Aia ʻoe ma ke kelepona me kahi hoaaloha ma ʻAmelika i kahi lā anu anuanu. "He \(40\) degere emi ma ʻaneʻi!" puana like olua. ʻO ka mea maʻamau, ʻo ia ka mea e wehewehe ai i ka manaʻo o Celsius a ʻo ia hoʻi ʻo Fahrenheit - akā ʻaʻole i kēia ʻano wela. No ke aha ia? ʻO kēia wale nō ka mahana e ʻae ai nā unahi Celsius a me Fahrenheit!
\(−40\) degere Fahrenheit pololei \(−40\) degere Celsius. ʻAʻole kēia he coincidence, akā he hopena pololei o ka pilina laina ma waena o nā unahi ʻelua. ʻO nā unahi wela ʻelua he hoʻololi affine (linear + shift) o ka nui kino like, "temperature." ʻO ka hoʻololi ʻana ma waena o kēia mau unahi ʻelua he mea paʻakikī. Eia nō naʻe, aia kekahi wahi hoihoi i loaʻa i nā unahi ʻelua ka waiwai helu like.
- Pākē Celsius (°C):
\(0^\circ\mathrm{C}\) Wehe hau o ka wai
\(100^\circ\mathrm{C}\) wahi paila o ka wai
Ka mamao ma waena o kēia mau kiko paʻa: \(100\) degere. - Pālākiō Fahrenheit (°F):
\(32^\circ\mathrm{F}\) Wehe hau o ka wai
\(212^\circ\mathrm{F}\) Puni paila o ka wai
Ka mamao ma waena o kēia mau kiko paʻa: \(212-32=180\) degere.
Hoʻoholo kēia i ka ratio (slope) ma waena o nā unahi:
\[
\frac{180}{100}=\frac{9}{5}
\]
'Oko'a ke kiko nul (offset): \(0^\circ\mathrm{C}\) pili i \(32^\circ\mathrm{F}\) .
No ka loaʻa ʻana o ke ʻano maʻamau, ʻimi mākou i kahi palapala affine o ke ʻano
\[
T_\mathrm{F}=a T_\mathrm{C}+b,
\]
ma kahi \(a\) ka pali (helu helu) a me \(b\) ka offset.
Ua lawa kēia mau kūlana ʻelua no ka mea ua hoʻoholo kūʻokoʻa ka palapala ʻāina affine ma o ʻelua mau kiko:
- \(T_\mathrm{C}=0 \Rightarrow T_\mathrm{F}=32 \Rightarrow 32 = a\cdot 0 + b \Rightarrow b=32.\)
- \(T_\mathrm{C}=100 \Rightarrow T_\mathrm{F}=212 \Rightarrow 212 = a\cdot 100 + 32 \Rightarrow a=\frac{212-32}{100}=\frac{180}{100}=\frac{9}{5}.\)
ʻO ka hoʻololi ʻana e hāʻawi i ke ʻano maʻamau:
\[
T_\mathrm{F}=\frac{9}{5} T_\mathrm{C}+32
\]
Loaʻa ka inverse (mai Fahrenheit a Celsius) ma ka hoʻoholo ʻana no \(T_\mathrm{C}\) :
\[
T_\mathrm{C}=\frac{5}{9}\left(T_\mathrm{F}-32\right)
\]
I kēia manawa ke ʻimi nei mākou i ka mahana \(T\) kahi i ʻike ʻia ai ka waiwai helu like ma nā unahi ʻelua:
\[
T_\mathrm{F}=T_\mathrm{C}\equiv T
\]
I kēia manawa e hoʻokomo i \(T_\mathrm{F}\) i loko o ke ʻano kumu maʻamau:
\[
T=\frac{9}{5}T+32 \Leftrightarrow T-\frac{9}{5}T=32
\]
a hope loa
\[
\left(1-\frac{9}{5}\right)T=32 \quad\Rightarrow\quad \left(\frac{5}{5}-\frac{9}{5}\right)T=32 \quad\Rightarrow\quad -\frac{4}{5}T=32.
\]
ʻO kēia ka hopena ma \(T\)
\[
T=-32\cdot\frac{5}{4}=-8\cdot5=-40
\]
a penei
\[
-40^\circ\mathrm{F} = -40^\circ\mathrm{C}.
\]
No nā waiwai Celsius maikaʻi, \(T_\mathrm{F}=\tfrac{9}{5}T_\mathrm{C}+32\) ʻoi aku ka nui o ka helu helu ma mua \(T_\mathrm{C}\) (e.g. \(0^\circ\mathrm{C} \rightarrow 32^\circ\mathrm{F}\), \(20^\circ\mathrm{C}\rightarrow68^\circ\mathrm{F})\). No nā waiwai Celsius maikaʻi ʻole, ʻo ka \(32\) ʻO nā degere ma ka hoʻomaka ʻana o ka unahi Fahrenheit aia ma lalo o ka ʻole. I kekahi manawa, hoʻopaʻi kēia i ka mea paona \(\frac{9}{5}\). ʻO kēia helu kaulike pololei \(−40\): aia ka hoʻololi hou \(+32\) nui wale i mea like nā helu helu ʻelua. Kiʻi kiʻi, \(T_\mathrm{F}= \tfrac{9}{5}T_\mathrm{C}+32\) (kahi laina pololei) a \(T_\mathrm{F}=T_\mathrm{C}\) (diagonal) – aia ka huina o ko lakou mau laina ma \((-40,-40)\).
ʻO ka ʻokoʻa, hāʻawi ʻia nā wela piha (e laʻa, no nā helu thermodynamic) ma Kelvin a i ʻole Rankine, kahi ʻaʻohe offset i ka hoʻololi ʻana i ka unahi (he kumu unahi maʻemaʻe wale nō). No ka laʻana, ma waena o Celsius a me Kelvin \(T_\mathrm{K} = T_\mathrm{C} + 273{,}15\) . ʻO ka loaʻa ʻana o kēia offset ʻo ia ke kumu e pili ai ka palapala ʻāina Celsius-Fahrenheit a ʻaʻole laina laina. ʻO ke kaulike \(-40^\circ\mathrm{F}=-40^\circ\mathrm{C}\) e hahai pololei ana mai ka pilina pili ma waena o Fahrenheit a me Celsius.
Inā hoʻololi ʻoe i \(T_\mathrm{F}=T_\mathrm{C}\) i \(T_\mathrm{F}=\tfrac{9}{5}T_\mathrm{C}+32\) a hoʻoholo, loaʻa maopopo iā ʻoe \(T=-40\) . ʻO kēia kahi e hui ai nā unahi ʻelua. ʻO kēia kuhi kuhi ma \(-40\) ʻo ia wale nō ke kiko e like ai nā helu helu o nā unahi ʻelua. Ma muli o ke ʻano laina laina o ka hoʻololi ʻana: ʻelua mau laina like ʻole e hui mau i ka kiko hoʻokahi. No laila i ka manawa aʻe e haʻi ai kekahi i \(-40\) degere, ʻaʻole pono ʻoe e nīnau maopopo i ke ʻano o ka nui o kā lākou manaʻo.