Kub thiab cua sov - teeb meem thiab kev daws teeb meem

Kub thiab cua sov - teeb meem thiab kev daws teeb meem

1. Ntawm lub ntsuas kub X, qhov chaw khov ntawm dej ntawm -30^o thiab qhov kub ntawm dej npau ntawm 90^o. 60^OX = ….. ^oC.

Paub:

Lub khov ntawm dej = -30^o

Lub ntsiab lus kub ntawm dej = 90^o

Xav tau: 60^oX = ….. ^oC

Tshuaj:

Nyob rau ntawm Fahrenheit scale, qhov khov ntawm dej yog 32^oF thiab lub ntsiab lus kub ntawm dej yog 212^oF. Nruab nrab ntawm qhov khov thiab qhov kub npau, 212^o - 32^o = 180^o.

Nyob rau ntawm Celsius nplai, qhov khov ntawm dej yog 0^oC thiab lub ntsiab lus kub ntawm dej yog 100^oC. Nruab nrab ntawm qhov khov thiab qhov kub npau, 100^o - 0^o = 100^o.

Ntawm qhov ntsuas X, qhov khov ntawm dej yog -30^oX thiab lub ntsiab lus kub ntawm dej yog 90^oX. Nruab nrab ntawm qhov khov thiab qhov kub npau, 90^o – (-30^o= 90 TZS^o + 30^o = 120^o.

Hloov qhov ntsuas X mus rau qhov ntsuas Celsius:

Thermal nthuav dav

2. Ib tug pas hlau uas tau cua sov los ntawm 30^oC rau 80^oC. Qhov ntev kawg ntawm tus pas nrig yog 115 cm. Tus coefficient ntawm kev nthuav dav linear is 3.10^{-3 o}C^-1. Qhov ntev pib ntawm tus pas hlau yog dab tsi?

Paub:

Qhov kub pib (T₁= 30 TZS^oC

Qhov kub kawg (T₂= 80 TZS^oC

Qhov kev hloov pauv ntawm qhov kub thiab txias (ΔT) = 80^oC - 30^oC = 50^oC

Tus coefficient ntawm linear expansion (α) = 3.10^{-3 o}C^-1

Qhov ntev kawg ntawm cov hlau (L) = 115 cm

Xav tau: Qhov ntev pib ntawm tus pas hlau (L_o)

Tshuaj:

Cov qauv ntawm kev nthuav dav linear:

L = L_o + ΔL

L = L_o + α L_o T

L = L_o (1 + α ΔT)

115 = L_o (1 + 3.10^-3.50)

115 = L_o (1 + 150.10^-3)

115 = L_o (1 + 0.15)

115 = L_o (1.15)

L_o = 115/1.15

L_o Luas = 100 cm

3. Qhov ntev pib ntawm ib tug pas nrig tooj dag yog 40 cm. Tom qab cua sov, qhov ntev kawg ntawm cov tooj dag yog 40.04 cm thiab qhov kub kawg yog 80^oC. Yog tias tus coefficient ntawm linear expansion ntawm tooj dag yog 2.0 x 10^{-5 o}C^-1, qhov kub pib ntawm tus pas nrig tooj dag yog dab tsi.

Paub:

Qhov kub kawg (T₂= 80 TZS^oC

Qhov ntev pib (L_o) = 40 cm

Qhov ntev kawg (L) = 40.04 cm

Qhov nce ntawm qhov ntev (ΔL) = 40.04 cm - 40 cm = 0.04 cm

Tus coefficient ntawm linear expansion (α) = 2.0 x 10^{-5 o}C^-1

Tshuaj: Kub pib (T₁)

Kev daws teeb meem;

Cov qauv ntawm kev nthuav dav linear:

L = L_o + α L_o T

L – L_o = α L_o T

ΔL = αL_o T

ΔL = αL_o (T₂ - T₁)

0.04 = (2.0 x 10^-5)(40)(80 – T₁)

0..04 = (80 x 10^-5)(80 – T₁)

0.04 = 0.0008 (80 – T₁)

0.04 = 0.064 – 0.0008 T₁

0..0008 T₁ = 0.064-0.040

0.0008 T₁ = 0.024

T₁ = 30^oC

Kev hloov pauv cua sov

4. Ob tug pas hlau uas muaj tib qhov loj tab sis txawv hom, raws li pom hauv daim duab hauv qab no. Lub thermal conductivity ntawm hlau I = 4 npaug ntawm lub thermal conductivity ntawm hlau II. Qhov kub ntawm ob lub hlau yog dab tsi.

Paub:

Qhov loj ntawm ob lub pas nrig yog tib yam.

Lub thermal conductivity ntawm hlau I = 4k

Lub thermal conductivity ntawm hlau II = k

Qhov kub ntawm ib kawg ntawm cov hlau I = 50⁰ C

Qhov kub ntawm ib kawg ntawm cov hlau II = 0⁰ C

SE pob: Qhov kub ntawm ob lub pas hlau

Tshuaj:

Kev sib npaug ntawm kev coj cua sov:

Q/t = tus nqi ntawm kev coj cua sov, k = thermal conductivity, Ib = thaj tsam hla, T₁-T₂ = qhov kev hloov pauv ntawm qhov kub thiab txias, l = qhov ntev ntawm tus pas nrig.

Qhov kub ntawm ob lub pas nrig:

Qhov kub ntawm qhov chaw nruab nrab ntawm ob lub pas hlau yog 40^oC.

5.

(1) Kev coj ua ntawm hlau

(2) Qhov sib txawv ntawm qhov kub thiab txias

(3) Qhov ntev ntawm cov hlau

(4) Qhov hnyav ntawm cov hlau

Cov yam uas txiav txim siab qhov nrawm ntawm kev coj cua sov ntawm cov hlau yog…..

Tshuaj:

Raws li qhov sib npaug ntawm kev xa cua sov, cov yam uas txiav txim siab qhov nrawm ntawm kev xa cua sov ntawm cov hlau yog kev xa hluav taws xob ntawm cov hlau (k), qhov sib txawv ntawm qhov kub thiab txias (T) thiab qhov ntev ntawm cov hlau (l).

6. Ob tug pas nrig uas loj ib yam tab sis muaj ntau hom sib txawv, raws li pom hauv daim duab hauv qab no. Qhov ua kom sov ntawm pas nrig P yog 2 npaug ntawm qhov ua kom sov ntawm pas nrig Q. Qhov kub ntawm ob tug pas nrig yog dab tsi.

Paub:

Ob lub pas nrig muaj tib qhov loj.

Kev ua kom sov ntawm cov pas nrig P (k)_P) = 2k

Lub thermal conductivity ntawm pas nrig Q (k)_Q) = k

SE pob: Qhov kub ntawm ob lub pas nrig

Tshuaj:

Kev sib npaug ntawm kev coj cua sov:

Q/t = tus nqi ntawm kev coj cua sov, k = thermal conductivity, Ib = thaj tsam hla, T₁-T₂ = qhov kev hloov pauv ntawm qhov kub thiab txias, l = qhov ntev ntawm tus pas nrig.

Qhov kub ntawm qhov chaw nruab nrab ntawm ob lub pas nrig:

Lub hauv paus ntsiab lus dub

8. 100 grams roj ntawm 20^oC thiab 50-gram hlau ntawm 75 ^oC raug muab tso rau hauv lub thawv hlau 200-gram. Qhov kub ntawm lub thawv nce ntxiv yog 5^oC thiab qhov kub tshwj xeeb ntawm roj yog 0.43 cal/g ^oC. Lub cua sov tshwj xeeb ntawm cov hlau yog dab tsi?

Paub:

Qhov hnyav ntawm lub thawv hlau (m) = 200 gr

Qhov kub pib ntawm lub thawv hlau (T₁) = qhov kub ntawm roj = 20^oC

Qhov kub kawg ntawm lub thawv hlau (T₂= 20 TZS^oC + 5^oC = 25^oC

Qhov hnyav ntawm cov roj (m) = 100 grams

Qhov kub tshwj xeeb ntawm cov roj (c_roj) = 0.43 cal/g ^oC

Qhov kub pib ntawm roj (T)₁= 20 TZS^oC

Qhov kub kawg ntawm roj (T)₂= 20 TZS^oC + 5^oC = 25^oC

Qhov hnyav ntawm hlau (m) = 50 grams

Qhov kub pib ntawm roj (T)₁= 75 TZS^oC

Qhov kub kawg ntawm roj (T)₂= 25 TZS^oC

Xav tau: Qhov kub tshwj xeeb ntawm hlau (c hlau)

Tshuaj:

Kub uas hlau tso tawm:

Q = mc ΔT = (50)(c)(75-25) = (50)(c)(50) = 2500c calorie

Kub uas lub thawv hlau nqus tau:

Q = mc ΔT = (200)(c)(25-20) = (200)(c)(5) = 1000c calorie

Kub uas roj nqus tau:

Q = mc ΔT = (100)(0.43)(25-20) = (43)(5) = 215 calories

Lub hauv paus ntsiab lus dub hais tias nyob rau hauv ib lub kaw lus cais tawm, cua sov tso tawm los ntawm cov khoom kub dua, nqus los ntawm cov khoom txias dua.

Q tso tawm = Q nqus

2500c = 1000c + 215

2500c – 1000c = 215

1500c = 215

c = 215/1500

c = 0.143 cal/g ^oC

9. Muab dej 200-gram tso rau hauv dej khov 50-gram ntawm -2°C. Yog tias qhov kub hloov pauv tsuas yog nyob nruab nrab ntawm dej thiab dej khov xwb, qhov kub kawg ntawm qhov sib tov yog dab tsi? Qhov kub tshwj xeeb ntawm dej yog 1 cal/gr°C, qhov kub tshwj xeeb ntawm dej khov yog 0.5 cal/gr°C, qhov kub ntawm kev sib xyaw rau dej khov yog 80 cal/gr.

Paub:

Qhov hnyav ntawm dej (m_dej) = 200 grams

Kub ntawm dej (T_dej= 20 TZS^oC

Qhov kub tshwj xeeb ntawm dej (c)_dej) = 1 cal/gr°C

Qhov hnyav ntawm dej khov (m_{Dej khov}) = 50 grams

Kub ntawm dej khov (T_{Dej khov}) = -2^oC

Qhov kub tshwj xeeb ntawm dej khov (c_{Dej khov}) = 0.5 cal/gr°C

Lub cua sov ntawm kev sib xyaw rau dej khov (L) = 80 calorie/gr

Tshuaj:

Kub ua rau dej khov nce ntxiv los ntawm -2^oC rau 0^oC:

Q = mc ΔT

Q = (50 gram)(0.5 cal/gr°C)(0^oC – (-2^oC))

Q = (50)(0.5 calorie)(2)

Q = 50 calories

Kub rau yaj tag nrho cov dej khov:

Q = m L = (50 grams) (80 calories/gram) = 4000 calories

Cua sov rau qhov kub ntawm txhua qhov dej los ntawm 20^oC rau 0^oC:

Q = mc ΔT

Q = (200 gram)(1 cal/gr°C)(0^oC – (20^oC))

Q = (200)(1 calorie)(-20)

Q = -4000 calories

Lub cim ntxiv qhia tias qhov kub tau ntxiv, lub cim rho tawm qhia tias qhov kub tau tso tawm.

50-calorie cua sov xav tau los ua kom qhov kub ntawm dej khov nce mus txog 0^oC thiab 4000-calorie xav tau los yaj tag nrho cov dej khov. Tag nrho cov cua sov = 4050 calories. Cov cua sov uas dej tso tawm yog 4000 calories.

Qee cov dej khov tsis yaj, yog li qhov kub kawg ntawm dej khov thiab dej yog 0^oC.

10. Ib lub txhuas 200-gram ntawm 20^oC muab tso rau hauv 100-gram dej ntawm 80^oC nyob rau hauv ib lub thawv. Lub cua sov tshwj xeeb ntawm txhuas yog 0.22 cal/g ^oC thiab qhov kub tshwj xeeb ntawm dej yog 1 cal/g ^oC. Qhov kub kawg ntawm txhuas yog dab tsi?

Paub:

Qhov hnyav ntawm txhuas = 200 grams

Kub ntawm txhuas = 20^oC

Qhov hnyav ntawm dej = 100 grams

Kub dej = 80^oC

Cov cua sov tshwj xeeb ntawm txhuas = 0.22 cal/g ^oC

Qhov kub tshwj xeeb ntawm dej = 1 cal/g ^oC

SE pob: Qhov kub kawg ntawm txhuas

Tshuaj:

Aluminium thiab dej nyob hauv qhov sib npaug ntawm thermal yog li qhov kub kawg ntawm aluminium = qhov kub kawg ntawm dej.

Kub tso tawm los ntawm dej kub (Q tso tawm) = kub nqus los ntawm txhuas (Q nqus)

m_dej c (ΔT) = m_txhuas c (ΔT)

(100)(1)(80 – T) = (200)(0.22)(T – 20)

(100)(80 – T) = (44)(T – 20)

8000 – 100T = 44T – 880

8000 + 880 = 44T + 100T

8880 = 144T

TXL = 62^oC

11. Muab ib lub hlau hnyav 50-gram tso rau hauv dej uas muaj qhov kub ntawm 85 °C thiab muab tso rau hauv dej uas muaj qhov kub ntawm 29.8 °C. Qhov kub tshwj xeeb ntawm dej = 1 cal.g ^—1 .°C^—1Qhov kub kawg yog 37 ° C. Lub cua sov tshwj xeeb ntawm cov hlau yog dab tsi.

Paub:

Qhov hnyav ntawm cov hlau (m_hlau) = 50 grams

Kub ntawm hlau = 85^oC

Qhov hnyav ntawm dej (m_dej) = 50 grams

Kub dej = 29,8^oC

Qhov kub tshwj xeeb ntawm dej (c)_dej) = 1 cal.g ^-1 .°C^-1

Qhov kub kawg ntawm dej = 37^oC

Xav tau: Qhov kub tshwj xeeb ntawm cov hlau (c hlau)

Tshuaj:

Cov cua sov uas cov hlau kub tso tawm (Q tso tawm) = cov cua sov uas dej nqus tau (Q nqus)

m_hlau c (ΔT) = m_dej c (ΔT)

(50)(c)(85 – 37) = (50)(1)(37 – 29.8)

(c)(85 – 37) = (1)(37 – 29.8)

48 c = 7.2

c = 0.15 cal.g ^-1 .°C^-1

12. Ib daim dej khov uas hnyav 50-gram ntawm 0°C thiab 200-gram dej ntawm 30°C, muab tso rau hauv ib lub thawv. . Yog tias qhov kub tshwj xeeb ntawm dej yog 1 cal.g^{- 1} ° C ^-1 thiab qhov kub ntawm kev sib xyaw rau dej khov yog 80 cal.g ^-1. Qhov kub kawg ntawm cov khoom sib tov yog dab tsi.

Paub:

Qhov hnyav ntawm dej khov (m_{Dej khov}) = 50 grams

Qhov kub ntawm dej khov = 0°C

Qhov hnyav ntawm dej (m_dej) = 200 grams

Kub dej = 30^oC

Qhov kub tshwj xeeb ntawm dej (c)_dej) = 1 cal.g^{- 1} ° C ^-1

Qhov kub ntawm kev sib xyaw rau dej khov (L)_{Dej khov}) = 80 cal.g ^-1

SE pob: Qhov kub kawg

Tshuaj:

Kwv yees qhov xwm txheej kawg:

Cov cua sov uas dej tso tawm los txo nws qhov kub ntawm 30^oC rau 0^oC:

Q_{tso tawm} = kuv_dej c_dej (ΔT) = (200)(1)(30-0) = (200)(30) = 6000

Kub xav tau los yaj tag nrho cov dej khov:

Q = m_{Dej khov} L_{Dej khov}= (50)(80) = 4000

Kub siv los yaj tag nrho cov dej khov yog 4000, thaum cua sov tso tawm los ntawm dej yog 6000. Yuav xaus lus tias qhov kub kawg ntawm qhov sib tov yog siab dua 0^oC.

Txoj cai dub:

Cov cua sov uas dej tso tawm = cua sov rau yaj tag nrho cov dej khov + cua sov kom ua rau cov dej khov kub ntxiv.

(m_dej)(c_dej)(ΔT) = (m_{Dej khov})(L_{Dej khov}) + (m_{Dej khov})(c_dej)(ΔT)

(200)(1)(30-T) = (50)(80) + (50)(1)(T-0)

(200)(30-T) = (50)(80) + (50)(T-0)

6000 – 200T = 4000 + 50T – 0

6000 – 4000 = 50T + 200T

2000 = 250T

T = 2000/250

TXL = 8^oC