Misalai 5 na tambayoyin faɗaɗa girma
1. An yi ƙwallon ƙarfe mai ƙarfi da aluminum tare da ma'aunin faɗaɗa layi na 24 x 10-6 oC-1. Idan zafin jiki ya kai 30oC girman ƙwallon shine 30 cm3 don haka ƙarar ƙwallon ta ƙaru zuwa 30,5 cm3, Dole ne a yi zafi da ƙwallon har sai ta kai zafin da ya kai na….. oC
Tattaunawa
An san cewa:
Ma'aunin faɗaɗa layi (α)= 24 x 10-6 oC-1
Ƙimar faɗaɗa ƙarar (γ) = 3 a = ba 3 x 24 x 10-6 oC-1 = 72 x10-6 oC-1
Zafin farko (T)1) = 30oC
Ƙaramin farko (V)1= 30 cm3
Ƙarar ƙarshe (V)2= 30,5 cm3
Canjin girma (ΔV) = 30,5 cm3 - 30 cm3 = 0,5 cm ba3
An tambaya: Zafin ƙarshe (T)2)
Amsa:
ΔV = g (V1)(ΔT)
ΔV = g (V1)(T2 - T1)
0,5 cm3 = (72 x 10-6 oC-1)(30 cm3)(T2 - 30oC)
0,5 ((2160 x 10-6)(T2 - 30)
0,5 ((2,160 x 10-3)(T2 - 30)
0,5 ((2,160 x 10-3)(T2 - 30)
0,5 / (2,160) x 10-3) = T2 - 30
0,23 x 103 = T ba2 - 30
0,23 x 1000 = T2 - 30
230=T2 - 30
230 + 30 = T2
T2 = 260oC
2. Ƙwallon da aka yi da gilashi mai rami yana da ma'aunin faɗaɗa layi na 9 x 10-6 oC-1A zafin jiki na 20oC diamita na ciki na ƙwallon shine 2,2 cm. Idan diamita na ciki na ƙwallon ya ƙaru zuwa 2,8 to, zafin jiki ƙarshen shine….
Tattaunawa
An san cewa:
Ma'aunin faɗaɗa layi (α)= 9 x 10-6 oC-1
Ƙimar faɗaɗa ƙarar (γ) = 3 α = 3 x 9 x 10-6 oC-1 = 27 x10-6 oC-1
Zafin farko (T)1) = 20oC
Diamita na farko (D)1= 2,2 cm
Diamita na ƙarshe (D)2= 2,8 cm
Radius na farko (r)1) = D1 / 2 = 2,2 cm3 / 2 = 1,1 cm3
Radius na ƙarshe (r)2) = D2 / 2 = 2,8 cm3 / 2 = 1,4 cm3
Ƙaramin farko (V)1) = 4/3 π r13 = (4/3)(3,14)(1,1 cm)3 = (4/3)(3,14)(1,331 cm)3= 5,57 cm3
Ƙarar ƙarshe (V)2) = 4/3 π r23 = (4/3)(3,14)(1,4 cm)3 = (4/3)(3,14)(2,744 cm)3= 11,48 cm3
Canjin girma (ΔV) = 11,48 cm3 - 5,57 cm3 = 5,91 cm ba3
An tambaya: Zafin ƙarshe (T2)
Amsa:
ΔV = g (V1)(ΔT)
5,91 cm3 = (27 x 10-6 oC-1)(5,57 cm3)(T2 - 20oC)
5,91 ((150,39 x 10-6)(T2 - 20)
5,91/150,39 x 10-6 = T ba2 - 20
0,039 x 106 = T ba2 - 20
39 x 103 = T ba2 - 20
39000=T2 - 20
T2 = 39020oC
3. Idan aka yi zafi da iska, karuwar girma tana daidai da...
A. Zafin farko
B. Zafin ƙarshe
C. Ƙara yawan zafin jiki
D. Kundin farko
E. Juzu'i na ƙarshe
Tattaunawa:
Ƙarar iska tana daidai da ƙaruwar zafin jiki ko canjin zafin jiki. Yayin da yawan ƙaruwar zafin jiki ke ƙaruwa, haka ƙaruwar girman take ƙaruwa.
4. Ana cika tukunyar gilashi mai lita 4 da ruwa, sannan a dumama ta yadda zafin zai tashi da 20oC. Sai ya zama cewa ruwa ya zube. An san cewa adadin faɗaɗa gilashi mai layi shine 9 x 10-6 oC-1; ma'aunin faɗaɗa yawan ruwa = 2,1 x 10-4 oC-1, to adadin ruwan da ke zuba shine…
A. lita 0,015
B. lita 0,018
C. lita 0,020
D. lita 0,021
E. lita 0,025
Tattaunawa
An san cewa:
Girman farko na gilashin da ruwa (V)o) = lita 4
Canje-canje a yanayin zafi na gilashi da ruwa (ΔT) = 20oC
Ma'aunin faɗaɗa gilashi mai layi (α) = 9 x 10-6 oC-1
Ma'aunin faɗaɗa girman gilashi (γ) = 3α = 3 (9 x 10)-6 oC-1= 27 x 10-6 oC-1
Yawan faɗaɗa ruwa (γ) = 2,1 x10-4 oC-1
An tambaya: Bruwa mai yawa da aka zubar
Amsa:
Tsarin faɗaɗa girma:
V = Vo + γ Vo ΔT
V-Vo = γ Vo ΔT
ΔV = γ Vo ΔT
Bayani:
V = ƙarar ƙarshe, Vo = ƙarar farko, ΔV = canjin girma, γ = ma'aunin faɗaɗa girma, ΔT = canjin yanayin zafi.
Lissafa canjin girma na gilashin jirgin ruwa:
ΔV = γ Vo ΔT = (27 x 10-6)(4)(20) = 2160 x 10-6 = 2,160 x10-3 = 0,002160 lita
Lissafa canjin da aka samu a yawan ruwa:
ΔV = γ Vo ΔT = (2,1 x 10-4)(4)(20) = 168 x 10-4 = 0,0168 lita
Sauyin da ake samu a yawan ruwa ya fi na gilashin, don haka wasu daga cikin ruwan na zuba.
Lissafa yawan ruwan da aka zubar:
0,0168 lita - 0,002160 lita = 0,01464 lita = 0,015 lita
Amsar da ta dace ita ce A.
5. Tukunya da aka yi da ƙarfe (ma'aunin faɗaɗa layi = 10-5 oC-1) yana da girman lita 6 cike da ruwan acetone (ƙimar faɗaɗa girma = 1,5 x 10-3 oC-1) Idan an yi musu zafi ta yadda zafin ɗakin zai tashi daga 0oC zuwa 40oC, to, ƙarar acetone da ya zube...
A. lita 0,35
B. lita 0,48
C. lita 0,58
D. lita 1,36
E. lita 1,48
Tattaunawa
An san cewa:
Ƙarar farko ta tasoshin ƙarfe da acetone (V)o) = lita 6
Canje-canje a cikin zafin jiki na tasoshin ƙarfe da acetone (ΔT) = 40oC
Ma'aunin faɗaɗar ƙarfe mai layi (α) = 10-5 oC-1
Ma'aunin faɗaɗa ƙarar ƙarfe (γ) = 3α = 3 (10)-5 oC-1= 3 x 10-5 oC-1
Faɗaɗar ƙarar acetone (γ) = 1,5 x 10-3 oC-1
An tambaya: Bruwa mai yawa da aka zubar
Amsa:
Tsarin faɗaɗa girma:
ΔV = γ Vo ΔT
Bayani:
ΔV = canjin girma, γ = ma'aunin faɗaɗa girma, Vo = ƙarar farko, ΔT = canjin yanayin zafi.
Lissafa canjin girma na jirgin ƙarfe:
ΔV = γ Vo ΔT = (3 x 10-5)(6)(40) = 720 x 10-5 = 0,00720 lita
Lissafin canjin acetone a cikin fitsari:
ΔV = γ Vo ΔT = (1,5 x 10-3)(6)(40) = 360 x 10-3 = 0,360 lita
Sauyin da ake samu a cikin ƙarar acetone ya fi na ƙarfen, don haka wani ɓangare na ruwan yana zubewa.
Lissafa yawan ruwan da aka zubar:
0,360 lita - 0,00720 lita = 0,3528 lita = 0,35 lita
Amsar da ta dace ita ce A.
