Usocingweni nomngane wakho e-USA ngosuku olubandayo lwasebusika. "Kungu- \(40\) degrees lapha!" nibabaze nobabili kanyekanye. Ngokuvamile, lokhu kungaba indaba yokucacisa ukuthi ubani osho i-Celsius nokuthi ubani osho Fahrenheit—kodwa hhayi ngaleli qondo lokushisa. Kungani kunjalo? Leli phuzu ukuphela kwezinga lokushisa okuvumelana ngalo isikali sikaCelsius nesiFahrenheit!
\(−40\) degrees Fahrenheit ncamashi \(−40\) degrees Celsius. Lokhu akukhona ukuqondana, kodwa umphumela oqondile wobudlelwano bomugqa phakathi kwalezi zilinganiso ezimbili. Zombili izikali zokushisa ziyi-affine ukuguqulwa (umugqa + shift) yenani elifanayo lomzimba, "izinga lokushisa." Ukuguqula phakathi kwalezi zilinganiso ezimbili kuvame ukuyisicefe. Nokho, kunephuzu elithakazelisayo lapho zombili izikali zinenani elifanayo lezinombolo.
- Isikali se-Celsius (°C):
\(0^\circ\mathrm{C}\) Indawo yokubanda yamanzi
\(100^\circ\mathrm{C}\) indawo abilayo yamanzi
Ibanga phakathi kwalawa maphoyinti angashintshi: \(100\) degrees. - Isikali sikaFahrenheit (°F):
\(32^\circ\mathrm{F}\) Indawo yokubanda yamanzi
\(212^\circ\mathrm{F}\) Indawo abilayo yamanzi
Ibanga phakathi kwalawa maphoyinti angashintshi: \(212-32=180\) amadigri.
Lokhu kunquma isilinganiso (umthambeka) phakathi kwezikali:
\[
\frac{180}{100}=\frac{9}{5}
\]
Iphoyinti elinguziro (offset) nalo lihlukile: \(0^\circ\mathrm{C}\) ihambisana \(32^\circ\mathrm{F}\) .
Ukuze sithole ifomula evamile, sibheka imephu ehlobene yefomu
\[
T_\mathrm{F}=a T_\mathrm{C}+b,
\]
lapho \(a\) iwumthambeka (isici sesikali) futhi \(b\) iyi-offset.
Izimo ezimbili ezilandelayo zanele ngoba imephu ehambisanayo ngamaphoyinti amabili inqunywa ngokuhlukile:
- \(T_\mathrm{C}=0 \Rightarrow T_\mathrm{F}=32 \Rightarrow 32 = a\cdot 0 + b \Rightarrow b=32.\)
- \(T_\mathrm{C}=100 \Rightarrow T_\mathrm{F}=212 \Rightarrow 212 = a\cdot 100 + 32 \Rightarrow a=\frac{212-32}{100}=\frac{180}{100}=\frac{9}{5}.\)
Ukufaka esikhundleni kunikeza ifomula evamile:
\[
T_\mathrm{F}=\frac{9}{5} T_\mathrm{C}+32
\]
Okuphambene (kusuka ku-Fahrenheit kuya ku-Celsius) kutholakala ngokuxazululela okuthi \(T_\mathrm{C}\) :
\[
T_\mathrm{C}=\frac{5}{9}\left(T_\mathrm{F}-32\right)
\]
Manje sibheka izinga lokushisa \(T\) lapho inani elifanayo lenombolo livela kuzo zombili izikali:
\[
T_\mathrm{F}=T_\mathrm{C}\equiv T
\]
Manje faka \(T_\mathrm{F}\) kufomula evamile:
\[
T=\frac{9}{5}T+32 \Leftrightarrow T-\frac{9}{5}T=32
\]
futhi ekugcineni
\[
\left(1-\frac{9}{5}\right)T=32 \quad\Rightarrow\quad \left(\frac{5}{5}-\frac{9}{5}\right)T=32 \quad\Rightarrow\quad -\frac{4}{5}T=32.
\]
Lokhu kubangela ukuthi \(T\)
\[
T=-32\cdot\frac{5}{4}=-8\cdot5=-40
\]
futhi kanjalo
\[
-40^\circ\mathrm{F} = -40^\circ\mathrm{C}.
\]
Ngamavelu e-Celsius ephozithivu, \(T_\mathrm{F}=\tfrac{9}{5}T_\mathrm{C}+32\) njalo inani lenombolo elikhulu kune \(T_\mathrm{C}\) (isib. \(0^\circ\mathrm{C} \rightarrow 32^\circ\mathrm{F}\), \(20^\circ\mathrm{C}\rightarrow68^\circ\mathrm{F})\). Kumanani anegethivu eCelsius anele, i \(32\) Amadigri ekuqaleni kwesikali sikaFahrenheit empeleni angaphansi kweziro. Ngesinye isikhathi, lokhu kunxephezela isici sesikali \(\frac{9}{5}\). Leli phuzu lokulinganisa injalo impela \(−40\): kukhona ushintsho olwengeziwe \(+32\) sikhulu ngokwanele ukuze amanani amanani afane. Ngokwesithombe, \(T_\mathrm{F}= \tfrac{9}{5}T_\mathrm{C}+32\) (umugqa oqondile) kanye \(T_\mathrm{F}=T_\mathrm{C}\) (diagonal) - indawo yokuhlangana yemigqa yabo iku \((-40,-40)\).
Ngokuphambene, amazinga okushisa aphelele (isb., ezibalweni ze-thermodynamic) anikezwa ku-Kelvin noma i-Rankine, lapho kungekho offset ekuguqulweni kwesikali (isici sesikali esimsulwa kuphela). Isibonelo, phakathi kweCelsius ne-Kelvin \(T_\mathrm{K} = T_\mathrm{C} + 273{,}15\) iyasebenza. Ukuba khona kwalokhu kususwa kuyisizathu esinembile sokuthi kungani imephu ye-Celsius-Fahrenheit ihambisana futhi ingaqondile nje. Ukulingana \(-40^\circ\mathrm{F}=-40^\circ\mathrm{C}\) kulandela ngokuqondile ubudlelwano obuphakathi kukaFahrenheit neCelsius.
Uma ufaka esikhundleni \(T_\mathrm{F}=T_\mathrm{C}\) kokuthi \(T_\mathrm{F}=\tfrac{9}{5}T_\mathrm{C}+32\) futhi uxazulule, uthola ngokusobala \(T=-40\) . Yilapho kanye izikali ezimbili zihlangana khona. Leli phuzu lokuhlangana kokuthi \(-40\) liwukuphela kwephoyinti lapho amanani ezinombolo azo zombili izikali afana khona. Lokhu kungenxa yemvelo yomugqa yokuguqulwa: imigqa emibili engahambelani njalo ihlangana endaweni eyodwa ncamashi. Ngakho-ke ngesikhathi esilandelayo lapho othile ekhuluma ngamadigri angu \(-40\) , akudingekile ukuthi ubuze ngokusobala ukuthi usho ukuthini isikali.