Usemnxebeni nomhlobo ose-USA ngemini ebandayo yasebusika. "Kuthabatha \(40\) degrees apha!" nikhwaza nobabini ngaxeshanye. Ngokuqhelekileyo, oku kuya kuba ngumcimbi wokucacisa ukuba ngubani othetha iCelsius kwaye ngubani othetha iFahrenheit-kodwa kungekhona kobu bushushu. Kutheni kunjalo? Eli nqanaba kuphela kweqondo lobushushu apho isikali sikaCelsius nesiFahrenheit sivumelanayo!
\(−40\) degrees Fahrenheit yi-− \(−40\) degrees Celsius kanye. Oku akuyonto nje yazenzekela, kodwa sisiphumo esithe ngqo sobudlelwane bomgca phakathi kwezikali zibini. Zombini izikali zeqondo lokushisa ziguquko ze-affine (umgca + wokutshintsha) wobungakanani obufanayo bomzimba, "ubushushu." Ukuguqula phakathi kwezi zikali zibini kudla ngokuba yindinisa. Nangona kunjalo, kukho inqaku elinomdla apho zombini izikali zinexabiso elifanayo lamanani.
- isikali sikaCelsius (°C):
\(0^\circ\mathrm{C}\) Indawo yomkhenkce wamanzi
\(100^\circ\mathrm{C}\) indawo yokubila yamanzi
Umgama phakathi kwezi ndawo zimiselweyo: \(100\) izidanga. - Isikali seFahrenheit (°F):
\(32^\circ\mathrm{F}\) Indawo yomkhenkce wamanzi
\(212^\circ\mathrm{F}\) Indawo yokubila yamanzi
Umgama phakathi kwezi ndawo zimiselweyo: \(212-32=180\) izidanga.
Oku kugqiba umlinganiselo (i-slope) phakathi kwezikali:
\[
\frac{180}{100}=\frac{9}{5}
\]
Inqaku elinguziro (offset) nalo lahlukile: \(0^\circ\mathrm{C}\) ihambelana \(32^\circ\mathrm{F}\) .
Ukufumana ifomula esemgangathweni, sijonga imephu ehambelanayo yefom
\[
T_\mathrm{F}=a T_\mathrm{C}+b,
\]
apho \(a\) slope (isikali factor) kunye \(b\) yi-offset.
Le miqathango mibini ilandelayo yanele kuba imephu ehambelanayo ngamanqaku amabini imiselwe ngokukodwa:
- \(T_\mathrm{C}=0 \Rightarrow T_\mathrm{F}=32 \Rightarrow 32 = a\cdot 0 + b \Rightarrow b=32.\)
- \(T_\mathrm{C}=100 \Rightarrow T_\mathrm{F}=212 \Rightarrow 212 = a\cdot 100 + 32 \Rightarrow a=\frac{212-32}{100}=\frac{180}{100}=\frac{9}{5}.\)
Ukutshintshanisa kuvelisa ifomyula eqhelekileyo:
\[
T_\mathrm{F}=\frac{9}{5} T_\mathrm{C}+32
\]
Uguqulo (ukusuka kuFahrenheit ukuya kuCelsius) lufunyanwa ngokusonjululwa kwe \(T_\mathrm{C}\) :
\[
T_\mathrm{C}=\frac{5}{9}\left(T_\mathrm{F}-32\right)
\]
Ngoku sijonge iqondo lobushushu \(T\) apho ixabiso elifanayo lamanani livela kuzo zombini izikali:
\[
T_\mathrm{F}=T_\mathrm{C}\equiv T
\]
Ngoku faka \(T_\mathrm{F}\) kwifomula eqhelekileyo:
\[
T=\frac{9}{5}T+32 \Leftrightarrow T-\frac{9}{5}T=32
\]
kwaye ekugqibeleni
\[
\left(1-\frac{9}{5}\right)T=32 \quad\Rightarrow\quad \left(\frac{5}{5}-\frac{9}{5}\right)T=32 \quad\Rightarrow\quad -\frac{4}{5}T=32.
\]
Oku kubangela ukuba \(T\)
\[
T=-32\cdot\frac{5}{4}=-8\cdot5=-40
\]
kwaye njalo
\[
-40^\circ\mathrm{F} = -40^\circ\mathrm{C}.
\]
Kumaxabiso akhuthazayo kaCelsius, \(T_\mathrm{F}=\tfrac{9}{5}T_\mathrm{C}+32\) lihlala linexabiso elikhulu kunani \(T_\mathrm{C}\) (umz. \(0^\circ\mathrm{C} \rightarrow 32^\circ\mathrm{F}\), \(20^\circ\mathrm{C}\rightarrow68^\circ\mathrm{F})\). Ukufumana ixabiso elaneleyo likaCelsius elikhabayo, i \(32\) Iidigri ekuqaleni kwesikali seFahrenheit ngokwenene zingaphantsi kwe-zero. Ngexesha elithile, oku kuhlawulela umlinganiselo wesikali \(\frac{9}{5}\). Le ndawo yokulinganisa yiyo kanye \(−40\): kukho utshintsho olongezelelweyo \(+32\) zinkulu ngokwaneleyo ukuze zombini amanani amanani afane. Ngokomzobo, \(T_\mathrm{F}= \tfrac{9}{5}T_\mathrm{C}+32\) (umgca othe ngqo) kunye \(T_\mathrm{F}=T_\mathrm{C}\) (i-diagonal) - indawo yokuhlangana yemigca yabo ikhona \((-40,-40)\).
Ngokwahlukileyo, amaqondo obushushu apheleleyo (umzekelo, ukubala kwe-thermodynamic) anikwe kwi-Kelvin okanye i-Rankine, apho kungabikho i-offset ekuguqulweni kwesikali (kuphela isikali esicocekileyo). Umzekelo, phakathi kukaCelsius noKelvin \(T_\mathrm{K} = T_\mathrm{C} + 273{,}15\) iyasebenza. Ubukho bolu hlaselo sesona sizathu sibangela ukuba imephu yeCelsius-Fahrenheit idityaniswe kwaye ingabi ngumgca ngokusulungekileyo. Ukulingana \(-40^\circ\mathrm{F}=-40^\circ\mathrm{C}\) kulandela ngokuthe ngqo kubudlelwane obusondeleyo phakathi kweFahrenheit kunye neCelsius.
Ukuba ubeka endaweni \(T_\mathrm{F}=T_\mathrm{C}\) kwi \(T_\mathrm{F}=\tfrac{9}{5}T_\mathrm{C}+32\) kwaye uyisombulule, ufumana ngokucacileyo \(T=-40\) . Kulapho kanye ezi zikali zidibana khona. Le ndawo yokuhlangana ku \(-40\) yindawo ekukuphela kwayo apho amaxabiso amanani ezikali zombini ayafana. Oku kungenxa yendalo yomgca woguqulo: imigca emibini engahambelaniyo ihlala idibana kanye kwindawo enye. Ke kwixesha elizayo xa umntu ekhankanya \(-40\) izidanga, akunyanzelekanga ukuba ubuze ngokucacileyo ukuba bathetha ukuthini na isikali.