Bɛyɛ mfe 1. Na 20 oC, ogologo mpempe akwụkwọ ígwè bụ 50 cm na obosara ya bụ 30 cm. Ọ bụrụ na ọnụọgụgụ nke Mgbasawanye ahịrị maka ígwè bụ 10-5 oC-1, chọpụta mgbanwe na mpaghara na mpaghara ikpeazụ na 60 oC.
A maara:
The mbụ okpomọkụ (T1) = 20oC
Okpomọkụ ikpeazụ (T)2) = 60oC
Mgbanwe na okpomọkụ (ΔT) = 60oC - 20oC=40oC
Mpaghara mbụ (A)1) = ogologo x obosara = 50 cm x 30 cm = 1500 cm2
Ọnụọgụ nke mgbasawanye ahịrị maka ígwè (α) = 10-5 oC-1
Ọnụ ọgụgụ nke mgbasawanye mpaghara maka ígwè (β) = 2α = 2 x 10-5 oC-1
A chọrọ: Mgbanwe na mpaghara (ΔA)
Ngwọta:
Mgbanwe na mpaghara (ΔA):
ΔA = β A1 ΔT
ΔA = (2 x 10-5 oC-1)(1500 cm)2(40.)oC)
ΔA = (80) X XUMUM-5)(1500 cm)2)
ΔA = 120,000 x 10-5 cm2
ΔA = 1.2 x 105 X XUMUM-5 cm2
ΔA = 1.2 cm2
Mpaghara ikpeazụ (A2):
A2 =A1 + ΔA
A2 = 1500 sentimita2 + 1.2 cm2
A2 = 1501.2 cm2
Bɛyɛ mfe 2. Na 30 oC, mpaghara nke mpempe akwụkwọ aluminom bụ 40 cm2 na ọnụọgụ nke mgbasawanye ahịrị bụ 24 x 10-6 /oC. Chọpụta okpomọkụ ikpeazụ ma ọ bụrụ na mpaghara ikpeazụ bụ 40.2 cm2.
A maara:
Okpomọkụ mbụ (T)1) = 30oC
Ọnụọgụ nke mgbasawanye ahịrị (α) = 24 x 10-6 oC-1
Ọnụọgụ nke mgbasawanye mpaghara (β) = 2a = 2 x 24 x 10-6 oC-1 = 48 x ihe 10-6 oC-1
Mpaghara mbụ (A)1) = 40cm2
Mpaghara ikpeazụ (A)2) = 40.2cm2
Mgbanwe na mpaghara (ΔA) = 40.2 cm2 - 40 cm2 = 0.2 sentimita2
A chọrọ: Chọpụta okpomọkụ ikpeazụ (T)2)
Ngwọta:
Usoro mgbanwe na mpaghara (ΔA) :
ΔA = β A1 ΔT
Okpomọkụ ikpeazụ (T)2):
ΔA = β A1 (T2 - A1)
0.2 cm2 = (48 x) 10-6 oC-1)(40 cm)2)(T2 - 30oC)
0.2 = (1920 x) 10-6)(T2 - 30)
0.2 = (1.920 x) 10-3)(T2 - 30)
0.2 = (2 x) 10-3)(T2 - 30)
0.2 / (2 X XUMUM-3) = T2 - 30
0.1 X XUMUM3 = T2 - 30
1 x 102 =T2 - 30
100=T2 - 30
100 + 30 = T2
T2 = 130
Okpomọkụ ikpeazụ = 130oC
3. radius nke mgbanaka na 20 oC bụ 20 cm. Ọ bụrụ na radius ikpeazụ dị na 100 oC bụ 20.5 cm, chọpụta ọnụọgụgụ nke mgbasawanye mpaghara na ọnụọgụgụ nke mgbasawanye ahịrị…
A maara:
Okpomọkụ mbụ (T)1) = 30oC
Okpomọkụ ikpeazụ (T)2) = 100oC
Mgbanwe na okpomọkụ (ΔT) = 100oC - 30oC=70oC
Mgbada mbụ (r)1) = 20cm
Mgbada ikpeazụ (r)2) = 20.5cm
A chọrọ: Ọnụọgụ nke mgbasawanye mpaghara (β)
Ngwọta:
Mpaghara mbụ (A)1) = π r12 = (3.14)(20 cm)2 = (3.14)(400 cm)2) = 1256cm2
Mpaghara ikpeazụ (A)2) = π r22 = (3.14)(20.5 cm)2 = (3.14)(420.25 cm)2) = 1319.585cm2
Mgbanwe na mpaghara (ΔA) = 1319.585 cm2 - 1256 cm2 = 63.585 sentimita2
Usoro mgbanwe na mpaghara (ΔA) :
ΔA = β A1 ΔT
Ọnụọgụ nke mgbasawanye mpaghara:
ΔA = β A1 ΔT
63.585 cm2 = b (1256 cm2(70.) oC)
63.585 = b (87,920 oC)
β = 63.585 / 87,920 oC
β = 0.00072 /oC
β = 7.2 X XUMUM0-4 /oC
β = 7.2 X XUMUM0-4 oC-1
Ọnụọgụ nke mgbasawanye ahịrị (α):
β = 2 α
α = β / 2
α = (7.2) X XUMUM0-4) /2
α = 3.6 X XUMUM0-4 oC-1
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