Faɗaɗa yanki - matsaloli da mafita

1. A digiri 20 na Celsius, tsawon takardar ƙarfe shine 50 cm kuma faɗin shine 30 cm. Idan ma'aunin faɗaɗa layi na ƙarfe shine 10 -5 o C -1 , ƙayyade canjin yankin da yankin ƙarshe a 60 o C.

An sani:

Zafin farko (T1 ) = 20 oC

Zafin ƙarshe (T2 ) = 60 oC

Canjin zafin jiki ( ΔT ) = 60 o C – 20 o C = 40 o C

Yankin farko (A 1 ) = tsayi x faɗi = 50 cm x 30 cm = 1500 cm 2

Ma'aunin faɗaɗa layi na ƙarfe ( α) = 10 -5 o C -1

Ma'aunin faɗaɗa yanki na ƙarfe ( β) = 2α = 2 x 10 -5 o C -1

Ana so: Canjin yanki ( ΔA )

Magani:

Canjin yanki ( ΔA ):

ΔA = βA 1 ΔT

ΔA = ( 2 x 10 -5 o C -1 )(1500 cm 2 )(40 o C)

ΔA = (80 x 10 -5 ) (1500 cm 2 )

ΔA = 1 20,000 x 10 -5 cm 2

ΔA = 1. 2 x 10 5 x 10 -5 cm 2

ΔA = 1.2 cm 2

Yankin ƙarshe ( A 2 ):

A 2 = A 1 + ΔA

A 2 = 1500 cm 2 + 1. 2 cm 2

A 2 = 1501. 2 cm 2

[irp]

2. A zafin digiri 30 na Celsius , yankin takardar aluminum shine 40 cm 2 kuma ma'aunin faɗaɗa layi shine 24 x 10 -6 / o C. Ƙayyade zafin jiki na ƙarshe idan yankin ƙarshe shine 40.2 cm 2.

An sani:

Zafin farko (T1 ) = 30 oC

Ma'aunin faɗaɗa layi ( α) = 24 x 10 -6 o C -1

Ma'aunin faɗaɗa yanki ( β) = 2a = 2 x 24 x 10 -6 o C -1 = 48 x 10 -6 o C -1

Yankin farko (A 1 ) = 40 cm 2

Yankin ƙarshe (A 2 ) = 40.2 cm 2

Canjin yanki ( ΔA) = 40.2 cm 2 – 40 cm 2 = 0.2 cm 2

Ana so: Ƙayyade zafin jiki na ƙarshe ( T2 )

Magani:

Tsarin canjin yanki ( ΔA) :

ΔA = βA 1 ΔT

Zafin ƙarshe (T2 ) :

ΔA = βA 1 (T 2 – T 1 )

0.2 cm2 = (48 x 10-6 oC-1)(40 cm2)(T2 - 30oC)

0.2 = (1920 x 10 -6 ) (T 2 – 30 )

0.2 = (1.920 x 10 -3 ) (T 2 – 30)

0.2 = (2 x 10 -3 ) (T 2 – 30)

0.2 / (2 x 10 -3 ) = T 2 – 30

0.1 x 10 3 = T 2 – 30

1 x 10 2 = T 2 – 30

100 = T 2 – 30

100 + 30 = T2

T2 = 130

Zafin ƙarshe = 130 oC

[irp]

3. Radius na zobe a 20 oC shine 20 cm. Idan radius na ƙarshe a 100 oC shine 20.5 cm, ƙayyade ma'aunin faɗaɗa yanki da ma'aunin faɗaɗa layi…

An sani:

Zafin farko (T1 ) = 30 oC

Zafin ƙarshe (T2 ) = 100 oC

Canjin zafin jiki ( ΔT ) = 100 o C – 30 o C = 70 o C

Radius na farko (r1 ) = 20 cm

Radius na ƙarshe (r2 ) = 20.5 cm

Ana so: Ma'aunin faɗaɗa yanki ( β )

Magani:

Yankin farko (A 1 ) = π r 1 2 = (3.14)(20 cm) 2 = (3.14)(400 cm 2 ) = 1256 cm 2

Yankin ƙarshe (A 2 ) = π r 2 2 = (3.14)(20.5 cm) 2 = (3.14)(420.25 cm 2 ) = 1319.585 cm 2

Sauyin yanki ( ΔA) = 1319.585 cm 2 – 1256 cm 2 = 63.585 cm 2

Tsarin canjin yanki ( ΔA) :

ΔA = βA 1 ΔT

Ma'aunin faɗaɗa yanki:

ΔA = βA 1 ΔT

63.585 cm 2 = b (1 256 cm 2 )(70 o C)

63.585 = b ( 87,920 o C)

β = 63.585 / 87,920 oC

β = 0.00072 / oC

β = 7.2 x 1 0 -4 / o C

β = 7.2 x 1 0 -4 o C -1

Ma'aunin faɗaɗa layi ( α ):

β = 2 α

α = β / 2

α = (7.2 x 1 0 -4 ) / 2

α = 3.6 x 1 0 -4 o C -1

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  1. Canza ma'aunin zafin jiki
  2. Fadada layin layi
  3. Faɗaɗa yanki
  4. Fadada ƙara
  5. Heat
  6. Daidaiton zafi na inji
  7. Ƙarfin zafi da zafi na musamman
  8. Zafin da ke ɓoye, zafin haɗuwa, zafin tururi
  9. Ajiye makamashi don canja wurin zafi

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