࢚ࢹࣗࢣ࣮ࢩࣙࣥ Qࢽ࣮ࣗࢺࣥࡢ෭༷ἲ๎㸦ࡑࡢ㸱㸧㸫ᙉไᑐὶᐇ㦂㸫
Newton’s Law of Cooling, Part 3,Experiment on Forced Convectionᅭᒣ 㔜┤㸦ඵᡞ㧗ᑓ㸧, Ᏺ㇂ ಟ୍㸦ᮾ໭኱Ꮫ㸧
Shigenao MARUYAMA (INT, Hachinohe College), Syuichi MORIYA (Tohoku University) e-mail: maruyama-o@hachinohe-ct.ac.jp㸯㸬ࡣࡌࡵ࡟
࢔࢖ࢨࢵࢡ࣭ࢽ࣮ࣗࢺࣥ㸦1642-1727㸧ࡢ෭༷ἲ๎࡟ࡘ࠸࡚ࡢㄽᩥࠕScala graduum Caloris.㸦A Scale ofthe Degree of Heat,ᗘࡢᑻᗘ㸧ࠖ[1][2]࡟ࡘ࠸࡚㸪๓ሗ㸦ࡑࡢ 1㸧[3]࡛ࡣ㸪㧗 ≀యࡢ ᗘィ ࡟ࡘ࠸࡚㆟ㄽࡋࡲࡋࡓ㸬๓ሗ㸦ࡑࡢ 2㸧[4]࡛ࡣ㸪ỈࡢἛⅬ௨ୗࡢ ᗘ࡟ࡘ࠸࡚㸪ࢽ࣮ࣗࢺࣥ ᗘࡢ⢭ᗘࡸ㸪ᙜ᫬ࡢ࢖ࢠࣜࢫࡢẼ ࡟ࡘ࠸࡚㆟ㄽࡋࡲࡋࡓ㸬ఏ⇕ᕤᏛࡢᩍ⛉᭩࡛㸪ᑐὶ⇕ఏ㐩ࡢᇶ♏ᘧ࡜ࡋ࡚౑ࢃࢀ࡚࠸ࡿࢽ࣮ࣗࢺࣥࡢ෭༷ἲ๎ࡣ㸪⇕ὶ᮰ q 㸪ὶయ࡜≀యࡢ ᗘᕪ T  Tf 㸪⇕ఏ㐩⋡ h ࡜ࡋࡓ࡜ࡁ㸪qh(T  Tf )(1)࡛グ㏙ࡉࢀ࡚࠸ࡲࡍ㸬ࢽ࣮ࣗࢺࣥࡢㄽᩥ[1]࡛ࡣ㸪≀యࡢ ᗘィ ࡀ୰ᚰ࡛㸪ᘧ(1)ࡣㄽᩥ୰࡟ࡣฟ࡚
ࡁࡲࡏࢇ㸬ࢽ࣮ࣗࢺࣥࡣ㸪≀యࡀ෭༷ࡍࡿ㏿ࡉࡣ≀య࡜࿘ᅖࡢ✵Ẽ ᗘࡢᕪ࡟ẚ౛ࡍࡿ࡜ࡋࡲࡋࡓ㸬ࡲࡓ㸪≀యࡣ㢼ࡀ྿࠸࡚࠸ࡿ≧ែ࡛෭ࡸࡋࡓ࡜࠸࠺グ㏙ࡀ࠶ࡾࡲࡍ㸬ࡇࡢ 2 ࡘࡢᩥ❶ࡀࠕࢽ࣮ࣗࢺࣥࡢ෭༷ἲ๎ࠖ
ࡢ㉳※࡜⪃࠼ࡽࢀࡲࡍ㸬⚾ࡓࡕࡣ㸪ࢽ࣮ࣗࢺࣥࡢㄽᩥࢆᙉไᑐὶ⇕ఏ㐩ࡢࡼࡾ࡝ࡇࢁ࡜ࡋ࡚࠸ࡲࡍࡀ㸪ㄽᩥ࡛ࡣ㢼ࡢ㏿ᗘࡣ᫂♧ࡉࢀ࡚࠸ࡲࡏࢇ㸬ᮏሗ࡛ࡣ㸪ࢽ࣮ࣗࢺࣥࡀࡇࡢᐇ㦂ࢆࡋࡓ࡜ࡁ㸪࡝ࡢᵝ࡞㢼ࡀ྿࠸࡚࠸ࡓࡢ࠿ࢆゎ᫂ࡍࡿࡓࡵ࡟㸪㢼Ὕᐇ㦂ࢆ⾜࠸ࡲࡋࡓ㸬ࡑࡢ⤖ᯝ࠿ࡽ㸪ࢽ࣮ࣗࢺࣥࡢᐇ㦂ࢆ෌⌧ࡍࡿࡇ࡜ࢆヨࡳࡲࡋࡓ㸬㸰㸬ࢽ࣮ࣗࢺࣥࡢᐇ㦂⤖ᯝࢽ࣮ࣗࢺࣥࡣ⊂⮬࡟ ᗘィࢆసࡾⰍࠎ࡞⌧㇟ࡢᗘࢆィ ࡋࡲࡋࡓ㸬ప ࡢ ᗘィ ࡣ๓ሗ㸦ࡑࡢ2㸧[4]࡟㸪㧗 ࡢ⌧㇟ࡣ๓ሗ㸦ࡑࡢ 1㸧[3]࡟グ㍕ࡋ࡚࠸ࡲࡍ㸬ࡑࢀࡽࢆ⧳ࡵࡓࡶࡢࢆᮏሗࡢ᭱ᚋ࡟グࡋ࡚࠸ࡿ⾲ 1 ࡟♧ࡋࡲࡍ㸬⾲࡟ࡣ㸪ࢽ࣮ࣗࢺࣥࡢㄽᩥ

ᅗ 1 ➼ẚᩘิ ᗘ㸦⾲ 1㸧ࢆ↓ḟඖ᫬㛫࡛⾲ࡋࡓࢽ࣮ࣗࢺࣥࡢᐇ㦂⤖ᯝ㸬ᅗ୰ࡢ␒ྕࡣ⾲ 1 ࡢࢹ࣮ࢱ␒ྕࢆ♧ࡋࡲࡍ㸬ఏ⇕ 2020 ᖺ 1 ᭶- 46 -J. HTSJ, Vol. 59, No. 246

࢚ࢹࣗࢣ࣮ࢩࣙࣥ QTf୰ࡢ⾲࡛♧ࡉࢀࡓ್࡟ຍ࠼࡚㸪ᩥ❶࡛グ㏙ࡉࢀࡓᗘࡶグ㍕ࡋ࡚࠸ࡲࡍ㸬T ' T '1  ࢽ࣮ࣗࢺࣥࡣ㸪㔜ࡉ 4.25 lb ࡢཌ࠸ᯈ≧ࡢ㕲ሢࢆྎᡤࡢࢥ࡛ࣥࣟ⇞࠼࡚࠸ࡿ▼Ⅳࡢ୰࡟ᢞධࡋ㉥ࡃຍ⇕ࡋࡲࡋࡓ㸬ࡑࡢ㉥⇕ࡋࡓ㕲ሢࢆྲྀࡾฟࡋ࡚㸪෭ࡓ࠸ሙᡤ࡟⨨ࡁࡲࡋࡓ㸬㕲ሢࡢୖ࡟ࡣ✀ࠎࡢ㔠ᒓࡸྜ㔠ࡢ⢏ࢆ⨨ࡁ㸪ࡑࢀࡀจᅛࡍࡿ᫬㛫ࢆ ᐃࡋࡲࡋࡓ[2]㸬ࡇࡢࡼ࠺࡟ࡋ࡚ ᐃࡋࡓ ᗘࢆ⾲ 1 ࡟♧ࡋ࡚࠸ࡲࡍ㸬 ࢽ࣮ࣗࢺࣥࡣ 2 ࡘࡢ ᗘ⾲グࢆ⏝࠸࡚࠸ࡲࡍ㸬୍ࡘࡣ㸪 T (N) ࡛グ㍕ࡍࡿ㏻ᖖࡢ ᗘ(Equal part ofheat)[2]࡛㸪ᘧ(2)࡛⾲グࡋࡲࡍ[4]㸬

T (Υ) T (N)×100/34(2)ࡶ࠺୍ࡘࡣᑐᩘ ᗘ࡟┦ᙜࡍࡿ➼ẚᩘิ ᗘ(degree of heat in geometrical progression)[2]࡛㸪ࢽ࣮ࣗࢺࣥ ᗘࢆ T (N) ࡜ࡋ࡚ḟᘧ࡛ᐃ⩏ࡋࡲࡍ㸬T'log 2 (T /12)  1(3)

⾲ 1 ୰࡟ࡣ㸪ࢽ࣮ࣗࢺࣥ ᗘ㸪ࢭࣝࢩ࢘ࢫ ᗘ㸪➼ẚᩘิ ᗘࢆ♧ࡋ࡚࠸ࡲࡍ㸬ࡉࡽ࡟㸪Grigull ࡀ᥎ᐃࡋࡓ ᗘ[5]ࡶ♧ࡋ࡚࠸ࡲࡍ㸬Grigull ࡢ ᗘࡣ㸪㧗 㒊ศ࡛ࡣ෬㔠Ꮫⓗ࡟᥎ᐃࡋࡓ ᗘ࡛࠶ࡾ㸪ࢽ࣮ࣗࢺࣥࡢ ᗘࡼࡾ㧗ࡃ࡞ࡗ࡚࠸ࡲࡍ㸬 ᅗ 1 ࡣ㸪⾲ 1 ࡢ್ࢆ➼ẚᩘิ ᗘ࡛⾲ࡋ࡚࠸ࡲࡍ㸬ࢽ࣮ࣗࢺࣥࡢㄽᩥ࡛ࡣ෭༷᫬㛫ࡀグ㍕ࡉࢀ࡚࠸࡞
࠸ࡢ࡛㸪ᅗ 1 ࡣ⾲ 1 ࡢ ᗘࢆᐇ㦂㛤ጞ࠿ࡽయ ࡟┦
ᙜࡍࡿ 12 N ࡟࡞ࡿࡲ࡛ࡢ᫬㛫࡛↓ḟඖ໬ࡋ࡚࠸ࡲࡍ㸬 ࢽ࣮ࣗࢺࣥࡢᐇ㦂࡛ࡣ㸪㕲ሢࡢ኱ࡁࡉ࡜㸪➼౯ᖹᆒ⇕ఏ㐩⋡ h ࠿ࡽ᥎ᐃࡉࢀࡿࣅ࢜ᩘࡣ 0.005㹼
0.011 ࡜ᑠࡉ࠸ࡢ࡛㸪㞟୰⇕ᐜ㔞⣔ࡀ㐺⏝࡛ࡁ࡚෭༷᭤⥺ࡣḟᘧ࡛⾲ࡉࢀࡲࡍ㸬c UVdTdt

 hS (T  Tf )ln(T1  Tf )  ln(T  Tf )ఏ⇕ 2020 ᖺ 1 ᭶hSt
c UV ln 2(6)࡜࡞ࡾࡲࡍ㸬ࡘࡲࡾ㸪➼ẚᩘิ ᗘ T ' ࢆ᫬㛫 t ࡛⾲ࡍ࡜㸪ᅗ 1 ࡟♧ࡍࡼ࠺࡟┤⥺࡜࡞ࡾ㸪๓ሗ㸦ࡑࡢ
㸯㸧[3]࡛♧ࡋࡓࡼ࠺࡟㸪 ᗘィ࡛ ࢀ࡞࠸ ᗘࢆ᥎ᐃࡍࡿࡇ࡜ࡀ࡛ࡁࡿࡢ࡛ࡍ㸬ࡑࡇࡀ㸪ࢽ࣮ࣗࢺࣥㄽᩥࡢ㔜せ࡞࡜ࡇࢁ࡛࠶ࡾ㸪ࢽ࣮ࣗࢺࣥࡢ෭༷ἲ๎ࡣࡑࢀࢆࢧ࣏࣮ࢺࡍࡿ௬ᐃ࡟ࡍࡂ࡞࠸ࡢ࡛ࡍ㸬 ࡓࡔࡋ㸪㞟୰⇕ᐜ㔞⣔ࢆ཯ᫎࡉࡏࡿࡓࡵ࡟ࡣ㸪ᘧ(3)ࡢ ᗘࡣ㸪࿘ᅖ✵Ẽ࡜ࡢ ᗘᕪ࡛࠶ࡿ࡭ࡁ࡛ࡍ㸬ࢽ࣮ࣗࢺࣥࡀᐇ㦂ࡋࡓ࡜ࡁࡢ⎔ቃ ᗘࡣ 2 N(5.9Υ)࡜᥎ᐃࡉࢀ [6]㸪ࢽ࣮ࣗࢺࣥࡀ┠ᣦࡋࡓ㧗 ≀యࡢᗘࡢ᥎ᐃ࡟ࡣ⎔ቃ ᗘࢆ 0 N ࡜ࡋ࡚ࡶ኱ᕪ࠶ࡾࡲࡏࢇ࡛ࡋࡓ㸬 ๓㏙ࡋࡓࡼ࠺࡟㸪ࢽ࣮ࣗࢺࣥࡢㄽᩥ࡛ࡣ㸪ᐇ㦂᫬࡟㢼ࡀ྿࠸࡚࠸ࡓ࡜࠸࠺グ㏙ࡣ࠶ࡾࡲࡍࡀ㸪ࡑࡢ㢼ࡢᙉࡉ࡟ࡘ࠸࡚ࡣゝཬࡋ࡚࠸ࡲࡏࢇ㸬≀యࡢ෭༷㏿ᗘࡣ㸪ࡩࡃᑕఏ⇕ࡶ⪃៖ࡋࡓ➼౯⇕ఏ㐩⋡࡟౫Ꮡࡍࡿࡢ࡛㸪෭༷᫬㛫ࡀศ࠿ࡽ࡞࠸࡜㢼㏿ࡢ᥎ᐃࡀ࡛ࡁ
ࡲࡏࢇ㸬Ruffner ࡣ෭༷᫬㛫ࢆ 60 ศ࡜௬ᐃࡋ [7]㸪Grigull ࡣ 77 ศ࡜᥎ᐃࡋࡲࡋࡓ[8]㸬࡝ࡕࡽࡶ᫂☜࡞᰿ᣐࡣ࠶ࡾࡲࡏࢇ㸬ࢽ࣮ࣗࢺࣥࡣࡇࡢᐇ㦂ࡢ௚࡟ࡶ㸪㕲ሢࡢ෭༷ᐇ㦂ࢆ⾜ࡗ࡚࠸ࡲࡍ㸬ࡑࡢ᫬ 100N ࠿ࡽ 12N ࡟෭༷ࡍࡿࡲ࡛ࡢ᫬㛫ࡣ 132 ศ࡛ࡋࡓ[6]㸬ࡋ࠿ࡋ㸪ࡑࡢᐇ㦂ࡀࡇࡢᐇ㦂[1]࡜ྠࡌ㢼㏿ୗ࡛⾜ࢃࢀࡓ࡜࠸࠺ドᣐࡣ࠶ࡾࡲࡏࢇ㸬 ࡑࡇ࡛㸪ࢽ࣮ࣗࢺࣥࡢᐇ㦂ࢆ෌⌧ࡍࡿࡓࡵ࡟㸪⡆᫆㢼Ὕࢆ〇సࡋ㸪㕲ሢࡢ෭༷ᐇ㦂ࢆ⾜࠸ࡲࡋࡓ㸬㸱㸬ᐇ㦂⿦⨨࠾ࡼࡧᐇ㦂᪉ἲ ⡆᫆㢼Ὕࡢ〇స ࢽ࣮ࣗࢺࣥࡢᐇ㦂ࢆ෌⌧ࡍࡿࡓࡵ࡟྿ࡁฟࡋᆺࡢ⡆᫆㢼Ὕࢆ〇సࡋࡲࡋࡓ㸬ᅗ
2 ࡣ㸪ࡑࡢ⡆᫆㢼Ὕ࡜ᐇ㦂⿦⨨ࡢᴫ␎ࢆ♧ࡋ࡚࠸ࡲࡍ㸬㢼Ὕࡣタ⨨ࢫ࣮࣌ࢫࢆᑠࡉࡃࡍࡿࡓࡵ࡟㸪㐲ᚰࣇ࢓ࣥ࠿ࡽᨺฟࡉࢀࡓ✵Ẽࢆ L Ꮠᆺ࡟೫ྥࡋ࡚྿ࡁฟࡋࣀࢬࣝ࠿ࡽᄇฟࡉࡏࡲࡋࡓ㸬L Ꮠᆺ㢼㊰࡟ࡣ࢔࣑ࣝ〇ࣁࢽ࣒࢝ࢆධࢀ࡚ᩚὶࡋ㸪ゅ㒊࡟ࡣ┤ᚄ
120mm ࡢࣅࢽ࣮ࣝࣃ࢖ࣉࢆษ᩿ࡋࡓ෇ᘼ⩼࡛ᵓᡂࡉࢀࡿ೫ὶᯈࢆタ⨨ࡋࡲࡋࡓ㸬㢼㊰㒊ࡢ᩿㠃✚ࡣ
450450 mm㸪ࣀࢬࣝฟཱྀ᩿㠃✚ࡣ 200200 mm
࡛ࡋࡓ㸬(4)ࡇࡇ࡛㸪 c ࡣ㕲ሢࡢẚ⇕㸪 U ᐦᗘ㸪 V య✚㸪 S ᗏ㠃ࢆ㝖࠸ࡓ⾲㠃✚㸪t ᫬㛫࡛ࡍ㸬ึᮇ ᗘࡀ T1 ࡛㸪ᑐὶ⇕ఏ㐩⋡࡜ࡩࡃᑕ⇕ఏ㐩⋡ࢆྜࢃࡏࡓ➼౯ᖹᆒ⇕ఏ㐩⋡ࡀ≀య ᗘ࡟ࡼࡽࡎ୍ᐃࡢ᫬㸪ᘧ(4)ࡣ
ḟᘧ࡛⾲ࡉࢀࡲࡍ㸬hS
tc UV0 ࡜ࡋ࡚㸪ᘧ(2)ࢆᘧ(5)࡟௦ධࡍࡿ࡜㸪(5)- 47 -J. HTSJ, Vol. 59, No. 246

࢚ࢹࣗࢣ࣮ࢩࣙࣥ Qࢀࡲࡍ㸬

H ࡑࡇ࡛㸪ᅗ 2 ࡟♧ࡍࡼ࠺࡟㸪ᐇ㦂୰ࡣᨺᑕ⋡ H ࢆ
1 ࡟タᐃࡋࡓ㉥እ⥺࣓࢝ࣛࢆタ⨨ࡋ࡚ᨺᑕ⋡ࡢኚ໬ࢆࣔࢽࢱ࣮ࡋࡲࡋࡓ㸬㉥እ⥺࣓࢝ࣛࡢ ᐃ ᗘࢆTIR (K) ࡜ࡍࡿ࡜㸪≀య⾲㠃ࡢᨺᑕ⋡ࡣḟᘧ࡛⾲ࡉ(7)㉥እ⥺࣓࢝ࣛࡢ ᐃ࡟ࡼࡿ࡜㸪㢼Ὕᐇ㦂୰ࡢ⾲㠃ᗘศᕸࡣ㗪㕲ᯈゅࡢ୍㒊௨እࡣ࡯ࡰ୍ᵝ࡛࠶ࡿࡇ࡜ࡀ☜ㄆࡉࢀࡲࡋࡓ㸬 ᐇ㦂᪉ἲ ኱ࡁࡉ 10310727 mm㸦⣙ 44
1 inch㸧㸪㉁㔞 1.93 kg㸦4.25 lb㸧ࡢ㗪㕲ᯈࢆタᐃ
ᗘ 800Υࡢຍ⇕⅔࡟ධࢀຍ⇕ࡋࡲࡋࡓ㸬 㢼㏿ࢆタᐃ㏿ᗘ࡟ㄪᩚࡋࡓ㢼Ὕࡢ ᐃ㒊࡟ࢥ࣮ࣔࣥ࣌ࣂࣞࣥ࢞ࢆᩜࡁ㸪ࡑࡢୖ࡟㗪㕲ᯈࢆ⨨࠸࡚㸪㗪㕲୰ኸ࡟タ⨨ࡉࢀࡓ┤ᚄ 1.5mm ࡢ K ᆺ⇕㟁ᑐ࡟ࡼࡾ෭༷ ᗘࢆ ᐃࡋࡲࡋࡓ㸬ࡑࡢ᫬㸪㗪㕲ᯈୖ㒊࡟タ⨨ࡉࢀࡓ㉥እ⥺࣓࡛࢝ࣛ⾲㠃 ᗘࢆࣔࢽࢱ࣮ࡋ࡚࠸ࡲࡍ㸬 㗪㕲ᯈࡢࣅ࢜ᩘࡀᑠࡉ࠸ࡢ࡛㸪ෆ㒊࡟タ⨨ࡉࢀࡓ⇕㟁ᑐࡢ ᗘࡣ㸪⾲㠃 ᗘ࡟㏆࠸್࡜᥎ᐃࡉࢀࡲࡍ㸬ᅗ 2 ⡆᫆㢼Ὕ࡟ࡼࡿᐇ㦂⿦⨨ ィ 㒊࡟࠾ࡅࡿ㢼㏿ศᕸࡣᶓ᪉ྥ 2㸣㸪⦪᪉ྥ4㸣࡛࠶ࡾ㸪ࣀࢬࣝ୰ኸ㏆ഐ࡛ࡣ୍ᐃ࡛ࡋࡓ㸬ࣀࢬࣝ୰ኸ㒊ࡢ ᐃ㒊࡛ࡢὶࢀࡢ஘ࢀᙉࡉࡣ 1㹼2㸣࡛ࡋࡓ㸬ᮏ㢼Ὕࡣ㐲ᚰࣇ࢓ࣥࡢᅇ㌿ᩘࢆ࢖ࣥࣂ࣮ࢱ࡛
ไᚚࡍࡿࡇ࡜࡟ࡼࡾ㸪2㹼25 m/s ࡢ㢼㏿ࢆᚓࡿࡇ࡜
ࡀ࡛ࡁࡲࡋࡓ㸬 ⾲㠃ᨺᑕ⋡ࡢ ᐃ 㧗 ≀యࡢఏ⇕࡟ࡣࡩࡃᑕࡀ኱ࡁࡃᐤ୚ࡋࡲࡍ㸬㉥⇕ࡋࡓ㕲ሢࢆྲྀࡾฟࡋࡓ
┤ᚋࡣ㸪ࡩࡃᑕఏ⇕㔞ࡣᑐὶ⇕ఏ㐩㔞࡟ẚ࡭࡚ 50ಸ௨ୖ࡜࡞ࡾࡲࡍ㸬(TIR4  Tf4 ) / (T 4  Tf4 )㸲㸬⤖ᯝ࡜⪃ᐹᅗ 3 ࡣ㸪㢼Ὕᐇ㦂࡜ࢽ࣮ࣗࢺࣥࡢᐇ㦂࡟ࡼࡿ㕲ሢ ᗘࢆᑐᩘ ᗘ┠┒ࡾ࡛♧ࡋ࡚࠸ࡲࡍ㸬⾲ 1 ࡟♧ࡍࢽ࣮ࣗࢺࣥㄽᩥࡢᐇ㦂ࡣ㸪᫬㛫ࡀᥖ㍕ࡉࢀ࡚࠸ࡿࢽ࣮ࣗࢺࣥࡢูᐇ㦂[6]࡛య ࡜࡞ࡗࡓ᫬㛫
㸦132 ศ㸧࡜࡞ࡿࡼ࠺࡟⾲♧ࡋࡲࡋࡓ㸬ᅗ୰࡟ࡣ㸪ᮏሗ࡛స〇ࡋࡓ⡆᫆㢼Ὕࡢ ᐃ㒊࡟ᅗ 3 㢼Ὕᐇ㦂࡛ࢽ࣮ࣗࢺࣥࡢᐇ㦂ࢆ෌⌧ࡋࡓᐇ㦂್࡜᥎ᐃᘧࡢẚ㍑㸪࠾ࡼࡧ㸪ࢽ࣮ࣗࢺࣥࡢᐇ㦂ࢹ࣮ࢱࢆ෌⌧ࡍࡿ㢼㏿ࡢ᥎ᐃఏ⇕ 2020 ᖺ 1 ᭶- 48 -J. HTSJ, Vol. 59, No. 246

࢚ࢹࣗࢣ࣮ࢩࣙࣥ Qຍ⇕ࡋࡓ㕲ሢࢆࣞࣥ࢞ୖ࡟⨨࠸ࡓሙྜࡢᐇ㦂್ࢆ♧ࡋ࡚࠸ࡲࡍ㸬ᐇ㦂ࢹ࣮ࢱࡣ 1 ⛊ࡈ࡜࡟ྲྀᚓࡋ㸪㕲ሢ ᗘࡀ✵Ẽὶ ᗘ࡜࡯ࡰ୍⮴ࡍࡿࡲ࡛ᐇ㦂ࢆ⥅⥆ࡋࡲࡋࡓ㸬㕲ሢࡢ෭༷ ᗘࡣḟᘧ࡛⾲ࡉࢀࡲࡍ㸬c UVdTdt

 S{hc (T  Tf )  H (T 4  Tf4 )} (8)1 ㎶ D ࡢṇ᪉ᙧ᩿㠃ゅᰕࡢᑐὶᖹᆒ⇕ఏ㐩⋡ hcࡢ᥎ᐃࡣ㸪Hilpert ࡢ⤒㦂ᘧ[9]Nu D

CReDm Pr 1/ 3 ,hc D / kࡇࡇ࡛ C0.102, m

0.675(9)ࢆ⏝࠸ࡲࡋࡓ㸬ࡓࡔࡋ㸪ᯈ≧㕲ሢࡣゅᰕ࡜ࡣᙧ≧ࡀ␗࡞ࡿࡢ࡛㸪D ࢆ㕲ሢࡢỈຊ┤ᚄ࡜ࡋ㸪ᐃᩘ C ࢆㄪᩚࡋ࡚ᐇ㦂್࡟ྜࢃࡏࡓ⤖ᯝ㸪ᘧ(9)ࡢ C ࢆ 0.26࡜ࡍࡿࡇ࡜࡛㸪ᐇ㦂್࡜Ⰻࡃ୍⮴ࡋࡲࡋࡓ㸬 㕲ሢࡢᨺᑕ⋡Ȝࡣ㸪㉥እ⥺࣓࢝ࣛ࠿ࡽᘧ(7)࡛ồࡵ㸪100Υ㹼500Υࡢࢹ࣮ࢱࢆᖹᆒࡋ࡚౑⏝ࡋࡲࡋࡓ㸬 ᅗ 3 ࡟ࡣྛ㢼㏿ࡢ㢼Ὕᐇ㦂࡜ᘧ(9)ࡢ᥎ᐃ್ࢆ♧ࡋ࡚࠸ࡲࡍࡀⰋࡃ୍⮴ࡋ࡚࠸ࡿࡇ࡜ࡀࢃ࠿ࡾࡲࡍ㸬 ḟ࡟㸪ࡇࡢᐇ㦂ᘧࢆ౑ࡗ࡚㸪ࢽ࣮ࣗࢺࣥㄽᩥࡢᐇ
㦂⤖ᯝࢆᶍᨃࡍࡿ㢼㏿ࢆ᥎ᐃࡋࡲࡋࡓ㸬ึᮇ ᗘࡣGrigull ࡢ᥎ᐃ ᗘ࠿ࡽጞࡲࡾ㸪ࢽ࣮ࣗࢺࣥࡢᐇ㦂ࡢ᮲௳[6]࡜⪃࠼ࡽࢀࡿẼ 5.9Υࡢ⎔ቃୗ࡛ࡢ㕲ሢࡢ ᗘపୗࢆ᥎ᐃࡋࡲࡋࡓ㸬ࡇࡢ᫬㸪ᨺᑕ⋡ࡣᐇ㦂ࢹ࣮ࢱ࠿ࡽ 0.75 ࡜タᐃࡋࡲࡋࡓ㸬 ࡶࡋ㸪㕲ሢࡀయ 㸦12 N㸧ࡲ࡛㸪෭༷ࡍࡿࡢ࡟
132 ศࢆせࡍࡿሙྜ㸪㢼㏿ࡣ 0.7 m/s ࡜࡞ࡾࡲࡍ㸬ࡲࡓ㸪Ruffner[7]ࡀ௬ᐃࡋࡓࡼ࠺࡟ 60 ศ࡛෭༷ࡍࡿ࡜௬ᐃࡍࡿ࡜㸪ࡑࡢ᫬ࡢ㢼㏿ࡣ 5.0 m/s ࡜᥎ᐃࡉࢀࡲࡍ㸬ࢽ࣮ࣗࢺࣥㄽᩥࡢᐇ㦂ࡣ㸪ࢽ࣮ࣗࢺࣥࡢูᐇ
㦂࡜඲ࡃ␗࡞ࡿ᮲௳࡛⾜ࡗࡓࡇ࡜ࡣ⪃࠼࡟ࡃ࠸ࡢ࡛㸪వࡾᙉ࠸㢼ࡣ྿࠸࡚࠸࡞࠿ࡗࡓྍ⬟ᛶࡀ⪃࠼ࡽࢀࡲࡍ㸬ࡲࡓ㸪㢼㏿࡟ࡼࡗ࡚෭༷᫬㛫ࡀ␗࡞ࡿࡇ࡜ࢆணഛᐇ㦂࡛ࡍ࡛࡟▱ࡗ࡚࠸࡚㸪ࢽ࣮ࣗࢺࣥࡢㄽᩥ
[1]࡛ࡣ㸪ᩒ࠼࡚ㄽᩥ࡛ࡣ᫬㛫ࢆ᭩࠿࡞࠿ࡗࡓࡢ࠿ࡶࡋࢀࡲࡏࢇ㸬 ࡶࡋ㸪㢼㏿ࡀᑠࡉ࠸ሙྜ㸪⮬↛ᑐὶ⇕ఏ㐩ࡣ↓ど࡛ࡁࡲࡏࢇ㸬㢼ࡀ඲ࡃ࡞࠸ሙྜ࡛ࡶྠᵝ࡞෭༷᭤⥺ࢆᚓࡿࡇ࡜ࡀ࡛ࡁࡲࡍ㸬㸳㸬࠾ࢃࡾ࡟⡆᫆㢼Ὕࢆ〇సࡋ㸪ࢽ࣮ࣗࢺࣥ࡜ྠᵝ࡞ᐇ㦂ࢆ⾜ఏ⇕ 2020 ᖺ 1 ᭶- 49 -࠸㸪ࢽ࣮ࣗࢺࣥࡀᐇ㦂ࡋࡓ࡜ࡁࡢ㢼ࡢ㏿ᗘࢆ᥎ᐃࡋࡲࡋࡓ㸬᥎ᐃࡉࢀࡿ㢼㏿ࡣ෭༷᫬㛫࡛␗࡞ࡾࡲࡍࡀ㸪ࢽ࣮ࣗࢺࣥࡢูᐇ㦂࡜ྠࡌ᫬㛫ࢆせࡋࡓሙྜ㸪᥎ᐃ㢼㏿ࡣ 0.7m/s ࡜࡞ࡾ㸪ࡇࡢ㡿ᇦ࡛ࡣ⮬↛ᑐὶࡀ↓ど࡛ࡁ࡞࠸⠊ᅖ࡜࡞ࡾࡲࡍ㸬ࡲࡓ㸪⮬↛ᑐὶࡢࡳ࡟ࡼࡿ෭༷ࡀ㉳ࡁ࡚࠸ࡓࡇ࡜ࡶྰᐃ࡛ࡁࡲࡏࢇ㸬ࢽ࣮ࣗࢺࣥࡣ࡞ࡐ㸪㢼ࡀ྿࠸࡚࠸ࡓࡇ࡜ࢆᩒ࠼࡚
グ㏙ࡋࡓࡢ࡛ࡋࡻ࠺࠿㸬ࡲࡓ㸪࡝ࡢࡼ࠺࡟ࡋ࡚㸪➼ẚᩘิ ᗘࢆ⏝࠸ࡿ࡜㧗 ࡀ᥎ᐃ࡛ࡁࡿࡇ࡜ࢆᛮ࠸ࡘ࠸ࡓࡢ࡛ࡋࡻ࠺࠿㸬➼ẚᩘิ ᗘ࡟ࡘ࠸࡚ࡣ㸪ࢽ࣮ࣗࢺࣥࡢྡⴭࠕࣉࣜࣥࢩࣆ࢔ࠖࡀ㛵ࢃࡗ࡚࠸ࡿྍ⬟ᛶࡀ࠶ࡾࡲࡍ㸬ࡇࢀࡽࡢ␲ၥ࡟ࡘ࠸࡚ࡣ㸪ḟሗ࡛㆟ㄽࡋࡓ࠸࡜ᛮ࠸ࡲࡍ㸬ཧ⪃ᩥ⊩
[1] “Scala graduum Caloris (A Scale of the Degreesof Heat)”, Philosophical Transactions, No. 270, pp.
824-829, (April 1701).
[2] “The Correspondence of Isaac Newton, VolumeIV, 1964-1709”, Edited by J.F. Scott, CambridgeUniversity Press, PP.357-365, (1967).
[3] ෇ᒣ㔜┤㸪ࢽ࣮ࣗࢺࣥࡢ෭༷ἲ๎㸦ࡑࡢ 1㸧㸪ఏ⇕㸪Vol. 54, No. 229, pp.31-34, (2015).
[4] ᅭᒣ㔜┤㸪Ᏺ㇂ಟ୍㸪ᒸᓥ῟அ௓㸪ࢽ࣮ࣗࢺࣥࡢ෭༷ἲ๎㸦ࡑࡢ 2㸧 ࢽ࣮ࣗࢺࣥࡢ ᗘࢫࢣ࣮ࣝ࡟ࡘ࠸࡚ࡢ⪃ᐹ㸪ఏ⇕㸪Vol. 57, No. 240,pp.65-69, (2018).
[5] Grigull, U., “Newton’s Temperature Scale and theLaw of Cooling,” Waerme und Stoffuebertrang,
Vol. 18, pp.195-199, (1984).
[6] Simms, D. L., “Newton’s Contribution to theScience of Heat”, Annals of Science, Vol. 61,pp.33-77, (2004).
[7] Ruffner, J. A., “Reinterpretation of the Genesis of
Newton’s Law of Cooling,” Archives of Historyof Exact Science, Vol. 2, pp. 138-152, (1964).
[8] Grigull, U., Das Newtonshe Abkühlungsgesetz,
Abh. Braunschweig. Wiss. Ges. 29, pp.7-31,(1978).
[9] Incropera, F.P., Dewitt, D.P., Bergman, T.L. andLavine, A.S., Fundamentals of Heat and MassTransfer, 6th Ed., John Wiley & Sons, pp.426-427,(2007).

J. HTSJ, Vol. 59, No. 246

࢚ࢹࣗࢣ࣮ࢩࣙࣥ Q⾲ 1 ࢽ࣮ࣗࢺࣥ ᗘ࡜ࡑࡢグ㏙㸦␒ྕࡣᚋ࡛௜ࡅࡓࡶࡢ㸪㸨ࡣᩥ❶࡟ࡼࡿ ᗘグ㏙ࢆ♧ࡋࡲࡍ㸬➼ẚᩘิ ᗘ࡟͊ࡀࡘ࠸࡚࠸ࡿࡶࡢࡣ➹⪅ࡢィ⟬್ࢆ♧ࡋ࡚࠸ࡲࡍ㸬㸧䝕䞊䝍␒ྕ1⌧㇟䛾グ㏙䛸ᗘỈ䛜෾䜚ጞ䜑䜛෤䛾Ẽ 䠊 䛣䛾 ᗘ䛿䠈 ᗘィ䜢○䛔䛯㞷䛾୰䛻⨨䛝䠈䛭䜜䛜⁐䛡䜛᫬䛻ṇ☜䛻ィ 䛥䜜䜛䠊23ᦤẶᗘ(ႏ)

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2.94

4

2-1.58͊

5.88

5

2-1.58͊

5.88

3-1.00͊8.82

7

4-0.58͊

11.76

8

4-0.58͊

11.76

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14.71

60.00͊

17.65

6

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10
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17.65

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ᗘィ䛜ேయ䛻᥋ゐ䛧䛶㐩䛩䜛᭱኱ ᗘ䠊 䛣䜜䛿䠈㫽䛾༸䛜Ꮴ໬䛩䜛 ᗘ䛸䜋䜌ྠ䛨䛷䛒䜛䠊12

135.2913㢼࿅䛾䛚‫‮‬䛻ᡭ䜢ᾐ䛧䛶䠈⤯䛘䛪ື䛔䛶䛔䜛≧ែ䛷䠈䛛䛺䜚䛾᫬㛫⪏䛘䜛䛣䛸䛜䛷䛝䜛᭱኱ ᗘ䠊 䛣䜜䛿᥇⾑䛧䛯䜀䛛䜚䛾⾑ᾮ䛸䜋䜌ྠ䛨䛷䛒䜛䠊

14.27

1.25

41.97

14㢼࿅䛻ᡭ䜢ື䛛䛥䛪ᾐ䛧䛶㛗᫬㛫⪏䛘䜛䛣䛸䛜䛷䛝䜛᭱㧗ᗘ䠊

171.550.00

15䛚‫‮‬䛾ୖ䛻ᾋ䛛䜆⁐⼥䝽䝑䜽䝇䛜จᅛ䛧ጞ䜑䛶䛭䛾㏱᫂ᗘ䜢ኻ䛖᫬䛾 ᗘ䠊

20.18

1.75

59.35

16

䝽䝑䜽䝇䛜ᾋ㐟䛧䛶䛔䜛䛚‫‮‬䛜ຍ⇕䛥䜜䠈Ἓ㦐䛫䛪䛻ᾮయ䜢ಖ䛴䛚‫‮‬䛾 ᗘ䠊

24270.59

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28.55

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83.97

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Ỉ䛿 33 ᗘ䛾 ᗘ䛷Ἓ㦐䛧ጞ䜑䜛䠊

33

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97.06

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20*
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35

2.54͊

102.9436

2.58͊

105.8837

2.62͊

108.82Ỉ䛜⃭䛧䛟Ἓ㦐䛩䜛 ᗘ䠈䛚䜘䜃䠈㖄 2䠈㘏 3䠈䝡䝇䝬䝇 5 䛾ྜ㔠䛜෭༷᫬䛻ᅛ໬䛩䜛 ᗘ䠊

34

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J. HTSJ, Vol. 59, No. 246

࢚ࢹࣗࢣ࣮ࢩࣙࣥ Q

23*Ἓ㦐䛩䜛䛚‫‮‬䛿䠈34.5 ᗘ௨ୖ䛻䛿䜋䛸䜣䛹㐩䛧䛺䛔䠊

34.5

2.52͊

101.4724

㖄 1䠈㘏 4䠈䝡䝇䝬䝇 5 䛾ྜ㔠䛜ຍ⇕䛥䜜⼥ゎ䛧䠈ᾮయ䜢ಖ䛴
᭱ప ᗘ䠊

40.36

2.75

118.71135

25*

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ᅛ䛩䜛䠊

47

2.97͊

138.24151

26

㘏 1䠈䝡䝇䝬䝇 1 䛾ྜ㔠䛜⼥ゎ䛩䜛᭱ప

483

141.18151

27

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57

3.25

167.65187

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68

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200.00218

29*㘏䛿෭༷䛩䜛䛸 70 ᗘ䛷จᅛ䛩䜛䠊

70

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205.88232

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72

3.58

211.76232

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䛩䜛䠊

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238.24271

32*

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㖄䛜⼥ゎ䛩䜛᭱ప⼥ゎ䛩䜛䠈

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䝬䝇 7䠈䜰䞁䝏䝰䞁 4 䛾ྜ㔠䛜෭༷᫬䛻จᅛ䛩䜛䠊

114

4.25

335.2942035

㧗 䛻ຍ⇕䛥䜜䛯య䛜ኪ㛫䛻䛿ග䛳䛶ぢ䛘䜛䛜䠈ⷧ䜔䜏䛷䛿䜎䛳䛯䛟┠䛷䛿☜ㄆ䛷䛝䛺䛔 ᗘ䠊䛣䛾 ᗘ䛷䠈䜰䞁䝏䝰䞁 2䠈䝡䝇䝬䝇䠍䛾ྜ㔠䠈䛺䜙䜃䛻䜰䞁䝏䝰䞁䠑䠈㘏䠍䛾ྜ㔠䛜෭༷᫬䛻จᅛ䛩䜛䠊

136

4.5

400.00561

36*䛭䛧䛶䠈䜰䞁䝏䝰䞁 2䠈㖡 1 䛾ྜ㔠䛿 140.5 ᗘ䛷จᅛ䛩䜛䠊

140.5

4.55͊

413.2437*

䜰䞁䝏䝰䞁䛿 146 ᗘ䛷จᅛ䛩䜛䠊

146

4.60͊

429.4138㧗 䛻ຍ⇕䛥䜜䛯≀య䛜ⷧ䜔䜏䛾୰䠈䛴䜎䜚᪥䛾ฟ䛾┤๓䜔᪥䛾ධ䜚䛾┤ᚋ䛻䠈䛿䛳䛝䜚ග䛳䛶ぢ䛘䜛䛜䠈᪥୰䛾ᬕኳ䛾ග䛾୰䛷䛿඲䛟ぢ䛘䛺䛔䛛䠈䜎䛯䛿䛤䛟䛛䛩䛛䛻䛧䛛┠ど䛷䛝䛺䛔 ᗘ䠊

161

4.75͊

473.5339䜅䛔䛤䜢౑䜟䛪䛻℡㟷Ⅳ䛜⇞䛘䜛ᑠ䛥䛺䝁䞁䝻䛾▼Ⅳ䛾ᗘ䠊 䛭䛾䜘䛖䛺ⅆ䛾୰䛷䠈ᙉ䛟㍤䛟㕲䛿ྠ䛨 ᗘ䛷䛒䜛䠊 ᮌ䜢⇞䜔䛧䛯ᑠ䛥䛺䝁䞁䝻䛾ⅆ䛾 ᗘ䛿䜒䛖ᑡ䛧㧗䛟䠈䛴䜎䜚
200 ᗘ䛛 210 ᗘ䛷䛒䜛䠊 ኱つᶍ䛺ⅆ䛾 ᗘ䛿䠈≉䛻䠈䜅䛔䛤䛻䜘䛳䛶䠄⇞↝䛜䠅ಁ㐍䛥䜜䜛ሙྜ䛿䠈᭦䛻㧗 䛻䛺䜛䠊

192

5564.71ఏ⇕ 2020 ᖺ 1 ᭶ᗘ䠊ᗘ䠊ᗘ䠊ຍ⇕䛥䜜䛯㖄䛿 96 䜎䛯䛿 97 ᗘ䛷

- 51 -631

J. HTSJ, Vol. 59, No. 246