߢߪ Ar ϼ Ar⁺ + e^- ߩ㔚㔌ᐔⴧ⁁ᘒߦኻߒߡߪ,Ꮧ߽ࠟࠬᮡḰ↢ᚑ‛⾰ߢlog Kf = 0ߢ޽ࠅ,

Kp(T) = P_Ar⁺ P_e^- / P_Ar

log Kp(T) =log Kf_Ar⁺ +log Kf_e^- - log Kf_Ar = log Kf_Ar⁺ Kp(T) = Kf_Ar⁺

㔚㔌ᐲǶ<<1ߩ᧦ઙਅߢ,Ƕ=лKf_Ar⁺ߣ⴫ߐࠇࠆ.⴫4ߦઍ⴫⊛᷷ᐲߦ߅ߌࠆᏗࠟࠬߩ㔚㔌ᐲࠍ␜ߔ.

⴫4 Ꮧࠟࠬߩ㔚㔌ᐲ

T/K Ƕ_Ar⁺ Ƕ_Ne⁺ Ƕ_He⁺ Ƕ_Kr⁺ Ƕ_Xe⁺ 300K

㪈㪇

㪈㪇

㪈㪇

㪈㪇

㪈㪇

1000K

㪈㪇

㪈㪇

㪈㪇

㪈㪇

㪈㪇

2000K

㪈㪇

㪈㪇

㪈㪇

㪈㪇

㪈㪇

3000K

㪈㪇

㪈㪇

㪈㪇

㪈㪇

㪈㪇

6000K

㪈㪇

㪈㪇

㪈㪇

㪈㪇

㪈㪇

ߘߩઁߩ C,N,H,Oࠃࠅวᚑߐࠇࠆࠗࠝࡦߩᐔⴧቯᢙߦߟ޿ߡߪ,NO2-,CO2-ߥߤᏱ᷷ߢ logKf>0ߩࠗࠝࡦ߽޽ࠆ.ߐࠄߦ

ᷙวࠟࠬߩ㔚㔌ߦߟ޿ߡߪ[P_M⁺]ҁ[P_e^-],[P_M^-]ҁ[P_e^-]ߢ޽ࠆ߆ࠄ,㔚ሶߩኒᐲ߇㕖Ᏹߦ㜞ߌࠇ߫,ࠗࠝࡦ߇↢ߓࠆน

⢻ᕈߪ޽ࠆ߇,ታ㓙໧㗴ߣߒߡߪ,㔚᳇⊛ߦਛᕈߢ޽ࠆⓨ᳇ߢߪᱜߩࠗࠝࡦߩᢙએ਄ߦߪ㔚ሶ߇ሽ࿷ߔࠆ⁁ᴫߪ޽ࠅᓧ ߥ޿.ᓟㅀߔࠆൻቇᐔⴧ⸘▚⚿ᨐߢߪ,ࠢ࡝࡯ࡦࠛࡦࠫࡦ⎇ⓥ߇ኻ⽎ߣߔࠆᄢ᳇߅ࠃ߮ࠛࡦࠫࡦౝㇱ⁁ᘒߦ߅޿ߡ,ߘߩ ࡕ࡞ಽ₸ߪ0.01%એਅߣߥߞߡ޿ࠆޕᓥߞߡ3000Kࠍ਄㒢ߣߔࠆࠟࠬ࠲࡯ࡆࡦࠨࠗࠢ࡞ࠍ⠨߃ࠆ਄ߢ㜞᷷ߢߩ㔚㔌ߪ

⠨ᘦߒߥ޿ߢࠃ޿ߎߣߦߥࠆ.

ᓥ᧪ߩ࠺࡯࠲ߦ㑐ߔࠆ⠨ኤ

૶↪ߐࠇࠆ࿶ജ᷷ᐲ▸࿐

ᶧൻࠟࠬࠍ㒰޿ߡߪ,ࠛࡦࠫࡦࠨࠗࠢ࡞ߦ૶↪ߐࠇࠆ࿶ജߪᎼ⥶น⢻ߥ㜞ᐲߦ߅ߌࠆᄢ᳇࿶ജ߆ࠄ㜞࿶ജᲧߩ࠲࡯

ࡏࡈࠔࡦ࿶❗ᯏ಴ญ࿶ജ,᷷ᐲߪૐ᷷ᣣߩᚑጀ࿤᷷ᐲ߆ࠄ,὇ൻ᳓⚛ߩᒰ㊂ᲧΆ὾᷷ᐲ⒟ᐲ߇ࠨࠗࠢ࡞⸃ᨆߦᔅⷐߥ▸

࿐ߢ޽ࠆ.৻ᣇߢ,ᐢߊ૶ࠊࠇߡ޿ࠆᾲജቇ‛ᕈ୯⴫ߪߐࠄߦᐢ޿▸࿐ߢ⸘▚ߐࠇߡ޿ࠆ.

ᄢ᳇⴫

2.2.1ߦㅀߴߚߣ߅ࠅ,ታ㓙ߩᄢ᳇⁁ᘒߢߪߥߊ,ࡕ࠺࡞ൻߐࠇߚᄢ᳇ߢ޽ࠆ㧚ਥߥ߽ߩߣߒߡઁߦ,

1) NACAߦࠃࠆ߽ߩ(ᢥ₂12~14), 2) ☨࿖᡽ᐭߦࠃࠆ߽ߩ(ᢥ₂15,16), 3) ☨࿖MILⷙᩰߦࠃࠆ߽ߩ(ᢥ₂17) 4) ᣣᧄ࿖᡽ᐭߦࠃࠆ⠡⸶(ᢥ₂18,19) 5) ቇળ╬ߦࠃࠆ߽ߩ(ᢥ₂20)

ߥߤ߽޽ࠆ㧚✲ᐲ,ቄ▵ߦࠃࠆᄌൻߥߤᔅⷐߦᔕߓߡ᜛ᒛߐࠇߡ޿ࠆ߇,ૐ㜞ᐲߩᮡḰᄢ᳇ߦߟ޿ߡߪ⋧੕ߦෳᾖߐࠇ ߡ߅ࠅ,⛔৻ߐࠇߡ޿ࠆ㧚๺ᦠߦ߽ᄙߊᒁ↪ߐࠇߡ޿ࠆ㧚

ᄢ᳇⴫ߦߟ޿ߡߪᦨᣂߩ߽ߩ߇ᅢ߹ߒ޿߇,U.S. Standard Atmosphere1962ᐕ એ㒠,ᚑጀ࿤એਅߢߪᄌᦝߪή޿.SI⴫␜

ߩ߽ߩ߇૶޿߿ߔ޿

ᾲജቇ࠺࡯࠲

ᾲജቇߩᢎ⑼ᦠߢߪ㊂⊛ߦᛒ޿߈ࠇߥ޿ታ↪⊛ߥ࠺࡯࠲ࠍଏߔࠆߚ߼,ᷙว᳇૕ߢ޽ࠆⓨ᳇ߣΆ὾ࠟࠬ╬ߩ‛ᕈࠍ

⸘▚ߔࠆߚ߼ߦᔅⷐߣߥࠆએਅߩࠃ߁ߥᾲജቇ࠺࡯࠲߇౏⴫ߐࠇߡ޿ࠆ.

ൻቇ⒳‛ᕈ⴫

ฎౖ⊛ߥHilsenrath et al., 1960²¹⁾,H. D. Baehr et al., 1961²²⁾,ቇળߩᓟ೚ࠅ㓸AGARD²³⁾,Ά὾ࠟࠬ⸘▚ߩ৻ㇱࠍߥߔ߽ߩ Pearson et al. ,1965²⁴⁾, J. H. Keena et al. , 1983²⁸⁾,࿖ኅ⊛ߥᾲജቇᢙ୯⴫JANAF²⁵⁾³⁰⁾,ᄢቇߦࠃࠆᢙ୯⴫W. C. Reynolds, 1979²⁶⁾,ᣣᧄߩቇળߦࠃࠆ߽ߩᵹ૕ߩᾲ‛ᕈ୯㓸,1983²⁷⁾,Ά὾Ꮏቇࡂࡦ࠼ࡉ࠶ࠢ, 1995²⁹⁾,ᯏ᪾Ꮏቇଢⷩ,2006³¹⁾,‛ℂ࠺࡯

࠲੐ౖ,2006³²⁾,ᄖ࿖ߩ‛ℂൻቇࡂࡦ࠼ࡉ࠶ࠢCRC Handbook of Chemistry and Physics, D. R. Lide et al. ,2009³³⁾

ᣂߒ޿߫߆ࠅߢߥߊ,⚦߆޿᷷ᐲ㑆㓒,૶↪ߔࠆ▸࿐ߢ૶޿߿ߔ޿⴫⃻,SI න૏ߩ߽ߩ߇ᅢ߹ߒ޿.․ߦෳᾖ᷷ᐲၮḰ߇ 0K,273.15K(0͠),298.15K,298.16K,ෳᾖ࿶ജ߇1᳇࿶,1barߢ޽ࠆ߆ߦᵈᗧ߇ᔅⷐߣߥࠆ㧚

ⓨ᳇‛ᕈ⴫

਄⸥ߩᢥ₂21~23,26~29,31~33ߦߪ,ᷙว᳇૕ߣߒߡߩⓨ᳇ߩ‛ᕈ୯߽ឝタߐࠇߡ޿ࠆ㧚ઁߦߪᭂ⿥㖸ㅦ㘧ⴕ,ᄢ᳇࿤

⓭౉,ᩭ‛ℂߥߤߢᔅⷐߣߥࠆ㜞࿶․ᕈ,㜞᷷ᐲ․ᕈࠍ⸘▚ߒߚ߽ߩ߇ᄙᢙ౏⴫ߐࠇߡ޿ࠆ 34~44㧚৻ቯ⚵ᚑߩ߽ߩ,ൻ ቇᐔⴧࠍ⠨ᘦߒߚ߽ߩ,ℂ⺰⊛ߦ᳞߼ߚ߽ߩ,ታ㛎⊛ߦ᳞߼ߚ߽ߩߥߤี๧߇ᔅⷐߢ޽ࠆޕᦨㄭߩ߽ߩߢߪ,Lemmon ߦ ࠃࠆ࡟ࡐ࡯࠻ߩᲧセ⊛ૐ޿࿶ജߩㇱಽ߇ෳ⠨ߦߥࠆ³⁴⁾㧚

ᄢ᳇ߩ࿶❗,Ά὾,ࠟࠬߩ⤘ᒛࠍ৻⽾ߒߡขࠅᛒ߁ߚ߼,ࠨࠗࠢ࡞⸘▚ߢߪⓨ᳇ߩᾲജቇ‛ᕈ୯ߪෳ⠨,޽ࠆ޿ߪࡊࡠ࠮

ࠬߩ੍᷹ߦ↪޿ࠆߦߣߤ߼ࠆ㧚৻ᣇ,ⷐ⚛⎇ⓥߢߪ࠺࡯࠲߇⼾ንߢ޽ࠆⓨ᳇ߩャㅍ‛ᕈ୯ࠍ↪޿ࠆߩ߇ᅷᒰߢ޽ࠆ㧚

ඨℂᗐ᳇૕ߣߒߡߩⓨ᳇‛ᕈ

ࠫࠚ࠶࠻ࠛࡦࠫࡦߩࠨࠗࠢ࡞ᬌ⸛ߦߪ,☨࿖ߩ⫳᳇⴫߿ᾲജቇᢎ⑼ᦠߩ⪺⠪ߣߒߡ᦭ฬߥKeenanߣKayeߦࠃࠆඨℂ ᗐⓨ᳇ߩᾲ‛ᕈ୯⴫߇Ꮏቇ਄ߒ߫ߒ߫૶↪ߐࠇߡ߈ߚ.ߒ߆ߒߥ߇ࠄΆ὾ࠟࠬߩ᷷ᐲߣ․ᕈߩផቯߦߪᦝߦᄙߊߩൻ ቇ⒳ߦߟ޿ߡ㜞᷷ၞߩᾲ‛ᕈ࠺࡯࠲߇ᔅⷐߣߥࠅ,ᾲ‛ᕈ࠺࡯࠲ߩ෼㓸߇ㅴࠎߛ㧚߹ߚ,ࠫࠚ࠶࠻ࠛࡦࠫࡦ߇㜞࿶ജᲧ ൻߔࠆߦߟࠇߡ,࿶❗ᯏ಴ญߥߤߢߪൻቇ⚵ᚑߩᄌൻ߇ήⷞߢ߈ߥߊߥߞߡ޿ࠆ㧚3.4 ߢൻቇᐔⴧⓨ᳇ߩᾲജቇ․ᕈࠍ

⸘▚ߔࠆߦᒰߚߞߡߪ,ല₸⊛ߢߪߥ޿߇ቯ⟵ߦᓥߞߡ,JANAFᾲജቇ⴫ߩ↢ᚑᐔⴧቯᢙlogKf_Mࠍ↪޿ߡᮡḰ↢ᚑ‛

ߣߩಽ࿶Ყࠍᰴߩࠃ߁ߦߒߡ⸘▚ߔࠆ.

޽ࠆ㔚㔌ߒߡ޿ߥ޿ಽሶM߇M=CaHbOcNdߥࠆൻว‛ߢ޽ࠆߣ߈ߩ↢ᚑ෻ᔕߪ aCO2+b/2H2O+(c/2-a-b/4)O2+d/4N2㧩CaHbOcNd

ߢ޽ࠅ,෻ᔕߩൻቇᐔⴧቯᢙߪฦಽሶߩಽ࿶ߣ↢ᚑᐔⴧቯᢙࠍ↪޿ߡ Kp_M(T)=[P_ CaHbOcNd]/[P_CO2]^a[P_H2O]^b/2[P_O2](c/2-a-b/4)[P_N2]^d/2

=Kf_CaHbOcNd/Kf_CO2aKf_H2O^b/2Kf_O2(c/2-a-b/4)Kf_N2d/2

ߣ⴫ߐࠇࠆ.

ࠗࠝࡦߩ㔚㔌ᐔⴧߦߟ޿ߡߪ⽶ࠗࠝࡦߩ႐ว

CaHbOcNd+e^-= CaHbOcNd-

Kp_M^-(T)=[P_ CaHbOcNd-]/[P_ CaHbOcNd][P_e^-]

=Kf_CaHbOcNd-/ Kf_CaHbOcNd Kf_e^- ᱜࠗࠝࡦߩ႐ว

CaHbOcNd= CaHbOcNd++e^-

Kp_M⁺(T)=[P_ CaHbOcNd+][P_e^-]/[P_ CaHbOcNd]

=Kf_CaHbOcNd+ Kf_e^-/ Kf_CaHbOcNd

ߣߒߡᐔⴧቯᢙ߇ቯ߹ࠆ㧚

JANAF⴫ߩ߁ߜ,H3O⁺ Hydromiumࠗࠝࡦߦ㑐ߒߡߪ,ਛᕈಽሶߣߒߡߩH3Oߩᾲജቇ࠺࡯࠲߇ή޿ߚ߼,หߓH-O♽ߩ

ࠗࠝࡦߩ߁ߜ↢ᚑᐔⴧቯᢙߩᄢ߈޿߽ߩࠍㆬ߮,߆ߟ෻㔚㔌෻ᔕߢಽሶᢙ߇ᄌൻߒߥ޿ 2H2O=H3O⁺+OH^- ߥࠆ෻ᔕᑼ ࠍ↪޿ߚ.ᐔⴧቯᢙߪ

Kp_H3O⁺(T)=[P_ H3O⁺][P_OH^-]/[P_ H2O]²

=Kf_H3O⁺ Kf_OH^-/ Kf_H2O²

ⓨ᳇‛ᕈ୯࠺࡯࠲ߩᲧセ

Hilsenrath,ᯏ᪾ቇળ,Lemmon ╬ߩᾲ‛ᕈ୯㓸ߩ1 ᳇࿶ߦ߅ߌࠆቯ࿶Ყᾲ࠺࡯࠲ߣᓟㅀߔࠆ⹜▚⚿ᨐࠍࠣ࡜ࡈߢᲧセߔ

ࠆߣ࿑1ߩ᭽ߢ޽ࠅ,450K߆ࠄ1500K߹ߢߩ▸࿐ߢߪ⦟޿৻⥌ࠍߒߡ޿ࠆ.1500Kએ਄ߢߪHilsenrathߩ୯ߪᄢ߈ߊߥ ࠅㆊ߉ࠆ.߹ߚ,⚵ᚑ৻ቯߩⓨ᳇‛ᕈߢߪ,3000K એ਄ߢ,ᾲ⸃㔌ߩᓇ㗀ߢൻቇᐔⴧⓨ᳇ߣߩᏅ⇣߇ᄢ߈ߊߥࠆ.3.4ߦ߅ߌ ࠆ⹜▚ߪ,ᣣᧄᯏ᪾ቇળߩ୯ߣ⦟ߊ৻⥌ߒߡ޿ࠆߎߣ߇ࠊ߆ࠆ.JANAFߩ╙3 ߣ╙4 ߢߪᏅߪ⹺߼ࠄࠇߥ޿ (ߚߛ ߒ╙3 ߦߪAr╬ߩ⒘ࠟࠬ߇฽߹ࠇߡ޿ߥ޿).৻ᣇ,ૐ᷷ߢߪ࿶❗₸ߩᓇ㗀ߢቯ࿶Ყᾲ߇਄᣹ߔࠆലᨐ߇ඨℂᗐ᳇૕ߢ ߪ⠨ᘦߐࠇߡ޿ߥ޿.ᚑጀ࿤ߢߪ200Kㄭㄝߢ޽ࠆߎߣ߆ࠄޔᾲജቇ㑐ᢙߩ⸘▚ߦߪታ࿷᳇૕ലᨐࠍ⠨ᘦߔࠆᔅⷐ߇޽

ࠆޕߥ߅,ⓨ᳇ߪᷙว᳇૕ߢ޽ࠆ߆ࠄൻቇ⒳,⚵ᚑࠍ޽ࠄ߆ߓ߼᳿߼ߥ޿ߣൻቇᐔⴧ⁁ᘒ߇⸘▚ߢ߈ߥ޿㧚ⓨ᳇‛ᕈ⴫

ࠍᲧセߔࠆߣ߈ߦ⇐ᗧߔߴ߈ὐߢ޽ࠆ㧚

࿑1 ฦᾲ‛ᕈ୯㓸ߦ߅ߌࠆⓨ᳇ߩቯ࿶ᲧᾲߩᲧセ

ㄭૃᑼ

ᾲജቇ‛ᕈߪㅪ⛯⊛ߥᕈะࠍ᦭ߔࠆߚ߼ᓥ᧪߆ࠄㄭૃᑼ߇ឭ᩺ߐࠇߡ޿ࠆ.⁁ᘒᣇ⒟ᑼ߇P,V,T㑐ଥࠍ⸥ㅀߒߡ޿ࠆߩ ߦኻߒ,ᾲജቇ㑐ᢙࠍ᷷ᐲ,޽ࠆ޿ߪ߹ߚ࿶ജߩ⸃ᨆ㑐ᢙߢ⴫⸥ߔࠆߣߎࠈ߇⇣ߥࠆ.߹ߚ,᷷ᐲၞߢㄭૃᑼࠍಽഀߔࠆ ߎߣ߽޽ࠆ.

1) PROTHERO⁴⁵⁾

Cp⁰= a1+a2x+a3x²+a4x³+a5x⁴+a6x⁵+a7x⁶ (0.3҇x҇2) Cp⁰= a8+a9x+a10x²+a11x³+a12x⁴+a13x⁵+a14x⁶ ( 2҇x҇6)

X=10^-3 T 2) ᳓⼱⁴⁶⁾

Cpj= a1+a2/ǰ+a3/ǰ²+a4/ǰ³+a5/ǰ⁴ (1.2҇ǰ) Cpj= a6+a7 ǰ+a8 ǰ²+a9 ǰ³+a10ǰ⁴ (ǰ҇1.2)

ǰ=T/1000,

CO,CO2,O2,H2,H2O,OH,H,O,NO,N2

3) REYNOLDS²⁴⁾

P=ǹRT+ǹ²[A1T+A2T^1/2+ǛAiT^3-i]+ǹ³ǛAiT^7-i+ǹ^㧠ǛAiT^11-i+ǹ⁵A13

+ǹ⁶(A14/T+A15/T²)+ǹ⁷A16/T+ǹ⁸(A17/T+A18/T²)+ǹ⁹A19/T² +[ǹ³(A20/T²+A21/T³)+ǹ⁵(A22/T²+A23/T⁴)+ǹ⁷(A24/T²+A25/T³)

+ǹ⁹(A26/T²+A27/T⁴)+ǹ¹¹(A28/T²+A29/T³) +ǹ¹³(A30/T²+A31/T³+A32/T⁴)]e-^ǫǹ2 Cv=mixture N2,O2,Ar

4) ᯏ᪾Ꮏቇଢⷩ²⁹⁾ Cp0=Ǜai(T/T0)^bi

3)ߪ㘻๺⁁ᘒ߆ࠄ200MPa߹ߢࠞࡃ࡯ߒߡ߅ࠅ,ቢోߦㄭ޿߇ቯᢙ߇32ߣᄙ޿㧚

⹜▚⚿ᨐ

JANAFᾲൻቇ⴫╙4 ߦ⸥タߐࠇߡ޿ࠆ,1087ൻቇ⒳ߩ߁ߜ,N,O,C,Hߩൻว‛߅ࠃ߮Ar,Ne,He,Kr,XeߩᏗࠟࠬߣߘߩ

ࠗࠝࡦ߅ࠃ߮ㆆ㔌㔚ሶ,⸘90ൻቇ⒳ߩ᳇૕࠺࡯࠲ࠍ߽ߣߦᮡḰᄢ᳇⚵ᚑߩⓨ᳇ߣߘߩൻቇᐔⴧ⁁ᘒࠍ⸘▚ߒߚ. 1) ৻ቯ⚵ᚑⓨ᳇ߩಽ࿶ߣ‛ᕈ୯

࿑2 ৻ቯ⚵ᚑⓨ᳇ߩಽ࿶ߣ‛ᕈ୯

2) ൻቇᐔⴧⓨ᳇ߩಽ࿶ߣ‛ᕈ୯(1, 10, 100bar)

࿑3 ൻቇᐔⴧⓨ᳇ߩಽ࿶ߣ‛ᕈ୯

࿑2ߣ࿑3ߩ‛ᕈ୯ࠍᲧセߔࠆߣ,2500K⒟ᐲ߹ߢߪൻቇᐔⴧߩᓇ㗀ߪዋߥ޿㧚ߎࠇࠍಽ࿶ߩࠣ࡜ࡈߢ⷗ࠆߣ2000Kߢ

⚂1%ߩNOߩ⊒↢߇޽ࠅ,ߎࠇએ਄ߩ᷷ᐲߢߪᓇ㗀߇ήⷞߢ߈ߥߊߥࠆߎߣࠍᗧ๧ߔࠆ㧚߹ߚ,ൻቇᐔⴧߢߪH2,CH4

ߪ,߶߷ో㊂߇O2ߣ෻ᔕߒߡߒ߹߁㧚㔚㔌ߩᓇ㗀ߪNO⁺ߣ㔚ሶ߳ߩ㔚㔌߇ਥߚࠆ߽ߩߢ޽ࠆ߇2500Kߢߪ10^-9⒟ᐲߦ ߣߤ߹ࠆޕ࿶ജߩᓇ㗀ߪ㜞࿶ߢߪ⸃㔌,㔚㔌ߩᓇ㗀ࠍዋߥߊߔࠆ௑ะ߇޽ࠆ㧚

߹ߣ߼

3 ߹ߢߢ,ࠢ࡝࡯ࡦࠛࡦࠫࡦࡊࡠࠫࠚࠢ࠻ߦ߅޿ߡࠨࠗࠢ࡞ᬌ⸛ࠍታᣉߔࠆ㓙ߩ᷷ᐲ,࿶ജ╬ߩ▸࿐,᳓ಽߩขࠅᛒ޿, Άᢱ,Ά὾↢ᚑ‛╬ߩ⠨ᘦߔߴ߈᧦ઙ߇᣿ࠄ߆ߣߥߞߚ.ߟ߉ߩࠃ߁ߥᣇ㊎ߣߔࠆ㧚

ൻቇ⒳࠺࡯࠲

ᒰ⹥ࡊࡠࠫࠚࠢ࠻ߦ߅޿ߡߪ,ඨℂᗐ᳇૕ߣߒߡߩࠟࠬ‛ᕈ୯ߪJANAF 4 ߩ୯ࠍណ↪ߒ,૶޿߿ߔ޿᷷ᐲߩ㑐ᢙߢ ㄭૃߔࠆ㧚߹ߚ,ታ࿷᳇૕ലᨐߪᔅⷐߦᔕߓߡCRC,߹ߚߪHilsenrathߩࡆ࡝ࠕ࡞ଥᢙࠍ↪޿ࠆ.

ᄢ᳇⴫

ᄢ᳇⚵ᚑ,ฦ㜞ᐲߦ߅ߌࠆ᷷ᐲ,࿶ജߪU.S. Standard Atmosphere1976ߦᓥ߁

ⓨ᳇‛ᕈ

ታ࿷᳇૕ߣߒߡߩ‛ᕈ୯ߪ Lemmon ߦࠃࠆ‛ᕈ୯⴫ࠍၮḰߣߔࠆ.ൻቇᾲജቇߩ⸘▚਄ߪ,N2,O2,Ar ߅ࠃ߮Ꮧࠟ

ࠬ,CO2ߣߔࠆ.࿶❗ㆊ⒟ߦߟ޿ߡ߽ห᭽ߩขࠅᛒ޿ߣߔࠆ

Ά὾ࠟࠬ

ൻቇ⒳࠺࡯࠲ࠍరߦൻቇᐔⴧࠍ⸘▚ߔࠆޕCဳឃ᳇ࡁ࠭࡞ࠍ↪޿ࠆ㒢ࠅߪ෻ᔕಓ⚿ࠍ⠨ᘦߒߥ޿

ᾲജቇߩ⸘▚ᣇᴺߦ㑐ߒߡߪ,ᄙߊߩᦠ☋,࡟ࡐ࡯࠻ߦ⸥タߐࠇߡ޿ࠆ(ᢥ₂47~54)㧚․ߦࡑ࠶ࠞ࡯࡝&ࠨࠗࡕࡦ⁵⁵⁾ߪ ᓳ⠌߽౗ߨߡ⹦ߒߊ⺒ࠎߛ㧚ߎߩవ,࿾⃿ᄢ᳇᧦ઙߢ,Ά὾ࠟࠬߩ‛ᕈ߇ᦨ߽ᄌൻߔࠆߩ߇᳓ಽߩಝ❗,ಝ࿕ߢ޽ࠅ,ߘߩ ᓇ㗀ࠍ⸘ࠆߦߪᢥ₂55ߩ⫳᳇⴫߇ᔅ㗇ߣߥࠆ㧚

ઃ㍳

ෳ⠨ᢥ₂߆ࠄߩᛮ☴

755VCPFCTF#VOQURJGTG ߩ೨ᢥᛮ☴

ޡ᳓⫳᳇࿾⴫㕙㧙ᄢ᳇ਛߩ᳓⫳᳇ߪ,޽ࠄࠁࠆ૕Ⓧߩㄭறߦ߅ߌࠆḨࠅ᳇ߩḝ಴Ḯߣๆ෼Ḯߦଐሽߒߡ޿ࠆ.ᄢ᳇ਛߩ

᳓⫳᳇ߪᄢㇱಽ߇ⓨ᳇ߩႺ⇇ጀࠍㅢߓߡ᳓႙߆ࠄ౉ࠅㄟࠎߢ᧪ࠆ.ᶧ૕,࿕૕ߩ᳓ߪ⫳᳇࿶ࠍ᦭ߒߡ߅ࠅ,ߘߩ⴫㕙᷷ᐲ ߣߣ߽ߦᜰᢙ⊛ߦჇടߔࠆ.߽ߒ,ߎߩ᷷ᐲ߇,⴫㕙ࠍⷒ߁ⓨ᳇ߩ㔺ὐࠍ⿥߃ࠆߣ⫳⊒߇⿠ߎࠅ,ⓨ᳇ߩ㘻๺᷷ᐲ(㔺ὐ)߇, ߘߩ᳓᷷ߦ╬ߒߊߥࠆ߹ߢㅴⴕߔࠆ.ㅢᏱߪߘࠇࠃࠅ௖߆ߦૐ޿㔺ὐߦ߅޿ߡᐔⴧߦ㆐ߔࠆ,ߣ޿߁ߩߪ,࿾㕙߆ࠄߩࠃ ࠅੇ޿ߚⓨ᳇ߣߩኻᵹߣᷙว߅ࠃ߮਄ᣇะ߳ߩ᳓⫳᳇ߩ࿾⴫߆ࠄߩ᜛ᢔ߇ߎࠇࠍᛥ೙ߔࠆ߆ࠄߢ޽ࠆ.

᳓ߩᦨ߽᷷߆޿႙ߪࡍ࡞ࠪࡖḧߢ޽ࠅ,ᄐቄߩ⴫㕙᷷ᐲߪ35͠ߦ㆐ߔࠆ.᳇⽎᷹ⷰ਄ߩᦨ㜞୯ߢ޽ࠆ34͠ߪࡍ࡞ࠪࡖ ḧጯߩࠨ࠙ࠫࠕ࡜ࡆࠕߩSharjahߢ᷹ⷰߐࠇߚ(Salmela and Grantham 1972).

⋧ኻḨᐲߩߺ߇‛ℂ⊛ߦᄢ᳇ਛߩ᳓⫳᳇ߩ᦭ᗧߥᜰ␜୯ߥߩߢߪߥߊ,ᷙวᲧ(න૏⾰㊂ߩੇ῎ⓨ᳇ߦኻߔࠆ᳓⫳᳇

⾰㊂㧦⛘ኻḨᐲ)ߦ឵▚ߐࠇࠆ.ᷙวᲧߪߎߎߢߪ,Ḩࠅ᳇ߩ଻ሽ⊛ߥᜰ␜୯ߣߒߡ૶ࠊࠇߡ޿ࠆ,ߣ޿߁ߩߪ,ⓨ᳇߆ࠄ᳓

⫳᳇߇⿷ߒᒁ߈ߐࠇߥ޿㒢ࠅ,ⓨ᳇߇ု⋥,᳓ᐔߦ⒖േߒߡ߽ߘߩ୯߇ᄌൻߒߥ޿߆ࠄߢ޽ࠆ.ᷙวᲧߩᦨ㜞㔺ὐ᷷ᐲ 34͠ߪᄢ᳇࿶ࠍ1000mbߣ઒ቯߔࠆߣ3.5˜10⁴[⾰㊂ppm]ߦ⋧ᒰߔࠆ.ߎࠇࠃࠅ㜞޿ᷙวᲧߪ᳓ࠍੱᎿ⊛ߦടᾲߔࠆ߆,

ᭂ߼ߡዪ࿾⊛ߦߒ߆↢ߓߥ޿.⍾Ṽ࿾Ꮺߩ᷷ᴰߢߐ߃߽,޽ࠆ࿾ၞ⊛ߥᐢ߇ࠅࠍᜬߟ߶ߤߩ㜞޿୯ࠍ↥ߺ಴ߔ੐ߪߢ߈ ߥ޿߶ߤ,᳓⫳᳇ߪ๟࿐ߩੇ῎ⓨ᳇ߦ᜛ᢔߒߡߒ߹߁.

࿾⴫ߩㄭߊߩ᳓⫳᳇ߩ‛ℂ⊛ᦨᄢ㒢ᐲߪ৻⥸ߦ,න⚐ߢᱜ⏕,਌ߟ㕖Ᏹߦᄙߊߩ᷹ⷰߦࠃࠅᓧࠄࠇߡ޿ࠆ.ㅒߦ,Ḩᐲ ߩᦨዊ୯ߪ⇣ߥࠆ‛ℂ⊛ㆊ⒟ߦࠃࠅዉ߆ࠇࠆ.ๆ෼Ḯߪ᳓႙ߩ᷷ᐲࠃࠅߪᄢ᳇᷷ᐲߦᓇ㗀ߐࠇࠆ.ⓨ᳇߇฽߻ߎߣߩ಴

᧪ࠆ᳓⫳᳇ߩ㊂ߪ᷷ᐲߩૐਅߣߣ߽ߦᜰᢙ⊛ߦ,Ᏹ᷷ߢ޽ࠇ߫10͠ߢඨಽߦ,ᭂૐ᷷ߢߪ 5͠ߢඨಽߦᷫዋߔࠆ.ߘߩࠃ ߁ߦ಄ළߪ᳓⫳᳇ࠍಝ❗ߐߖࠆߚ߼,ᦨૐ᷷ᐲߦ߅޿ߡᦨዊߩ᳓⫳᳇ࠍ฽߻ߎߣߦߥࠆ.ධᭂߩ Vostok㧔ᮡ㜞 3470m㧕 ߢ⸥㍳ߐࠇߚ-88.2͠㧔Riordan 1970㧕߇ᦨૐ࿾⴫᷷ᐲ⸥㍳ߢ޽ࠆ.

-88͠ߩ㔮ὐߢߪᷙวᲧߪ 0.1ppm ߢ޽ࠅ,ᚑጀ࿤ߦ߅ߌࠆ୯ࠃࠅ߽৻ᩴዊߐ޿.හߜ,࿾⴫ߦ߅ߌࠆ᳓⫳᳇㊂ߪ㧡ᩴએ਄

ߩ▸࿐ߢᄌൻߔࠆߎߣ߇ࠊ߆ࠆ.৻⥸ߦ,࿾⴫ߩ⫳᳇ߪ✲ᐲߣߣ߽ߦᷫዋߔࠆ߇,ዪ࿾⊛ߥḝ಴Ḯߣๆ෼Ḯߦࠃߞߡᄌൻ ߒߡ޿ࠆ.

ኻᵹ࿤㧙ኻᵹ࿤ߦ߅ߌࠆ⋧ኻḨᐲߣߘߩ᷷ᐲߪ➅ࠅ㄰ߒታᣉߐࠇߚᮡḰ᳇⽎តᩏ(࡜ࠫࠝ࠱ࡦ࠺)ߦࠃࠅ⸘᷹ߐࠇߡ޿

ࠆ.ᱷᔨߥ߇ࠄ,ᄙߊߩ࡜ࠫࠝ࠱ࡦ࠺ߪ-40͠ߦㄭߠߊߣ᷷ᐲߩᗵᐲ߇ᄬࠊࠇߡߒ߹߁.⚿ᨐ⊛ߦᭂ࿾ߩ౻ߩߎߩ᳇᷷ઃ

ㄭߦ߅ߌࠆḨᐲ࠺࡯࠲ߪᓧࠄࠇߡ޿ߥ޿.ᦨ߽ᥦ߆޿ᄢ᳇⁁ᘒߢ߽㜞ᐲ 10km ࠍ⿥߃ࠆḨᐲ᷹ⷰߪᱴߤή޿.⋧ኻḨᐲ

࠮ࡦࠨߩᗵᐲߦ೙⚂ߪ޽ࠆ߽ߩߩ,8km ߹ߢߩ᳓⫳᳇ߩಽᏓߦ㑐ߔࠆ࠺࡯࠲ߪචಽߦᓧࠄࠇߡ޿ࠆ.Ḩᐲߩ਎⇇࿾࿑߇ ߎࠇࠄߩ࠺࡯࠲߆ࠄ↢ᚑߐࠇߡ޿ࠆ(Gringorten ઁ 1966).ߎࠇߪർඨ⃿ߩ 400mb ߹ߢߩ࿶ജ㕙,⚂ 6㨪8km ߦ߅޿

ߡ,5,25,50,75,95%ߩḨᐲࠍ⴫ߒߡ޿ࠆ.⎇ⓥ࠺࡯࠲ߣߒߡߪᚑጀ࿤ߩḨᐲ᷹ⷰߦ߅޿ߡઃ㓐⊛ߦᓧࠄࠇߚ਄ㇱኻᵹ࿤ߩ

࠺࡯࠲߇ሽ࿷ߔࠆ.ޢ

,#0#(6JGTOQEJGOKECN6CDNGU^UVೋ ߩ೨ᢥ

ޡ1950 ᐕઍඨ߫,὇⚛,᳓⚛,㉄⚛,⓸⚛,Ⴎ⚛,ࡈ࠶⚛ߣ޿ߞߚฎౖ⊛ߥర⚛એᄖߩర⚛߇ࡠࠤ࠶࠻ផㅴ೷ߦ฽߹ࠇࠆࠃ ߁ߦߥࠆߣ,ℂ⺰ᕈ⢻ߩ⸘▚ߦ࿎㔍߇↢ߓߚ.ᦨೋߩᄢ߈ߥ໧㗴ߪߘߩ⸘▚ߩᣇᴺߢ޽ࠅ,ੑ⇟⋡ߦߪ♖⏕ߥᾲജቇ࠺࡯

࠲ߩᰳᅤ߇޽ߞߚ.

ᐕᧃߦߪ⸘▚ᛛᴺߦ㑐ߒߡߪ

⥄↱ࠛࡀ࡞ࠡ࡯ᦨዊൻᴺࠍ࠺ࠫ࠲࡞⸘▚ᯏߦㆡ↪ߔࠆߎߣߢ߶߷⸃᳿ߒߚ

ߎߩ

ᤨὐߢ⸘▚ߪߘߩၮ␆ߣߥࠆᾲജቇ࠺࡯࠲ߣห⒟ᐲߦ♖⏕ߣߥߞߚ

ߒ߆ߒߥ߇ࠄ૶↪ߢ߈ࠆ࠺࡯࠲ߣߪᷓೞߥ㓒ߚ ࠅ߇޽ߞߚ

ផㅴ೷ᚑಽߦ㑐ߒߡߪ

⸘▚਄ᔅⷐߥ࠺࡯࠲ߪ↢ᚑࠛࡦ࠲࡞ࡇߩߺߢ޽ࠆ߇

ߎߩ࠺࡯࠲ߪ㕖Ᏹߦ♖⏕ߢߥ ߌࠇ߫ߥࠄߥ޿

Ά὾↢ᚑ‛ߦ㑐ߒߡߪࠛࡦ࠲࡞ࡇߣࠛࡦ࠻ࡠࡇ࡯߇ᮡḰ↢ᚑᾲߦ⋧ኻ⊛ߥ᷷ᐲߩ㑐ᢙߣߒߡ⍮ࠄࠇ ࠆᔅⷐ߇޽ߞߚ

ߎߩ໧㗴ࠍ⸃᳿ߔࠆߚ߼ߦ⋧ᒰߥᾲജቇ⊛ታ㛎⎇ⓥ⸘↹߇

ߩ

ࡊࡠࠫ

ࠚࠢ࠻ߣߒߡ㐿ᆎߐࠇ

หᤨߦផㅴ೷ߩΆ὾↢ᚑ‛ߩᾲജቇ․ᕈ⴫ߩ⹏ଔߣ㓸Ⓧ߇ቝቮ↥ᬺߦࠃࠆ೑↪ߩὑߦ㐿ᆎߐ

ࠇߚ

ᾲൻቇ⴫ߣߒߡ⍮ࠄࠇࠆߎߩࡊࡠࠫࠚࠢ࠻ߪ

␠ߦࠃߞߡታᣉߐࠇߚ

ࡊࡠࠫࠚࠢ࠻ߩ⋡⊛

ߪ↥ᬺ⇇ో૕ߣߒߡ૶↪ߢ߈ࠆ໑৻ߩᦨ⦟ߩ࠺࡯࠲ࠍឥ߃ࠆߎߣߢ޽ߞߚ߆ࠄ

ᾲൻቇࡄࡀ࡞ߪߘߩ౏⴫ߣ㈩ Ꮣߦవ┙ߞߡ࡟ࡆࡘ࡯ࠍታᣉߒߚ

ߎߩᣇᑼߦࠃࠅ⴫ߪน⢻ߥ㒢ࠅ㜞ຠ⾰ߥ߽ߩߣߥߞߚ

ޢ

⸘▚࠺࡯࠲㓸

⴫

৻ቯ⚵ᚑⓨ᳇

T [K] Cp⁰

[J/molK]

S⁰ [J/molK]

[G⁰-H⁰(Tr)]/T [J/molK]

H⁰-H⁰(Tr) [kJ/mol]

Ӡ

298.15 29.101 198.821 192.701 0.000 -0.12357

500 29.819 213.999 195.063 5.932 -0.12361

1000 33.047 235.673 204.582 21.662 -0.12391

1500 35.075 249.500 211.882 38.746 -0.12424

2000 36.207 259.758 217.319 56.590 -0.12459

2500 36.945 267.921 221.464 74.849 -0.12504

3000 37.479 274.707 224.681 93.501 -0.12563

3500 37.887 280.516 227.201 112.346 -0.12637

4000 38.212 285.598 229.180 131.374 -0.12725

4500 38.489 290.115 230.727 150.550 -0.12825

5000 38.761 294.184 231.922 169.862 -0.12936

5500 39.046 297.891 232.824 189.311 -0.13061

6000 39.400 301.303 233.478 208.919 -0.13200

⴫

ൻቇᐔⴧⓨ᳇

T [K] Cp⁰

[J/molK]

S⁰ [J/molK]

[G⁰-H⁰(Tr)]/T [J/molK]

H⁰-H⁰(Tr) [kJ/mol]

Ӡ

298.15 29.101 198.816 192.699 0.000 -0.12361

500 29.818 213.994 195.062 5.932 -0.12365

1000 33.047 235.671 204.579 21.662 -0.12073

1500 35.075 249.585 211.788 38.746 -0.00465

2000 36.200 260.184 216.712 56.584 0.67550

2500 36.822 268.792 218.930 74.654 3.58296

3000 36.629 274.388 216.043 91.697 15.37266

3500 35.075 273.805 208.023 105.037 43.28322

4000 33.293 269.962 202.727 116.264 71.47294

4500 32.534 269.204 200.984 129.412 85.59067

5000 32.217 270.186 197.471 143.400 97.69987

5500 31.785 270.327 189.457 156.031 120.58383

6000 31.041 267.618 176.641 165.322 164.32865