Su'aalo Tusaale ah iyo Doodo ku saabsan Burburka Muuqaalka ah
Quusitaanka Lahjadaha (Exponential Delayed) waa dhacdo dabiici ah oo laga helo qaybo kala duwan sida fiisigiska, kiimikada, bayoolajiga, iyo dhaqaalaha. Sida qaab xisaabeed, quusitaanka lahjadaha (Exponential Delayed) wuxuu qeexayaa habka tirada la bixiyay ay si siman ugu hooseyso tirada hadda jirta. Xisaabta, quusitaanka lahjadaha (Exponential Delayed) wuxuu raacaa qaabka guud:
\[ N(t) = N_0 e^{-\lambda t} \]
Halkee:
– \( N(t) \) waa tirada ku hartay waqtiga \( t \),
– \( N_0 \) waa lambarka bilowga ah,
– \( \lambda \) waa joogtada burburka (badanaa loo yaqaan heerka burburka),
– \( t \) waa waqti,
– \( e \) waa saldhigga logarithm-ka dabiiciga ah (qiyaastii 2.718).
Maqaalkan, waxaan ka hadli doonnaa tusaalooyin ka mid ah dhibaatooyinka burburka ee soo noqnoqda iyo xalalkooda si aan si qoto dheer u fahanno fikraddan.
Su'aal Tusaale ah 1: Burburka Raajada
Su'aal:
Walax shucaac ah waxay leedahay nus cimri 5 sano ah. Haddii markii hore ay jiri lahayd 100 garaam oo walax ah, intee in le'eg ayaa ka harsan lahayd 15 sano ka dib?
Dood:
Qulqulka shucaaca waxaa lagu qaabeyn karaa iyadoo la adeegsanayo qaacidada qudhunka ee exponential. Nolosha badhkeed (\( t_{1/2} \)) waa waqtiga loo baahan yahay in kala bar qaddarka walxaha shucaaca uu qudhmo. Waa la ogyahay in \( t_{1/2} = 5 \) sano.
Marka hore waxaan u baahanahay inaan helno joogtada burburka \( \lambda \) oo leh qaacidada:
\[ \lambda = \frac{\ln 2}{t_{1/2}} \]
\[ \lambda = \frac{\ln 2}{5} \qiyaastii 0.1386 \qoraal{sanad}^{-1} \]
Sidaa darteed, qaacidada burburka ee jibbaaran waa:
\[ N(t) = N_0 e^{-\lambda t} \]
\[ N(t) = 100 e^{-0.1386 \jeer 15} \]
Hadda, waxaan xisaabineynaa qiimaha:
\[ N(t) = 100 e^{-2.079} \]
\[ N(t) = 100 \jeer 0.125 \]
\[ N(t) \qiyaastii 12.5 \qoraal{ garaam} \]
Markaa, 15 sano ka dib, qiyaastii 12.5 garaam oo walxo shucaac ah ayaa harsan.
Tusaale 2: Burburka Kondensarka
Su'aal:
Kapastarada leh dallac bilow ah \( Q_0 = 200 \text{ C} \) ayaa loo oggol yahay inay ku sii dayso wareeg. Joogtada waqtiga waa \( \tau = 4 \text{ s} \). Immisa dallac ayaa harsan 10 ilbiriqsi ka dib?
Dood:
Haddii ay dhacdo burburka dallacaadda kataliyaha, qaabka jibbaaran ee la isticmaalay waa:
\[ Q(t) = Q_0 e^{-t/\tau} \]
La siiyay \( Q_0 = 200 \text{ C} \) iyo \( \tau = 4 \text{ s} \). Waxaan u baahanahay inaan helno \( Q(10) \):
\[ Q(10) = 200 e^{-10/4} \]
\[ Q(10) = 200 e^{-2.5} \]
Xisaabinta qiimayaasha jibbaaran:
\[ Q(10) = 200 \jeer 0.0821 \]
\[ Q(10) \qiyaastii 16.42 \qoraal{ C} \]
Markaa, 10 ilbiriqsi ka dib, kharashka haray ee ku jira kalkuleytarka waa qiyaastii 16.42 C.
Su'aal Tusaale ah 3: Burburka Kiimikada
Su'aal:
Kiimikadu waxay leedahay joogto ah oo qudhun ah oo ah \( \lambda = 0.05 \text{ days}^{-1} \). Intee in le'eg ayay qaadanaysaa in kiimikadu hoos ugu dhacdo 25% xaddigeedii asalka ahaa?
Dood:
Waxaan ku bilaabaynaa qaacidada guud ee burburka jibbaaran:
\[ N(t) = N_0 e^{-\lambda t} \]
Waxaan rabnaa in N(t) uu noqdo 25% ee \( N_0 \), si:
\[ 0.25 N_0 = N_0 e^{-0.05 t} \]
Ka saarista \( N_0 \) labada dhinac:
\[ 0.25 = e^{-0.05 t} \]
Adeegsiga logarithms-ka dabiiciga ah si loo xalliyo kiisaska jibbaaran:
\[ \ln 0.25 = -0.05 t \]
\[ -1.3863 = -0.05 t \]
Xal u helidda \( t \):
\[ t = \frac{1.3863}{0.05} \]
\[ t \qiyaastii 27.726 \qoraal{ maalmood} \]
Markaa, waqtiga loo baahan yahay in kiimikada la dhimo ilaa 25% qaddarkeeda bilowga ah waa qiyaastii 27.726 maalmood.
Su'aal Tusaale ah 4: Burburka Dadweynaha ee Bakteeriyada
Su'aal:
Tirada bakteeriyada ayaa hoos ugu dhacda heer sare taasoo keentay in 3 saacadood ka dib, tirada dadku ay noqoto kala bar tiradii hore. Haddii tirada dadka bilowga ah ay ahayd 8000 oo bakteeriya ah, imisa bakteeriya ayaa hartay 9 saacadood ka dib?
Dood:
Waa la ogyahay in nus-nolosha \( t_{1/2} = 3 \) saacadood. Marka hore waxaan helnaa joogtada burburka \( \lambda \):
\[ \lambda = \frac{\ln 2}{t_{1/2}} \]
\[ \lambda = \frac{\ln 2}{3} \qiyaastii 0.231 \qoraal{saacad}^{-1} \]
Intaa ka dib, waxaan isticmaalnaa qaacidada burburka ee loo yaqaan 'exposure destruction fraction':
\[ N(t) = N_0 e^{-\lambda t} \]
\[ N(9) = 8000 e^{-0.231 \times 9} \]
Xisaabinta qiimayaasha jibbaaran:
\[ N(9) = 8000 e^{-2.079} \]
\[ N(9) = 8000 \jeer 0.125 \]
\[ N(9) \qiyaastii 1000 \]
Markaa, 9 saacadood ka dib, qiyaastii 1000 bakteeriya ayaa sii jiri doonta.
Gabagabo
Qaabka burburka ee koronka ah wuxuu bixiyaa hab wax ku ool ah oo lagu xalliyo dhibaatooyinka la xiriira hababka burburka ee codsiyada sayniska iyo injineernimada kala duwan. Marka la fahmo fikradaha aasaasiga ah sida joogtada burburka, nolosha badhkeed, iyo isticmaalka qaacidooyinka koronka ah, waxaan si fudud u xisaabin karnaa isbeddelka tirada waqti ka dib. Dhibaatooyinka dhaqanka ee kor lagu falanqeeyay waa inay naga caawiyaan inaan fahanno oo aan ku dabaqno fikradda burburka koronka ah xaaladaha aadka u adag.
