Chiziqli kengayish faqat qattiq jismlar tomonidan sodir bo'ladi; hajm kengayishi barcha jismlar, ham qattiq, ham suyuq va gazsimon jismlar tomonidan sodir bo'ladi. Hajm kengayishi tenglamasi chiziqli kengayish tenglamasiga o'xshaydi.
Tavsif: V o = Boshlang'ich hajm, V = Yakuniy hajm, ΔV = V – V o = Hajm o'zgarishi, T o = Boshlang'ich harorat, T = Yakuniy harorat, ΔT = T – T o = Harorat o'zgarishi, β = hajm kengayish koeffitsienti. β birliklari = (C o ) -1
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Yuqoridagi hajm kengayish tenglamasi faqat jismlarning (ham qattiq, ham suyuq, ham gazsimon) hajmidagi o'zgarishlar jismning asl hajmidan kichik bo'lgandagina qo'llaniladi. Agar jism hajmidagi o'zgarish jismning boshlang'ich hajmidan katta bo'lsa, hajm kengayish tenglamasi to'g'ri natijalarni bermaydi. Odatda, qattiq jismlar tomonidan sodir bo'ladigan hajm o'zgarishlari juda katta bo'lmaydi. Boshqa tomondan, suyuqlik va gazning hajm kengayish koeffitsienti katta bo'ladi. Gazsimon moddalar uchun hajm kengayish koeffitsientini harorat o'zgarganda ham o'zgartirish oson. Shuning uchun yuqoridagi formula faqat qattiq jismlarning kengayishi uchun ishlatiladi.
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1. 30 ° C da alyuminiy sharning hajmi 30 sm3 ga teng . Chiziqli kengayish koeffitsienti 24 x 10-6 ° C -1 ga teng . Agar oxirgi hajm 30.5 sm3 bo'lsa , alyuminiy sharning oxirgi harorati qanday?
Ma'lum:
Chiziqli kengayish koeffitsienti ( α ) = 24 x 10 -6 o C -1
Hajm kengayish koeffitsienti ( β ) = 3 α = 3 x 24 x 10 -6 o C -1 = 72 x 10 -6 o C -1
Boshlang'ich harorat (T1 ) = 30 o C
Boshlang'ich hajm (V1 ) = 30 sm3
Yakuniy hajm (V2 ) = 30.5 sm3
Hajmning o'zgarishi ( ΔV ) = 30.5 sm3 – 30 sm3 = 0.5 sm3
Kerakli: Yakuniy harorat ( T2 )
yechim:
Δ V = β (V1 ) ( ΔT )
Δ V = β (V1 ) ( T2 – T1 )
0.5 sm3 = (72 x 10-6 oC-1)(30 sm.)3)(T)2 - 30oC)
0.5 = (2160 x 10 -6 ) (T 2 – 30 )
0.5 = (2.160 x 10 -3 ) (T 2 – 30 )
0.5 = (2.160 x 10 -3 ) (T 2 – 30 )
0.5 / (2.160 x 10 -3 ) = T 2 – 30
0.23 x 10 3 = T 2 – 30
0.23 x 1000 = T 2 – 30
230 = T 2 – 30
230 + 30 = T2
T2 = 260 ° C
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2. Metall sharning chiziqli kengayish koeffitsienti 9 x 10 -6 o C -1 ga teng . Metall sharning 20 o C da ichki diametri 2.2 sm ga teng. Agar oxirgi diametri 2.8 sm bo'lsa, oxirgi harorat qanday bo'ladi!
Ma'lum:
Chiziqli kengayish koeffitsienti ( α ) = 9 x 10 -6 o C -1
Hajm kengayish koeffitsienti ( β) = 3 α = 3 x 9 x 10 -6 o C -1 = 27 x 10 -6 o C -1
Boshlang'ich harorat (T1 ) = 20 o C
Dastlabki diametr (D1 ) = 2.2 sm
Yakuniy diametr (D2 ) = 2.8 sm
Boshlang'ich radius (r1 ) = D1 / 2 = 2.2 sm3 / 2 = 1.1 sm3
Yakuniy radius (r2 ) = D2 / 2 = 2.8 sm3 / 2 = 1.4 sm3
Boshlang'ich hajm (V1 ) = 4/3 π r13 = ( 4/3 )(3.14)(1.1 sm) 3 = (4/3)(3.14)(1.331 sm3 ) = 5.57 sm3
Yakuniy hajm (V2 ) = 4/3 π r3 = ( 4/3 )( 3.14 )(1.4 sm2) 3 = (4/3)(3.14)(2.744 sm3 ) = 11.48 sm3
Hajmning o'zgarishi ( Δ V) = 11.48 sm 3 – 5.57 sm 3 = 5.91 sm 3
Kerakli: Yakuniy harorat ( T2 )
yechim:
Δ V = β (V1 ) ( ΔT )
5.91 sm3 = (27 x 10-6 oC-1)(5.57 sm3)(T)2 - 20oC)
5.91 = (150.39 x 10 -6 ) (T 2 – 20)
5.91 / 150.39 x 10 -6 = T 2 – 20
0.039 x 10 6 = T 2 – 20
39 x 10 3 = T 2 – 20
39,000 = T 2 – 20
39,000 + 20 = T2
T2 = 39,020 o C
3. 2000 sm3 alyuminiy idish, 0 da suv bilan to'ldirilganoC. Va keyin 90 darajaga qadar qizdiriladioC. Agar alyuminiy uchun chiziqli kengayish koeffitsienti 24 x 10 ga teng bo'lsa-6 (oC)-1 va suv uchun hajm kengayish koeffitsienti 6.3 x 10 ga teng-4 (oC)-1, to'kilgan suv hajmini aniqlang.
Ma'lum:
Alyuminiy idish va suvning boshlang'ich hajmi (V o ) = 2000 sm 3 = 2 x 10 3 sm 3
Alyuminiy idish va suvning boshlang'ich harorati (T1 ) = 0 o C
Alyuminiy idish va suvning oxirgi harorati (T2 ) = 90 o C
Alyuminiy uchun chiziqli kengayish koeffitsienti (α) = 24 x 10 -6 ( o C ) -1
Alyuminiy uchun hajm kengayish koeffitsienti (γ) = 3α = 3 (24 x 10 -6 ( o C ) -1 ) = 72 x 10 -6 o C -1
Suv uchun hajm kengayish koeffitsienti (γ) = 6.3 x 10 -4 ( o C ) -1
Kerakli: To'kilgan suv hajmi
yechim:
Hajm kengayishining tenglamasi:
V = V o + γ V o ΔT
V – V o = γ V o ΔT
ΔV = γ V o ΔT
V = yakuniy hajm, V o = boshlang'ich hajm, ΔV = hajmning o'zgarishi, γ = hajm kengayish koeffitsienti, ΔT = haroratning o'zgarishi
Alyuminiy idish hajmining o'zgarishini hisoblang:
ΔV = γ V o ΔT = (72 x 10 -6 )(2 x 10 3 )(90) = 12960 x 10 -3 = 12.960 sm 3
Suv hajmining o'zgarishini hisoblang:
ΔV = γ V o ΔT = (6.3 x 10 -4 )(2 x 10 3 )(90) = 1134 x 10 -1 = 113.4 sm 3
Suv hajmining o'zgarishi alyuminiy idishdagidan kattaroq, shuning uchun bir oz suv to'kilgan.
To'kilgan suv hajmini hisoblang:
113.4 sm 3 – 12 960 sm 3 = 100.44 sm 3
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- Chiziqli kengayish
- Hududni kengaytirish
- Hajmni kengaytirish
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- Maxsus issiqlik va issiqlik sig'imi
- Yashirin issiqlik, erish issiqligi, bug'lanish issiqligi
- Issiqlik uzatish uchun energiya tejash
