Kev nthuav dav ntawm thermal - teeb meem thiab kev daws teeb meem

Kev nthuav dav ntawm thermal - teeb meem thiab kev daws teeb meem

Kev nthuav dav ntawm thaj chaw

1. Ib daim hlau ntawm 20^oC muaj qhov loj raws li qhia hauv daim duab hauv qab no. Yog tias tus coefficient ntawm lpob ntseg nthuav dav rau hlau yog 10^{-5 o}C^-1 ces qhov kev hloov pauv hauv thaj chaw ntawm 60 yog dab tsi?^oC.

Paub:

Qhov ntev ntawm cov hlau = 40 cm

Dav ntawm hlau = 20 cm

Tus pib ntawm thaj chaw hlau (A_o) = (40)(20) = 800 cm²

Tus coefficient ntawm linear expansion (α) = 10^{-5 o}C^-1

Tus coefficient ntawm thaj chaw nthuav dav (β) = 2 x coefficient ntawm linear expansion (2α) = 2 x 10^{-5 o}C^-1

Qhov kev hloov pauv ntawm qhov kub thiab txias (ΔT) = 60^oC - 20^oC = 40^oC

Xav tau: Qhov kev hloov pauv hauv thaj chaw ntawm cov hlau ntawm 60^oC

Tshuaj:

Kev sib npaug ntawm thaj chaw nthuav dav:

ΔA = βA_o T

ΔA = qhov nce ntawm thaj tsam ntawm cov hlau, β = Tus coefficient ntawm thaj chaw nthuav dav, A_o = thaj chaw pib, ΔT = qhov hloov pauv ntawm qhov kub = qhov kub kawg - qhov kub pib

Qhov nce ntxiv nyob rau hauv thaj chaw ntawm cov hlau:

ΔA = βA_o T

ΔA = (2 x 10^-5)(800)(40) = 0.64 cm

2. Ib lub phaj hlau ntawm 20^oC tau pom hauv daim duab hauv qab no. Yog tias qhov kub thiab txias nce mus txog 100^oC thiab tus coefficient ntawm linear expansion ntawm hlau yog 1.1 x 10^{-7 o}C^-1, ces thaj chaw kawg ntawm lub phaj yog dab tsi.

Paub:

Qhov ntev ntawm lub phaj = 2 m

Dav ntawm lub phaj = 2 m

Thaj chaw pib ntawm hlau (A_o) = (2)(2) = 4 m²

Tus coefficient ntawm linear expansion rau hlau (α) = 1.1 x 10^{-7 o}C^-1

Tus coefficient ntawm thaj chaw nthuav dav rau hlau (β) = 2 x tus coefficient ntawm linear expansion rau hlau (2α) = 2.2 x 10^{-7 o}C^-1

Qhov kev hloov pauv ntawm qhov kub thiab txias (ΔT) = 100^oC - 20^oC = 80^oC

xav : Thaj chaw ntawm hlau ntawm 100^oC

Tshuaj:

Qhov ntev nce ntxiv:

ΔA = βA_o T

ΔA = (2.2 x 10^-7)(4)(80) = 704 x 10^-7 = 0,0000704 m²

Thaj chaw ntawm hlau:

Thaj chaw ntawm hlau = thaj chaw pib + qhov nce ntawm thaj chaw

Thaj tsam ntawm hlau = 4 m² + 0.0000704 m²

Thaj tsam ntawm hlau = 4.0000704 m²

3. Ib lub phaj tooj liab nrog cov coefficient ntawm linear expansion α = 18.10^{-6 o}C^-1 Ntawm 0^oC muaj qhov loj raws li qhia hauv daim duab hauv qab no. Yog tias lub phaj raug cua sov ntawm 80 ^oC, ces qhov nce ntawm thaj tsam ntawm lub phaj yog dab tsi.

Paub:

Qhov ntev ntawm tooj dag = 40 cm = 0.4 meters

Dav ntawm tooj liab = 20 cm = 0.2 meters

Thaj chaw pib ntawm tooj dag (A_o) = (0.4)(0.2) = 0.08 m²

Tus coefficient ntawm linear expansion rau tooj liab (α) = 18 x 10^{-6 o}C^-1

Tus coefficient ntawm thaj chaw nthuav dav rau tooj dag (β) = 2 x Tus coefficient ntawm linear expansion (2α) = 36 x 10^{-6 o}C^-1

Qhov kev hloov pauv ntawm qhov kub thiab txias (ΔT) = 80^oC - 0^oC = 80^oC

Xav tau: Qhov nce ntawm thaj chaw rau tooj liab ntawm 80^oC

Tshuaj:

Qhov nce ntawm thaj chaw rau tooj liab:

ΔA = βA_o T

ΔA = (36 x 10^-6)(0.08)(80) = 230.4 x 10^-6 Luas = 2.304 x 10^-4 m²

Kev nthuav dav ntawm ntim

4. Ib lub thawv iav uas muaj 4 liv dej puv, ces ua kom sov kom txog thaum qhov kub nce mus txog 20^oC. Muaj dej nchuav. Tus coefficient ntawm linear expansion rau iav = 9 x 10^{-6 o}C^-1tus coefficient ntawm qhov ntim nthuav dav rau dej = 2.1 x 10^{-4 o}C^-1Txheeb xyuas seb cov dej ntws ntau npaum li cas.

Paub:

Qhov ntim pib ntawm cov roj thiab dej (V)_o) = 4 liv

Qhov nce ntawm qhov kub ntawm lub khob thiab dej (ΔT) = 20^oC

Tus coefficient ntawm linear expansion rau iav (α) = 9 x 10^{-6 o}C^-1

Tus coefficient ntawm qhov ntim nthuav dav rau iav (γ) = 3α = 3 (9 x 10^{-6 o}C^-1) = 27 x 10^{-6 o}C^-1

Tus coefficient ntawm qhov ntim nthuav dav rau dej (γ) = 2.1 x 10^{-4 o}C^-1

Xav tau: Qhov ntim ntawm cov dej ntws tawm

Tshuaj:

Cov qauv ntawm qhov ntim nthuav dav:

V = V_o + γ V_o T

V - V_o = γ V_o T

ΔV = γV_o T

V = tau qhov kawg, V_o = thawj qhov ntim, ΔV = qhov kev hloov pauv ntawm qhov ntim, γ = tus coefficient ntawm kev nthuav dav ntim, ΔT = qhov kev hloov pauv ntawm qhov kub thiab txias.

Qhov kev hloov pauv ntawm qhov ntim ntawm lub thawv iav:

ΔV = γV_o ΔT = (27 x 10^-6)(4)(20) = 2160 x 10^-6 Luas = 2.160 x 10^-3 = 0.002160 liv

Qhov kev hloov pauv ntawm qhov ntim ntawm cov dej:

ΔV = γV_o ΔT = (2.1 x 10^-4)(4)(20) = 168 x 10^-4 = 0.0168 liv

Qhov kev hloov pauv ntawm cov dej ntim ntau dua li lub thawv iav, yog li qee cov dej nchuav.

Tus nqi ntawm cov dej ntws tawm:

0.0168 litres - 0.002160 litres = 0.01464 litres = 0.015 litres

5. Lub thawv hlau (tus coefficient ntawm linear expansion = 10^{-5 o}C^-1) nrog rau qhov ntim ntawm 6 liv uas muaj acetone (qhov coefficient ntawm qhov ntim nthuav dav = 1.5 x 10^{-3 o}C^-1). Yog tias lub thawv thiab acetone raug cua sov los ntawm 0^oC rau 40^oC, qhov ntim ntawm acetone uas nchuav yog dab tsi?

Paub:

Qhov ntim pib ntawm lub thawv thiab acetone (V)_o) = 6 liv

Qhov kev hloov pauv ntawm qhov kub ntawm lub thawv thiab acetone (ΔT) = 40^oC

Tus coefficient ntawm linear expansion rau hlau (α) = 10^{-5 o}C^-1

Tus coefficient ntawm kev nthuav dav rau hlau (γ) = 3α = 3 (10^{-5 o}C^-1) = 3 x 10^{-5 o}C^-1

Tus coefficient ntawm kev nthuav dav ntim rau acetone (γ) = 1.5 x 10^{-3 o}C^-1

Xav tau: Qhov ntau ntawm acetone uas tau nchuav tawm

Tshuaj:

Cov qauv ntawm kev nthuav dav ntawm ntim:

ΔV = γV_o T

ΔV = qhov kev hloov pauv ntawm qhov ntim, γ = tus coefficient ntawm kev nthuav dav ntim, V_o = thawj qhov ntim, ΔT = qhov kev hloov pauv ntawm qhov kub thiab txias.

Qhov kev hloov pauv ntawm qhov ntim ntawm lub thawv hlau:

ΔV = γV_o ΔT = (3 x 10^-5)(6)(40) = 720 x 10^-5 = 0.00720 liv

Kev hloov pauv ntawm qhov ntim ntawm acetone:

ΔV = γV_o ΔT = (1.5 x 10^-3)(6)(40) = 360 x 10^-3 = 0.360 liv

Qhov kev hloov pauv ntawm qhov ntim ntawm tshuaj txhuv yog loj dua li qhov steel thawv, yog li qee qhov acetone sntsiav tshuaj.

Cov tsos mob ntawm acetone hauv cov zis: +

0.360 litres - 0.00720 litres = 0.3528 litres = 0.35 litres

1. Kev nthuav dav thermal yog dab tsi?
   • teb: Kev nthuav dav thermal yog hais txog qhov kev hloov pauv ntawm cov khoom kom hloov nws qhov ntim los teb rau qhov kev hloov pauv ntawm qhov kub thiab txias.
2. Kev nthuav dav thermal cuam tshuam li cas rau qhov ceev ntawm ib yam khoom?
   • teb: Thaum ib yam khoom dhau los ntawm kev nthuav dav thermal, nws qhov ntim nce ntxiv, uas ua rau nws qhov ceev txo qis, xav tias nws qhov hnyav tseem nyob ruaj khov.
3. Vim li cas thiaj muaj qhov sib txawv ntawm cov ntu ntawm cov choj thiab txoj kev tsheb ciav hlau?
   • teb: Cov qhov sib txawv no, feem ntau hu ua cov pob qij txha nthuav dav, yog tsim los pab txhawb kev nthuav dav thiab kev sib cog lus ntawm cov khoom vim muaj kev hloov pauv ntawm qhov kub thiab txias, tiv thaiv kev hloov pauv lossis kev puas tsuaj.
4. Qhov txawv ntawm linear, volumetric, thiab area expansion yog dab tsi?
   • teb: Kev nthuav dav linear yog hais txog kev hloov pauv hauv ib qho ntev (zoo li qhov ntev ntawm ib tug pas nrig); kev nthuav dav cheeb tsam yog hais txog kev hloov pauv hauv ob qhov ntev (zoo li thaj tsam ntawm daim ntawv); thiab kev nthuav dav volumetric yog hais txog kev hloov pauv hauv txhua peb qhov ntev (zoo li qhov ntim ntawm cov kua).
5. Yuav ua li cas thiaj txiav txim tau qhov coefficient ntawm linear expansion?
   • teb: Nws yog txhais tias yog qhov kev hloov pauv me me ntawm qhov ntev ib degree hloov pauv ntawm qhov kub thiab txias ntawm qhov siab tas li. Rau ib yam khoom, qhov kev hloov pauv ntawm qhov ntev (∆L) vim yog qhov kub thiab txias hloov pauv (∆T) yog muab los ntawm ∆L=αL₀​∆T, qhov twg L₀​ yog qhov ntev pib thiab $\alpha$ yog tus coefficient ntawm linear expansion.
6. Vim li cas cov bimetallic strips khoov thaum cua sov lossis txias?
   • teb: Ib daim hlau bimetallic muaj ob hom hlau sib txawv uas sib txuas ua ke. Vim tias txhua hom hlau muaj nws tus kheej coefficient ntawm thermal expansion, lawv nthuav dav lossis cog lus ntawm cov nqi sib txawv thaum qhov kub hloov pauv. Qhov kev nthuav dav sib txawv no ua rau daim hlau khoov.
7. Qhov xwm txheej ntawm kev nthuav dav thermal cuam tshuam li cas rau qib dej hiav txwv nce siab?
   • teb: Ib feem ntawm qhov nce ntawm dej hiav txwv tuaj yeem yog vim qhov thermal nthuav dav ntawm dej hiav txwv. Thaum lub ntiaj teb kub nce siab, dej hiav txwv sov, ua rau dej nthuav dav thiab ua rau dej hiav txwv nce siab.
8. Yuav ua li cas tshwm sim hauv "kev nthuav dav tsis zoo ntawm dej"?
   • teb: Tsis zoo li feem ntau cov khoom, dej nthuav dav thaum nws txias ntawm 4°C mus rau 0°C, thiab tom qab ntawd nws poob thaum nws khov. Qhov txawv txav no txhais tau tias dej muaj nws qhov ceev tshaj plaws ntawm 4°C. Yog vim li cas dej khov (uas tsis ntom dua li dej ua kua) ntab saum dej.
9. Vim li cas kev nthuav dav thermal thiaj li tseem ceeb hauv kev tsim kho thiab kev tsim kho?
   • teb: Cov ntaub ntawv nthuav dav lossis luv thaum qhov kub hloov pauv. Yog tsis suav nrog kev nthuav dav thermal, cov qauv yuav muaj kev ntxhov siab, kev hloov pauv, lossis kev ua tsis tiav. Cov kws ua vaj tse thiab cov kws kes duab vajtse suav nrog cov yam ntxwv tsim qauv los tswj cov kev hloov pauv no kom muaj kev nyab xeeb.
10. Puas tuaj yeem thim rov qab qhov kev nthuav dav thermal?

• teb: Yog, feem ntau thaum cov khoom siv txias, nws yuav raug cua sov contraction, uas yog qhov sib txawv ntawm thermal expansion. Qhov degree thiab qhov xwm txheej ntawm qhov kev contraction no yuav nyob ntawm cov khoom siv thiab cov xwm txheej.