Ihe atụ atọ nke ajụjụ gbasara mgbasawanye mpaghara
1. Mpempe akwụkwọ ígwè dị n'okpomọkụ nke 20 oC nwere ogologo 50 cm na obosara 30 cm. Ọ bụrụ na ọnụọgụgụ nke mgbasawanye ígwè dị larịị bụ 10 -5 o C -1 mgbe ahụ mmụba na mpaghara na mkpokọta mpaghara na okpomọkụ nke 60 o C bụ….
Mkparịta ụka
A maara na:
Okpomọkụ mbụ (T 1 ) = 20 oC
Okpomọkụ ikpeazụ (T2 ) = 60 oC
Mgbanwe okpomọkụ (Δ T) = 60 o C – 20 o C = 40 o C
Mpaghara mbụ (A 1 ) = Ogologo x obosara = 50 cm x 30 cm = 1500 cm 2
Ọnụọgụ nke mgbasawanye ahịrị nke ígwè (α ) = 10 -5 o C -1
Ọnụọgụ nke mgbasawanye nke ígwè (β ) = 2a = 2 x 10 -5 o C -1
Ajụjụ: Mmụba na mpaghara (Δ A )
Mmụba na mpaghara (Δ A ):
ΔA = βA 1Δ T
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
Mpaghara niile ( A2 ) :
A 2 = A 1 + Δ A
A 2 = 1500 cm 2 + 1.2 cm 2
A 2 = 1501 , 2 cm 2
2. Efere aluminom nwere oke mgbasa nke linear nke 24 x 10 -6 / o C nwere mpaghara nke 40 cm 2 na okpomọkụ nke 30 o C. Chọpụta okpomọkụ ikpeazụ ma ọ bụrụ na mpaghara nke efere aluminom abawanye ruo 40,2 cm 2.
Mkparịta ụka
A maara na:
Okpomọkụ mbụ (T 1 ) = 30 oC
Ọnụọgụ nke mgbasawanye ahịrị nke aluminom (α ) = 24 x 10 -6 o C -1
Ọnụọgụ nke mgbasawanye mpaghara nke aluminom (β ) = 2α = 2 x 24 x 10 -6 o C -1 = 48 x 10 -6 o C -1
Mpaghara mbụ (A 1 ) = 40 cm 2
Mpaghara ikpeazụ (A 2 ) = 40,2 cm 2
Mgbanwe na mpaghara (Δ A) = 40,2 cm 2 – 40 cm 2 = 0,2 cm 2
Ajụjụ: Chọpụta okpomọkụ ikpeazụ ( T2 )
Azịza:
Usoro maka mgbanwe na mpaghara (Δ A) :
ΔA = βA 1 Δ T
Okpomọkụ ikpeazụ (T2 ) :
ΔA = βA 1 ( T2 – T1 )
0,2 cm2 = (48 x) 10-6 oC-1)(40 cm)2)(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 = T 2
T 2 = 130
Okpomọkụ ikpeazụ = 130 oC
3. Ihe okirikiri dị na okpomọkụ nke 20 o C nwere radius nke 20 cm. Ọ bụrụ na okpomọkụ nke 100 o C, radius ahụ na-abawanye ruo 20,5 cm, mgbe ahụ, ọnụọgụ nke mgbasawanye ahịrị nke ihe ahụ bụ….
Mkparịta ụka
A maara na:
Okpomọkụ mbụ (T 1 ) = 30 oC
Okpomọkụ ikpeazụ (T2 ) = 100 oC
Mgbanwe okpomọkụ (Δ T) = 100 o C – 30 o C = 70 o C
Mgbada mbụ (r 1 ) = 20 cm
Oke njedebe (r 2 ) = 20,5 cm
Ajụjụ: Ọnụọgụ nke mgbasawanye mpaghara nke ihe ahụ ( b )
Azịza:
Mpaghara mbụ nke okirikiri ahụ (A 1 ) = π r 1 2 = (3,14)(20 cm) 2 = (3,14)(400 cm 2 ) = 1256 cm 2
Mpaghara ikpeazụ nke okirikiri ahụ (A 2 ) = π r 2 2 = (3,14)(20,5 cm) 2 = (3,14)(420,25 cm 2 ) = 1319,585 cm 2
Mmụba n'ógbè okirikiri (Δ A) = 1319,585 cm 2 – 1256 cm 2 = 63,585 cm 2
Usoro maka mgbanwe na mpaghara (Δ A) :
ΔA = βA 1 ΔT
Ọnụọgụ mgbasawanye mpaghara:
ΔA = βA 1 ΔT
63,585 cm 2 = β (1 256 cm 2 ) (70 o C)
63,585 = β ( 87920 o C)
β = 63,585 / 87920 o C
β = 0,00072 / o C
β = 7,2 x 1 0 -4 / o C
β = 7,2 x 1 0 -4 o C -1
Ọnụọgụ nke mgbasawanye ahịrị (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
