Matsalolin da aka Magance a fannin Fizik na Asali

1. Tsawon madubin da ke da santsi shine 10 cm kuma nisan abu shine 20 cm. Kayyade (a) nisan hoton (b) girman hoton

An sani:

Tsawon mai da hankali (f) = -10 cm

Alamar cirewa tana nuna cewa wurin da madubin convex ke haskakawa yana kama-da-wane

Nisa tsakanin abu ( d _o ) = 20 cm

Magani:

Tsarin hoto ta hanyar madubi mai lanƙwasa:

Nisa ta hoton (d _i ):

1/ d _i = 1/f – 1/ d _o = -1/10 – 1/20 = -2/20 – 1/20 = -3/20

d _i = -20/3 = -6.7 cm

Alamar cirewa tana nuna cewa hoton na kama-da-wane ne.

Girman hoto:

m = – d _i / d _o = -(-6.7)/20 = 6.7/20 = 0.3

m = ƙaramin abu sau 0,3 fiye da abin.

Alamar ƙarin tana nuna cewa hoton yana sama.

[irp]

2. An sanya wani abu mai tsayin santimita 10 a gaban madubi mai lanƙwasa mai tsawon santimita 20. A tantance tsayin hoton idan nisan abin shine (a) 10 cm (b) 30 cm (c) 40 cm (d) 50 cm

An sani:

Tsawon madubin mai lanƙwasa (f) = -20 cm

Alamar cirewa tana nuna cewa wurin da aka fi mayar da hankali shi ne na kama-da-wane

Radius na lanƙwasa ( r ) = 2 f = 2(20) = 40 cm

Tsawon abu (h) = 10 cm

Magani:

a) tsawon mai da hankali (f) = -20 cm da nisan abu (d _o ) = 10 cm

Nisa ta hoton (d _i ) :

1/ d _i = 1/f – 1/ d _o = -1/20 – 1/10 = -1/20 – 2/20 = -3/20

d _i = -20/3 = -6.7

Alamar ragewa tana nuna cewa hoton na kama-da-wane ne ko kuma hoton yana bayan madubi.

Girman hoto ( m ):

m = – d _i / d _o = -(-6.7)/10 = 6.7/10 = 0.67

Alamar da aka ƙara tana nuna cewa hoton yana tsaye.

Hoton ya fi ƙanƙanta da abin da aka yi amfani da shi a girmansa 0.67.

Tsawon hoton (h _i ):

m = h _i / h _o

h _i = h _o m = (10 cm)(0.67) = 6.7 cm

b) tsawon mai da hankali (f) = -20 cm da nisan abu ( d _o ) = 30 cm

Nisa ta hoton ( d _i ):

1/ d _i = 1/f – 1/ d _o = -1/20 – 1/30 = -3/60 – 2/60 = -5/60

d _i = -60/5 = -12

Alamar ragewa tana nuna cewa hoton na kama-da-wane ne ko kuma hoton yana bayan madubi.

Girman hoto ( m ):

m = – d _i / d _o = -(-12)/30 = 12/30 = 0.4

Alamar da aka ƙara tana nuna cewa hoton yana tsaye.

Hoton ya fi ƙanƙanta da abu sau 0,4.

Tsawon hoton (h _i ):

m = h _i / h _o

h _i = h _o m = (10 cm)(0.4) = 4 cm

c) Tsawon mai da hankali (f) = -20 cm da nisan abu ( d _o ) = 40 cm

Nisa ta hoton ( d _i ):

1/ d _i = 1/f – 1/ d _o = -1/20 – 1/40 = -2/40 – 1/40 = -3/40

d _i = -40/3 = -13.3

Alamar ragewa tana nuna cewa hoton na kama-da-wane ne ko kuma hoton yana bayan madubin da ke da santsi.

Girman hoto ( m ):

m = – d _i / d _o = -(-13.3)/40 = 13.3/40 = 0.3

Alamar da aka ƙara tana nuna cewa hoton yana tsaye.

Hoton ya fi ƙanƙanta da abin da aka yi amfani da shi a girmansa 0.3.

Tsawon hoton ( h _{i )} :

m = h _i / h _o

h _i = h _o m = (10 cm)(0.3) = 3 cm

d) Tsawon mai da hankali (f) = -20 cm da nisan abu ( d _o ) = 50 cm

Nisa ta hoton ( d _i ):

1/ d _i = 1/f – 1/ d _o = -1/20 – 1/50 = -5/100 – 2/100 = -7/100

d _i = -100/7 = -14.3

Alamar ragewa tana nuna cewa hoton na kama-da-wane ne ko kuma hoton yana bayan madubin da ke da santsi.

Girman hoto ( m ):

m = – d _i / d _o = -(-14.3)/50 = 14.3/50 = 0.3

Alamar da aka ƙara tana nuna cewa hoton yana tsaye.

Hoton ya fi ƙanƙanta da abin da aka yi amfani da shi a girmansa 0.3.

Tsawon hoton (h _i ) :

m = h _i / h _o

h _i = h _o m = (10 cm)(0.3) = 3 cm

[irp]

3. A kan abu yana da nisan santimita 20 a gaban madubin mai lanƙwasa . Idan tsayin hoton ya ninka tsayin abu sau 1/5, a tantance ( a) tsawon hoton b) tsawon mai da hankali c) halayen hoton

An sani:

Nisa tsakanin abu ( d _o ) = 20 cm

Tsawon hoton (h _i ) = 1/5 h = 0.2 h

Tsawon abu (h) = h

Magani:

a) nisan hoton ( d _i )

Tsarin girman hoto :

m = h _i / h _o = 0.2h / h = 0.2

Alamar da aka ƙara tana nuna cewa hoton yana tsaye.

Hoton ya fi ƙanƙanta da abin da aka yi amfani da shi a girmansa 0.2.

Nisa ta hoton ( d _i ):

– d _i = md _o

d _i = – m d _o = -(0.2)(20 cm) = -4 cm

Alamar ragewa tana nuna cewa hoton na kama-da-wane ne ko kuma hoton yana bayan madubin da ke da santsi.

b) Tsawon mai da hankali ( f)

Tsawon mai da hankali (f):

1/f = 1/ d _o + 1/ d _i = 1/20 – 1/4 = 1/20 – 5/20 = -4/20

f = -20/4 = -5 cm

Alamar ragewa tana nuna cewa wurin da aka fi mayar da hankali a kai shine kama-da-wane.

c) Halayen hoton:

- Tsaye

- Ƙarami

- kama-da-wane

4. Haske ya bugi madubi mai lanƙwasa a layi ɗaya da axis zai haskaka….

A. zuwa ga madogarar madubi mai haske

B. kamar daga wurin madubi mai haske

C. ta tsakiyar lanƙwasa madubin

D. daidai da madubin jirgin sama

Magani

An zana matsalar a cikin hoton da ke ƙasa.

Amsar da ta dace ita ce B.

5. Mai keke yana ganin hoton babur a bayansa sau 1/6 girmansa na asali lokacin da nisan da ke tsakanin mai keken da babur ya kai mita 30. A tantance radius na lanƙwasa na madubin baya…

A. 7.14 m

B. 8.57 m

C. mita 12.00

D. 24.00 m

An sani:

Girman hoto (M) = sau 1/6

Nisa tsakanin abu (d) = mita 30

Ana so: Radius na lanƙwasa na madubin hangen baya (R)

Magani:

Lissafa nisan hoton (d')

Tunda an san girman hoto (M) da nisan abu (s), ana iya sanin nisan hoton ta amfani da dabarar girman hoto:

Alamar da ba ta da kyau tana nufin hoton na kama-da-wane ne. Hoton yana da mita 5 a bayan madubin da ke da lanƙwasa.

Lissafa tsawon mai da hankali (f)

Tunda nisan abu (d) da nisan hoton (d'), to ana iya ƙididdige tsawon mai da hankali ta amfani da dabarar madubi:

Radius na lanƙwasa (R)

Radius na lanƙwasa madubin mai lanƙwasa ya ninka tsawon madubin mai lanƙwasa sau biyu.
R = 2 f = 2 (mita 6) = mita 12
Tsawon lanƙwasa na madubin convex shine mita 12.
Madaidaicin amsar ita ce C.

6. An zaɓi madubin mai lanƙwasa a matsayin madubin kallon baya na babur saboda halayen hoton da madubin ya samar sune…

A. na gaske, a tsaye, an rage girmansa

B. na gaske, a miƙe, an faɗaɗa

C. kama-da-wane, a tsaye, an rage girmansa

D. kama-da-wane, a tsaye, an faɗaɗa

Magani:

Dangane da siffofi biyu da ke sama, za a iya kammala da cewa halayen hoton suna kama-da-wane, a tsaye, an rage su.

Madaidaicin amsar ita ce C.

7. Abu yana da nisan santimita 12 a gaban madubi mai lanƙwasa tare da radius na santimita 6. Sifofin hoton sune…

A. ainihin, an juya shi a nesa na 12 cm

B. na gaske, a tsaye a nesa na 4 cm

C. kama-da-wane, a tsaye a nesa na 2.4 cm

D. kama-da-wane, an juya shi a nesa na 6 cm

An sani:

Nisa tsakanin abu (d) = 12 cm

Radius na madubin mai lanƙwasa (r) = 6 cm.

Tsawon madubin mai lanƙwasa (f) = 6 cm / 2 = -3 cm

Tsawon madubin da ke da kusurwar kusurwa an sanya masa alama mara kyau saboda kama-da-wane ne. Kama-da-wane saboda ba a wuce shi ta hanyar haske.

Ana so: Halayen hoto

Magani:

Nisa daga hoton (d'):

1/d' = 1/f – 1/d = -1/3 – 1/12 = -4/12 – 1/12 = -5/12

d' = -12/5 = -2.4 cm

Nisa da aka sanya wa hannu a kan hoton mara kyau yana nufin hoton na kama-da-wane ne.

Girman hoto (m):

m = -d' / d = -(-2.4) / 12 = 2.4 / 12 = sau 0.2

Girman hoton da aka sanya alama mai kyau yana nufin cewa hoton yana tsaye kuma girman hoton shine 0.2 yana nufin girman hoton ya fi ƙanƙanta fiye da girman abu (wanda aka rage).

Madaidaicin amsar ita ce C.

[wpdm_package id='860′]

1. Matsaloli da mafita na madubin Concave
2. Matsaloli da mafita na madubin convex
3. Matsalolin ruwan tabarau masu bambanta da mafita
4. Haɗa matsalolin ruwan tabarau da mafita
5. Kayan aikin gani matsalolin ido da mafita na ɗan adam
6. Matsaloli da mafita na kayan aikin gani da ruwan tabarau na tuntuɓa
7. Gilashin ido na kayan aiki na gani
8. Matsaloli da mafita na kayan aikin ƙara girman gilashin gani
9. Na'urar microscope ta gani - matsaloli da mafita
10. Matsaloli da mafita na na'urorin hangen nesa na gani

Karin bayani

1. An sanya wani abu a nisan santimita 10 daga madubi mai lanƙwasa . Tsawon abin da aka mayar da hankali a kai shine santimita 5. A tantance (a) Nisan hoton (b) girman hoton

An sani:

Tsawon mai da hankali (f) = 5 cm

Nisa tsakanin abu ( d _o ) = 10 cm

Mafita :

Tsarin hoto ta hanyar madubi mai lanƙwasa:

Nisa ta hoton:

1/ d _i = 1/f – 1/ d _o = 1/5 – 1/10 = 2/10 – 1/10 = 1/10

d _i = 10/1 = 10 cm

Nisa tsakanin hotunan shine 10 cm.

Girman:

m = – d _i / d _o = -10/10 = -1

1 yana nufin cewa hoton iri ɗaya ne da abin.

Alamar ragewa tana nuna cewa hoton ya juya. Idan alamar ta kasance tabbatacce to hoton ya miƙe.

[irp]

2. An sanya wani abu mai tsayin santimita 5 a gaban madubi mai lanƙwasa mai tsawon santimita 20. A tantance tsayin hoton idan nisan abin shine santimita 5, santimita 15, santimita 20, da santimita 30.

An sani:

Radius na lanƙwasa ( r ) = 20 cm

Tsawon mai da hankali (f) = R/2 = 20/2 = 10 cm

Tsawon abu (h _o ) = 5 cm

Magani:

a) tsawon mai da hankali (f) = 10 cm da nisan abu ( d _o ) = 5 cm

Tsarin hoto ta hanyar madubi mai lanƙwasa:

Nisa ta hoton ( d _i ):

1/ d _i = 1/f – 1/ d _o = 1/10 – 1/5 = 1/10 – 2/10 = -1/10

d _i = -10/1 = -10 cm

Alamar ragewa tana nuna cewa hoton na kama-da-wane ne ko kuma hoton yana bayan madubi.

Girman hoto ( m ):

m = – d _i / d _o = -(-10)/5 = 10/5 = 2

Alamar da aka ƙara tana nuna cewa hoton yana tsaye.

Tsawon hoton ( h _i ):

m = h _i / h _o

h _i = h _o m = (5 cm)(2) = 10 cm

Tsawon hoton shine 10 cm.

b) Tsawon mai da hankali (f) = 10 cm da nisan abu ( d _o ) = 15 cm

Tsarin hoto ta hanyar madubi mai lanƙwasa:

Nisa ta hoton ( d _i ):

1/ d _i = 1/f – 1/ d _o = 1/10 – 1/15 = 3/30 – 2/30 = 1/30

d _i = 30/1 = 30 cm

Alamar da aka ƙara tana nuna cewa hoton gaskiya ne ko kuma hoton yana da nisan santimita 30 a gaban madubi, a gefe ɗaya da abin.

Girman hoto ( m ):

m = – d _i / d _o = -30/15 = -2

Alamar cirewa tana nuna cewa hoton ya juya.

Hoton ya fi abin girma sau biyu.

Tsawon hoton (h _i ):

m = h _i / h _o

h _i = h _o m = (5 cm)(2) = 10 cm

Tsawon hoton shine 10 cm.

c) Tsawon mai da hankali (f) = 10 cm da nisan abu ( d _o ) = 20 cm

Tsarin hoto ta hanyar madubi mai lanƙwasa:

Nisa ta hoton (d _i ):

1/ d _i = 1/f – 1/ d _o = 1/10 – 1/20 = 2/20 – 1/20 = 1/20

d _i = 20/1 = 20 cm

Alamar da ke nuna cewa hoton gaskiya ne ko kuma hoton yana da nisan santimita 20 a gaban madubi, a gefe ɗaya da abin.

Girman hoto ( m ):

m = – d _i / d _o = -20/20 = -1

Alamar mara kyau tana nufin hoton ya juya.

Tsawon hoton ( hi ):

m = h _i / h _o

h _i = h m = (5 cm)(1) = 5 cm

d) Tsawon mai da hankali (f) = 10 cm da nisan abu ( d _o ) = 30 cm

Nisa ta hoton ( d _i ):

1/ d _i = 1/f – 1/ d _o = 1/10 – 1/30 = 3/30 – 1/30 = 2/30

d _i = 30/2 = 15 cm

Alamar da aka ƙara tana nuna cewa hoton gaskiya ne ko kuma hoton yana da nisan santimita 15 a gaban madubi, a gefe ɗaya da abin.

Girman hoto ( m) :

m = – d _i / d _o = -15/30 = -0.5

Alamar cirewa tana nuna cewa hoton ya juya.

Hoton ya fi ƙanƙanta da abin da aka yi amfani da shi a girmansa 0.5.

Tsawon hoton (h _i ):

m = h _i / h _o

h _i = h _o m = (5 cm)(0.5) = 2.5 cm

[irp]

3. Hoton da madubi mai lanƙwasa ya ƙirƙira ya fi girman abu sau 4. Idan radius na lanƙwasa ya kai santimita 20, a ƙayyade nisan abin da ke gaban madubin!

An sani:

Girman hoto ( m ) = 4

Radius na lanƙwasa ( r ) = 20 cm

Tsawon mai da hankali (f) = r /2 = 20/2 = 10 cm

Ana so : Nisa tsakanin abu ( d _o )

Magani:

m = – d _i / d _o

4 = – d _{i /} d _o

– d _i = 4 d _o

d _i = – 4 d _o

1/f = 1/ d _o + 1/ d _i

1/10 = 1/ d _o + 1/4 d _o

4/40 = 4/4 d _o + 1/4 d _o

4/40 = 5/4 d _o

(4)(4) = (5)(40)

16 d _o = 200

d _o = 12.5 cm

Nisa tsakanin abu = 12.5 cm.

[irp]

4. An sanya wani abu mai tsayin santimita 1 a nisan santimita 10 daga madubi mai lanƙwasa tare da tsawon mai da hankali, f = santimita 15. A ƙayyade:

A. Nisan hoton?

B. Tsawon hoton?

C. Abubuwan da ke cikin hoton da madubin da ke da lanƙwasa ya samar?

An sani:

Tsawon abu (h) = 1 cm

Nisa tsakanin abu (d _o ) = 10 cm

Tsawon madubin mai lanƙwasa (f) = 15 cm

Magani:

A. Nisa ta hoton (d _i )

1/f = 1/d _o + 1/d _i

1/d _i = 1/f – 1/d _o = 1/15 – 1/10 = 2/30 – 3/30 = -1/30

d _i = -30/1 = -30 cm

Alamar mara kyau tana nuna cewa hoton na kama-da-wane ne ko kuma hoton yana bayan madubi.

B. Tsawon hoton (h _i )

Girman hoton (M):

M = -d _i /d _o = h _i /h _o

M = -(-30)/10 = 30/10 = sau 3

Tsawon hoton (h _i ):

M = h _i / h _o

3 = h _i / 1 cm

h _i = 3 (1 cm)

h _i = 3 cm

Tsawon hoton shine 3 cm. Alamar ƙari tana nuna cewa hoton yana sama.

C. Halayen hoton:

Na zahiri, sama, ya fi girma fiye da abu

[irp]

5. Girman hoton, bisa ga hoton da ke ƙasa.

An sani:

Nisa tsakanin abu (d _o ) = 60 cm

Tsawon mai da hankali (f) = 20 cm

Ana so: Girman hoto (M)

Magani:

Nisa ta hoton:

1/f = 1/d _o + 1/d _i

1/d _i = 1/f – 1/d _o = 1/20 cm – 1/60 cm = 3/60 cm – 1/60 cm = 2/60 cm

d _i = 60/2 cm = 30 cm

Girman hoton (M):

M = d _i / d _o = 30 cm / 60 cm = 1/2 sau

6. Idan an sanya abin a nisan santimita 6 daga madubi mai lanƙwasa, nisan hoton shine santimita 12 kamar yadda aka nuna a hoton da ke ƙasa. Menene nisan hoton idan an motsa abin daga matsayinsa na asali santimita 1 daga madubin.

An sani:

Nisa tsakanin abu (d _o ) = 6 cm

Nisa tsakanin hoton (d _i ) = 12 cm

Ana so: idan nisan abu (d _o ) = 7 cm to nisan hoton shine ...

Magani:

1/f = 1/yi + 1/di = 1/6 + 1/12 = 2/12 + 1/12 = 3/12

f = 12/3 = 4 cm

Tsawon abin da aka mayar da hankali yana da kyau, ma'ana cewa abin da aka mayar da hankali a kai gaskiya ne ko kuma haskoki suna wucewa ta wurin.

Nisa ta hoton:

1/d _i = 1/f – 1/d _o = 1/4 – 1/7 = 7/28 – 4/28 = 3/28

d _i = 28/3 = 9.3 cm

7. Likitan hakori yana lura da kuma duba haƙoran majiyyaci ta amfani da madubi mai radius na santimita 8. Domin likita ya ga ramin a sarari, menene tazara tsakanin haƙoran majiyyaci da madubin?

A. ƙasa da santimita 4 a gaban madubi mai lanƙwasa

B. ƙasa da santimita 4 a gaban madubi mai lanƙwasa

C. fiye da 4 cm a gaban madubin mai lanƙwasa

D. fiye da 4 cm a gaban madubin mai lanƙwasa

An sani:

Radius na madubi (r) = 8 cm

Tsawon madubi mai da hankali (f) = r / 2 = 8/2 = 4 cm

Ana so: Nisa tsakanin haƙoran majiyyaci da madubi

Magani:

Madubin da ake amfani da shi madubi ne mai lanƙwasa ko madubi mai lanƙwasa? Domin a ga ramin haƙorin a fili ga likita, madubin da ake amfani da shi ya kamata ya iya faɗaɗa hoton haƙorin kuma hoton dole ne ya kasance a tsaye. Madubi mai lanƙwasa koyaushe yana samar da hotuna masu lanƙwasa kuma girman hoton ya fi ƙanƙanta da girman abin. Akasin haka, madubi mai lanƙwasa zai iya samar da hoto mai tsayi idan nisan abu (d) ya fi ƙanƙanta da tsayin mai lanƙwasa (f). Idan nisan abu ya fi tsayin mai lanƙwasa (f) to madubin mai lanƙwasa yana samar da hoto mai lanƙwasa.

Tsawon madubin mai lanƙwasa (f) shine 4 cm, don haka haƙoran majiyyaci ya kamata su kasance ƙasa da 4 cm a gaban madubin mai lanƙwasa.

Amsar da ta dace ita ce A.

8. Madubin da ke da siffar lanƙwasa yana da tsawon santimita 24. Idan an sanya abin a nesa da santimita 20 a gaban madubin, to a tantance halayen hoton.

A. Na gaske, a miƙe kuma an faɗaɗa

B. Na gaske, an juya kuma an faɗaɗa

C. Na gani, a tsaye kuma an faɗaɗa shi

D. Na gani, an juya kuma ƙarami

An sani:

Radius na lanƙwasa (r) = 24 cm

Tsawon maƙasudi (f) = R/2 = 24/2 = +12 cm

Tsawon madubin da ke da siffar kusurwa yana da kyau ko kuma na gaske domin hasken yana ratsawa ta cikin madubin da ke da siffar kusurwa.

Nisa tsakanin abu (d) = 20 cm

Ana so: Halayen hoto

Magani:

Hoton na kama-da-wane ne ko na gaske? Lissafa nisan hoton (s'):

1/d + 1/d' = 1/f

1/d' = 1/f – 1/d

1/d' = 1/12 – 1/20

1/d' = 5/60 – 3/60

1/d' = 2/60

d' = 60/2

d' = 30 cm

Nisa da aka sanya hannu a kai a matsayin tabbatacce yana nufin cewa hoton gaskiya ne saboda haske ne ke wucewa.

An faɗaɗa hoton? A tsaye ko an juya shi? Da farko ana ƙididdige girman hoton (M):

M = -d' / d = -30/20 = -1.5

M > 1 yana nufin an faɗaɗa hoton, M yana da alamar korau yana nufin hoton da aka juya. Don haka halayen hoton na gaske ne, an juya shi, an faɗaɗa shi.

Amsar da ta dace ita ce B.

9. Madubin zagaye yana samar da hoton da girmansa ya ninka abin da ke kan allo sau 5, nisan mita 5 daga abin. Madubin yana…..

A. mai siffar kunkuntar mai tsawon 25/24 m

B. mai lanƙwasa tare da tsawon mai da hankali na 25/24 m

C. mai siffar kunkuntar tare da tsawon mai da hankali na mita 24/25

D. mai lanƙwasa tare da tsawon mai da hankali na 24/25 m

An sani:

Girman hoto (M) = sau 5

Nisa tsakanin abu da hoto = mita 5

Magani:

Girman hoton da madubin da ke da siffar lanƙwasa ya samar koyaushe ya fi girman abin ƙanƙanta, saboda haka, madubin madubi ne mai siffar lanƙwasa.

Nisa tsakanin abu (d) = x

Nisa tsakanin hotuna (d') = x + 5

Girman hoto (M) = sau 5

Tsarin girman hoto:

Tsarin tsawon mai da hankali (f):

Amsar da ta dace ita ce A.

[wpdm_package id='858′]

1. Matsaloli da mafita na madubin Concave
2. Matsaloli da mafita na madubin convex
3. Matsalolin ruwan tabarau masu bambanta da mafita
4. Haɗa matsalolin ruwan tabarau da mafita
5. Kayan aikin gani matsalolin ido da mafita na ɗan adam
6. Matsaloli da mafita na kayan aikin gani da ruwan tabarau na tuntuɓa
7. Gilashin ido na kayan aiki na gani
8. Matsaloli da mafita na kayan aikin ƙara girman gilashin gani
9. Na'urar microscope ta gani - matsaloli da mafita
10. Matsaloli da mafita na na'urorin hangen nesa na gani

Karin bayani

1. Ruwa kilogiram 1 a 100 ^oC a gauraya da ruwa kilogiram 1 a 10 ^oC a cikin tsarin da aka keɓe. Takamaiman zafin ruwan shine 4200 J/kg ^o C. A ƙayyade zafin ƙarshe na cakuda!

An sani:

Nauyin ruwan zafi (m ₁ ) = 1 kg

Zafin ruwan zafi (T1 ₎ = 100 ^oC

Nauyin ruwan sanyi (m2 ₎ = 1 kg

Zafin ruwan sanyi (T2 ₎ = 10 ^oC

Ana so: Zafin jiki na ƙarshe (T)

Magani:

An rasa zafi = An sami zafi (tsarin da aka keɓe)

m c Δ T = m c Δ T

m Δ T = m Δ T

m ₁ (T ₁ – T) = m ₂ (T – T ₂ )

(1)(100 – T) = (1)(T – 10)

100 – T = T – 10

100 + 10 = T + T

110 = 2T

T = 110 / 2

T = 55

Zafin ƙarshe shine 55 ^o C.

[irp]

2. Tushen gubar mai nauyin kilogiram 3 a nauyin kilogiram 80^o An sanya shi a cikin kilogiram 10 na ruwa. Takamaiman zafin gubar shine 1400 J.kg^-1C^-1 kuma takamaiman zafin ruwan shine 4200 J.kg^-1C^-1Zafin ƙarshe a cikin ma'aunin zafi shine 20^oC. Ƙayyade zafin farko na ruwa!

An sani:

Nauyi (m ₁ ) = 3 kg

Takamaiman zafin gubar (c1 ₎ = 1400 J.kg ^-1 C ^-1

Zafin gubar (T1 ₎ = 80 ^oC

Nauyin ruwa (m2 ₎ = 10 kg

Takamaiman zafin ruwa (c2 ₎ = 4200 J.kg ^-1 C ^-1

Zafin ma'aunin zafi ( T) = 20 ^oC

Ana so: Zafin ruwa na farko ( _T2 )

Magani:

An rasa zafi = An sami zafi

Q gubar = Q ruwa

m ₁ c ₁ ΔT = m ₂ c ₂ ΔT

(3)(1400)(80-20) = (10)(4200)(20-T)

(4200)(60) = (42,000)(20-T)

252,000 = 840,000 – 42,000 T

42,000 T = 840,000 – 252,000

42,000 T = 588,000

T = 588,000 / 42,000

T = 14

Zafin ruwa na farko shine 14 ^oC.

[irp]

3. Toshe na tagulla a 100^oC an zuba a cikin gram 128 na ruwa a cikin 30 ^oC. Takamaiman zafin ruwa shine 1 cal.g^-1oC^-1 kuma takamaiman zafin jan ƙarfe shine 0.1 cal.g^-1oC^-1. Idan zafin jiki na ma'aunin zafi ya kasance 36 ^oC, tantance nauyin jan ƙarfe!

An sani:

Zafin jan ƙarfe (T1 ₎ = 100 ^oC

Takamaiman zafin jan ƙarfe (c1 ₎ = 0.1 c al.g ^-1o C ^-1

Nauyin ruwa (m2 ₎ = gram 128

Zafin ruwa (T2 ₎ = 30 ^oC

Takamaiman zafin ruwa (c2 ₎ = 1 c al.g ^-1o C ^-1

Zafin ma'aunin zafi ( T) = 36 ^oC

Ana nema: Nauyin jan ƙarfe (m ₁ )

Magani:

An rasa zafi = An sami zafi

Q jan ƙarfe = Q ruwa

m ₁ c ₁ ΔT = m ₂ c ₂ ΔT

(m ₁ )(0.1)(100-36) = (128)(1)(36-30)

(m ₁ )(0.1)(64) = (128)(1)(6)

(m ₁ )(6.4) = 768

m ₁ = 768 / 6.4

m ₁ = 120

Nauyin jan ƙarfe shine gram 120.

[irp]

4. Tushen kankara na M-kg a 0^oC an zuba a cikin gram 340 na ruwa a cikin 20^oC a cikin kwalba. Idan zafin haɗuwa na ruwa = 80 kalori g^-1, zafin ruwa na musamman shine 1 kalori g^{-1 o}C^-1. Duk kankara yana narkewa da kuma zafin jiki na thermal ma'auni is 5^oC, tantance yawan kankara!

An sani:

Nauyin ruwa (m) = gram 340

Zafin kankara ( T _kankara ) = 0 ^oC

Zafin ruwa ( T _ruwa ) = 20 ^oC

Zafin ma'aunin zafi (T) = 5 ^oC

Zafin haɗa ruwa ( L ) = 80 c al g ^-1

Takamaiman zafin ruwa (c _ruwa ) = 1 kalori g ^{-1 o} C ^-1

Ana nema: Nauyin kankara (M)

Magani:

An rasa zafi = An sami zafi

Ruwa Q = Q ice

m c ( ΔT) = m _es L _es + m c ( Δ T)

(340)(1)(20-5) = M (80) + M (1)(5-0)

(340)(15) = 80M + 5M

5100 = 85M

M = 5100/85

M = gram 60

[wpdm_package id='714′]

1. Canza ma'aunin zafin jiki
2. Fadada layin layi
3. Faɗaɗa yanki
4. Fadada ƙara
5. Heat
6. Daidaiton zafi na inji
7. Ƙarfin zafi da zafi na musamman
8. Zafin da ke ɓoye, zafin haɗuwa, zafin tururi
9. Ajiye makamashi don canja wurin zafi

Karin bayani

4 Zafi Mai Layi Zafin Haɗawa Zafin tururi - Matsaloli da Magani

1. Lissafa adadin zafi da aka ƙara wa gram 1 na zinariya don canza mataki daga daskararre zuwa ruwa. Zafin haɗakar zinariya shine 64.5 x 10 ³ J/kg.

An sani:

Nauyi (m) = gram 1 = 1 x 10 ^-3 kg

Zafin haɗuwa (L _F ) = 64.5 x 10 ³ J/kg

Ana so: Zafi (Q)

Magani:

Q = m L _F

Q = (1 x 10 ^-3 kg)(64.5 x 10 ³ J/kg)

Q = Joules 64.5

[irp]

2. Lissafa adadin zafin da aka saki ta hanyar gram 1 na mercury don canza yanayin daga ruwa zuwa tauri. Zafin haɗakar mercury shine 11.8 x 10 ³ J/kg.

An sani:

Nauyi (m) = gram 1 = 1 x 10 ^-3 kg

Zafin haɗuwa (L _F ) = 11.8 x 10 ³ J/kg

Ana so: Zafi (Q)

Magani:

Q = m L _F

Q = (1 x 10 ^-3 kg)(11.8 x 10 ³ J/kg)

Q = Joules 11.8

3. Kayyade adadin zafi da ruwa mai nauyin kilogiram 1 ke sha don canza yanayin daga ruwa zuwa tururi (tururi). Zafin tururi don ruwa = 2256 x 10 ³ J/kg

An sani:

Nauyi (m) = 1 kg

Zafin tururi (L _V ) = 2256 x 10 ³ J/kg

Ana so: Zafi (Q)

Magani:

Q = m L _V

Q = (1 kg)( 2256 x 10 ³ J/kg)

Q = 2256 x 10 Joule ³

[irp]

4. Ƙayyade adadin zafi da nitrogen ke fitarwa don canza lokaci daga tururi zuwa ruwa. Zafin tururi don nitrogen = 200 x 10 ³ J/kg

An sani:

Nauyi (m) = gram 1 = 1 x 10 ^-3 kg

Zafin tururi (L _V ) = 200 x 10 ³ J/kg

An sani: Zafi (Q)

Magani:

Q = m L _V

Q = (1 x 10 ^-3 kg)( 200 x 10 ³ J/kg)

Q = Joules 200

1. Canza ma'aunin zafin jiki
2. Fadada layin layi
3. Faɗaɗa yanki
4. Fadada ƙara
5. Heat
6. Daidaiton zafi na inji
7. Ƙarfin zafi da zafi na musamman
8. Zafin da ke ɓoye, zafin haɗuwa, zafin tururi
9. Ajiye makamashi don canja wurin zafi

Karin bayani

1. Jiki mai nauyin kilogiram 2 yana shan zafi kalori 100 lokacin da zafin jikinsa ya ƙaru daga 20 ^oC zuwa 70 ^oC . Menene takamaiman zafin jiki?

An sani:

Nauyi (m) = 2 kg = 2000 gr

Zafi (Q) = 100 c al

Canjin zafin jiki ( ΔT ) = 70 ^o C – 20 ^o C = 50 ^o C

Ana so: Takamaiman zafi (c)

Magani:

c = Q / m Δ T

c = 100 kalori / (2000 gr)(50 ^o C)

c = 100 kalori / 100,000 gr ^o C

c = 10 ² kalori / 10 ⁵ gr ^o C

c = (10 ² kalori)( 10 ^-5 gr ^{-1 o} C ^-1 )

c = 10 ^-3 kalori gr ^{-1 o} C ^-1

c = 10 ^-3 kalori/ gr ^o C

Takamaiman zafin jiki shine 10-3 ^kcal / gr ^oC

[irp]

2. Takamaiman zafin ruwan shine 4180 J/kg C ^o . Nawa ne ƙarfin zafin ruwan kilogiram 2…

An sani:

Takamaiman zafin (c) = 4180 J/kg C ^o

Nauyi (m) = 2 kg

Ana buƙata: Ƙarfin zafi (C)

Magani:

C = mc

C = (2 kg)(4180 J/kg C ^o )

C = (2)(4180 J/C ^o )

C = 8360 J/C ^o

3. Takamaiman zafin aluminum shine 900 J/kg C ^o . Nawa ƙarfin zafi na aluminum gram 2…..

An sani:

Takamaiman zafin aluminum (c) = 900 J/kg C ^o = 9 x 10 ² J/kg C ^o

Nauyi (m) = gram 2 = 2/1000 kg = 2/10 kg ³ = 2 x 10 ^-3 kg

Ana buƙata: Ƙarfin zafi (C)

Magani:

C = mc

C = (2 x 10 ^-3 kg) ( 9 x 10 ² J/kg C ^o )

C = 18 x 10 ^-3 x 10 ² J/C ^o

C = 18 x 10 ^-1 J/C ^o

C = 1.8 J/C ^o

[wpdm_package id='710′]

1. Canza ma'aunin zafin jiki
2. Fadada layin layi
3. Faɗaɗa yanki
4. Fadada ƙara
5. Heat
6. Daidaiton zafi na inji
7. Ƙarfin zafi da zafi na musamman
8. Zafin da ke ɓoye, zafin haɗuwa, zafin tururi
9. Ajiye makamashi don canja wurin zafi

Karin bayani

1. 2kcal ( kiloc kalori e ) = ….. c kalori e?

Magani

1 kcal = 1000 kcal

2kcal kalori = 2 (1000c kalori e ) = 2000c kalori e

2. 4 C kalori e = .... c kalori e?

Magani

1 calori e ( a Capital C ) = 1 kcal = 1000 kalori e

4 C kalori e = 4 (1000 c kalori e ) = 4000 c kalori e

3. 10 c calorie e = .... Joule?

Magani

Kalori 1 e = Joules 4.186

10 c kalori e = 10 (4.186 Joules) = 41.86 Joules

[irp]

4. 5 kcal = ….. Joule?

Magani

1 kcal = 1000 c alarie = 4186 Joules

5 kcal = 5 (4186 Joules) = 20930 Joules

5. Joules 2000 = ….. k cal?

Magani

4186 Joules = 1 kcal

Jimillar 8372 = 8372 / 4186 = 2 kcal

Jimillar 2000 = 2000 / 4186 = 0.4777 kcal

[wpdm_package id='706′]

1. Canza ma'aunin zafin jiki
2. Fadada layin layi
3. Faɗaɗa yanki
4. Fadada ƙara
5. Heat
6. Daidaiton zafi na inji
7. Ƙarfin zafi da zafi na musamman
8. Zafin da ke ɓoye, zafin haɗuwa, zafin tururi
9. Ajiye makamashi don canja wurin zafi

Karin bayani

9 Zafi na Musamman na Yawan Zafi Canjin zafin jiki - Matsaloli da Magani

1. Ana dumama gubar mai nauyin kilogiram 2 daga 50^oC zuwa 100^oC. Da takamaiman zafi na gubar shine 130 J.kg^{-1 o}C^-1. Nawa zafi gubar ta mamaye shi?

An sani:

Nauyi (m) = 2 kg

Takamaiman zafin (c) = 1 3 0 J.kg ^-1 C ^-1

Sauyin yanayin zafi ( Δ T) = 100 ^o C – 50 ^o C = 50 ^o C

Ana so: Zafi (Q)

Magani:

Q = mc Δ T

Q = zafi , m = taro, c = takamaiman zafi , Δ T = canjin zafin jiki

Zafin da gubar ke sha:

Q = (2 kg)(1 3 0 J.kg ^-1 C ^-1 )(50 ^o C)

Q = (100)(1 3 0)

Q = Joules 1 3,000

Q = 1.3 x Joules ¹⁰⁴

[irp]

2. Takamammen zafin jan ƙarfe shine 390 J/kg g ^o C, canjin zafin shine 40 ^o C. Idan jan ƙarfe ya sha Joules 40 na zafi, menene nauyin jan ƙarfe!

An sani:

Takamaiman zafin jan ƙarfe (c) = 390 J/kg g ^o C

Canjin zafin jiki ( ΔT ) = 40 ^oC

Zafi ( Q) = 40 J

Ana nema: Nauyin jan ƙarfe (m)

Magani:

Q = mc Δ T

40 J = (m)( 390 J/kg g ^o C)(40 ^o C)

40 = (m)( 390 /kg g)(40)

40 = (m)( 390 / kg )(4)

40 = (m)( 1560 / kg )

m = 40 / 1560

m = 0.026 kg

m = gram 26

3. Zafin farko na gram 20 na ruwa shine 30 ^oC . Takamaiman zafin ruwan shine 1 cal g ^{-1 oC -1} . Idan ruwa ya sha kalori 300 na zafi, a tantance zafin ƙarshe!

An sani:

Nauyi (m) = 20 gr

Zafin farko (T1 ₎ = 30 ^oC

Takamaiman zafin ruwa (c) = 1 kalori gr ^{-1 o} C ^-1

Zafi (Q) = 300 cal

Ana so: Zafin ruwa na ƙarshe

Magani:

Q = mc ΔT

300 cal = (20 gr)( 1 cal gr ^{-1 o} C ^-1 )( T ₂ -30 )

300 = (20)(1)( T2 _-30 )

300 = 20 ( T ₂ -30 )

300 = 20 T ₂ – 600

300 + 600 = 20T ₂

900 = 20T ₂

T ₂ = 900 / 20

T2 = ₄₅

Sauyin yanayin zafi shine 45 ^o C – 30 ^o C = 15 ^o C.

 [irp]

4. Tcanjin zafin jiki na ruwan teku is 1^oC lokacin da ruwa ke shan zafi mai girman Joules 3900. Takamaiman zafin ruwan teku shine 3.9 × 10³ J/kg°C, Menene nauyin ruwan teku?

An sani:

Canjin zafin jiki ( ΔT ) = 1 ^oC

Zafi (Q) = Joule 3900

Takamaiman zafin ruwan teku (c) = 3.9 x 10 ³ J/ k g°C = 3900 J/Kg°C

Ana nema: Girma (m)

Magani:

Q = mc Δ T

Q = zafi , m = taro, c = takamaiman zafi , Δ T = canjin zafin jiki

m = Q / c Δ T = 3900 / (3900)(1) = 3900 / 3900 = 1 kg

5. Tagulla mai nauyin kilogiram 2 yana shan zafi 39,000 J a 30°C. Idan takamaiman zafin tagulla shine 390 J/kg °C, menene zafin ƙarshe na tagullar …

An sani:

Nauyi (m) = 2 kg

Zafin farko (T1 ₎ = 30 ^oC

Zafi (Q) = Joule 39,000

Takamammen zafi (c) na jan ƙarfe = 390 J/kg ^o C

Ana so : Zafin jiki na ƙarshe ( _T2 )

Magani:

Q = mc ΔT

Q = zafi , m = taro, c = takamaiman zafi , ΔT = canjin zafin jiki

Q = mc ΔT = mc (T ₂ – T ₁ )

39,000 = (2)( 390)(T ₂ – 30)

100 = (2)(1)(T ₂ – 30)

100 = (2)(T ₂ – 30)

50 = T ₂ – 30

T2 = 50 + ₃₀

T ₂ = 80 ^o C

[irp]

6. Ana dumama ruwan kilogiram 5 daga 15°C zuwa 40°C. Menene zafin da ruwa ke sha. Takamammen zafin ruwa shine 4.2 × 10 ³ J/Kg° C.

An sani:

Nauyi (m) = 5 kg

Zafin farko (T ₁ ) = 15°C

Zafin ƙarshe (T2 ₎ = 40°C

Takamaiman zafin ruwa (c) = 4.2 × 10 ³ J/kg° C

Ana so: Zafi (Q)

Magani:

Q = mc ΔT

Q = (5 kg)( 4.2 × 10 ³ J/kg°C)(40°C – 15°C)

Q = (5)( 4.2 × 10 ³ J)(25)

Q = 525 x 10 ³ J

Q = Joules 525,000

7. Ana dumama ruwan kilogiram 2 daga 24°C zuwa 90°C. Menene zafin da ruwa ke sha. Takamammen zafin ruwa shine 4.2 × 10 ³ J/Kg° C.

An sani:

Nauyi (m) = 2 kg

Zafin farko (T ₁ ) = 24°C

Zafin ƙarshe (T2 ₎ = 90°C

Takamaiman zafin ruwa (c) = Joules 4,200/kg°C

Ana so :: Zafi (Q)

Magani:

Q = m c ΔT

Q = (2 kg)( 4,200 Joules/kg°C)(90°C – 24°C)

Q = (2 kg)( 4,200 Joules/kg°C)(66°C)

Q = (132)( Joules 4,200)

Q = Joules 554,400

[irp]

8. Ana dumama ruwan gram 5 daga 10°C zuwa 40°C. Menene zafin da ruwa ke sha. Takamammen zafin ruwa shine 1 × 10 ³ cal / g r ° C.

An sani:

Nauyi (m) = gram 5

Zafin farko ( T ₁ ) = 10 ^oC

Zafin ƙarshe (T2 ₎ = 40 ^oC

Takamaiman zafin ruwa (c) = 1 c al/ gr°C

Ana so : Zafi

Magani:

Q = mc ΔT

Q = (gram 5)( 1 kalori/gr°C)(40 ^o C – 10 ^o C)

Q = (5)( 1 c al)(30)

Q = kalori 150

9. Ruwa mai nauyin kilogiram 0.2 yana shan Joules 42,000 na zafi a 25 oC ^. Takamaiman zafin ruwan shine 4200 J/kg ^o C, menene zafin ruwan ƙarshe.

An sani:

Nauyin ruwa (m) = 0.2 kg

Zafi (Q) = Joule 42,000

Takamaiman zafin ruwa (c) = 4200 J/kg ^o C

Zafin farko (T1 ₎ = 25 ^oC

Ana so: Zafin ƙarshe ( _T2 )

Magani:

Q = mc ΔT = mc (T ₂ – T ₁ )

Q= zafi, m = taro, c = takamaiman zafi, ΔT = canjin zafin jiki, T₁ = zafin farko, T₂ = zafin ƙarshe

Q = mc (T ₂ – T ₁ )

42,000 = (0.2)(4200)(T ₂ – 25)

42,000 = 840 (T ₂ – 25)

42,000 = 840 T ₂ – 21,000

42,000 + 21,000 = 840 T ₂

63,000 = 840 T ₂

T ₂ = 63,000 / 840

T ₂ = 75 ^o C

1. Canza ma'aunin zafin jiki
2. Fadada layin layi
3. Faɗaɗa yanki
4. Fadada ƙara
5. Heat
6. Daidaiton zafi na inji
7. Ƙarfin zafi da zafi na musamman
8. Zafin da ke ɓoye, zafin haɗuwa, zafin tururi
9. Ajiye makamashi don canja wurin zafi

Karin bayani

Faɗaɗar layi tana samuwa ne kawai ta hanyar abubuwa masu ƙarfi; dukkan abubuwa suna fuskantar faɗaɗar girma, duka na daskararru, ruwa, da iskar gas. Daidaiton faɗaɗar girma yayi kama da daidaiton faɗaɗar layi.

Bayani: V _o = Ƙarar farko, V = Ƙarar ƙarshe, ΔV = V – V _o = Canjin girma, T _o = Zafin farko, T = Zafin ƙarshe, ΔT = T – T _o = Canjin zafi, β = ma'aunin faɗaɗa girma. Raka'o'in β = (C ^o ) ^-1

[irp]

Lissafin faɗaɗa girma da ke sama yana aiki ne kawai lokacin da canje-canje a cikin girman abubuwan (duka mai ƙarfi, ruwa, da iskar gas) suka ƙanƙanta fiye da girman asali na abu. Idan canjin girma na abu ya fi girman farko na abu, lissafin faɗaɗa girma ba ya bayar da sakamako mai kyau. Yawanci, canje-canje a cikin girma da abubuwa masu ƙarfi suka fuskanta ba su da girma sosai. A gefe guda kuma, ƙimar faɗaɗa girma na ruwa da iskar gas yana da girma. Hakanan ana iya canza ƙimar faɗaɗa girma ga abubuwan iskar gas idan yanayin zafi ya canza. Saboda haka, ana amfani da dabarar da ke sama kawai don faɗaɗa abubuwa masu ƙarfi.

[irp]

1. A zafin digiri 30 ^{na Celsius} , girman wani yanki na aluminum shine 30 cm ^3. Matsakaicin faɗaɗa layi shine 24 x 10 ^{-6 o} C ^-1 . Idan girman ƙarshe shine 30.5 cm ³ , menene zafin ƙarshe na ɓangaren aluminum?

An sani:

Ma'aunin faɗaɗa layi ( α ) = 24 x 10 ^{-6 o} C ^-1

Ma'aunin faɗaɗa girma ( β ) = 3 α = 3 x 24 x 10 ^{-6 o} C ^-1 = 72 x 10 ^{-6 o} C ^-1

Zafin farko (T1 ₎ = 30 ^oC

Ƙarar farko (V ₁ ) = 30 cm ³

Ƙarar ƙarshe (V ₂ ) = 30.5 cm ³

Sauyin girma ( Δ V) = 30.5 cm ³ – 30 cm ³ = 0.5 cm ³

Ana so: Zafin jiki na ƙarshe ( _T2 )

Magani:

Δ V = β (V1 ₎ ( ΔT )

Δ V = β (V1 ₎ ( _T2 – _T1 )

0.5 cm³ = (72 x 10^{-6 o}C^-1)(30 cm³)(T₂ - 30^oC)

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

T ₂ = 260 ^o C

[irp]

2. Ma'aunin faɗaɗa layin ƙarfe shine 9 x 10 ^{-6 o} C ^-1 . Diamita na ciki na ƙarfe a 20 ^o C shine 2.2 cm. Idan diamita na ƙarshe shine 2.8 cm, menene zafin ƙarshe!

An sani:

Ma'aunin faɗaɗa layi ( α ) = 9 x 10 ^{-6 o} C ^-1

Ma'aunin faɗaɗa girma ( β) = 3 α = 3 x 9 x 10 ^{-6 o} C ^-1 = 27 x 10 ^{-6 o} C ^-1

Zafin farko (T1 ₎ = 20 ^oC

Diamita na farko (D ₁ ) = 2.2 cm

Diamita na ƙarshe (D ₂ ) = 2.8 cm

Radius na farko (r ₁ ) = D _1/2 = 2.2 cm ^3/2 = 1.1 cm ³

Radius na ƙarshe (r2 ₎ = D _2/2 = 2.8 cm ^3/2 = 1.4 cm ³

Ƙarar farko (V ₁ ) = 4/3 π r ₁ ³ = (4/3)(3.14)(1.1 cm) ³ = (4/3)(3.14)(1.331 cm ³ ) = 5.57 cm ³

Ƙarar ƙarshe (V ₂ ) = 4/3 π r ₂ ³ = (4/3)(3.14)(1.4 cm) ³ = (4/3)(3.14)(2.744 cm ³ ) = 11.48 cm ³

Sauyin girma ( Δ V) = 11.48 cm ³ – 5.57 cm ³ = 5.91 cm ³

Ana so: Zafin jiki _{na ƙarshe} ( T2 )

Magani:

Δ V = β (V1 ₎ ( ΔT )

5.91 cm³ = (27 x 10^{-6 o}C^-1)(5.57 cm³)(T₂ - 20^oC)

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

T ₂ = 39,020 ^o C

3. A 2000-cm³ aluminum ganga, cike da ruwa a 0^oC. Sannan a dumama shi zuwa digiri 90^oC. Idan ma'aunin faɗaɗa layi na aluminum shine 24 x 10^-6 (^oC)^-1 kuma ma'aunin faɗaɗa yawan ruwa shine 6.3 x 10^-4 (^oC)^-1, ƙayyade yawan ruwan da ya zube.

An sani:

Girman farko na akwatin aluminum da ruwa (Vo ₎ = 2000 cm ³ = 2 x 10 ³ cm ³

Zafin farko na akwatin aluminum da ruwa (T 1 ₎ = 0 ^oC

Zafin ƙarshe na akwatin aluminum da ruwa (T2 ) ₌ 90 ^oC

Ma'aunin faɗaɗa layi don aluminum (α) = 24 x 10 ^-6 ( ^oC ) ^-1

Ma'aunin faɗaɗa girma na aluminum (γ) = 3α = 3 (24 x 10 ^-6 ( ^oC ) -1 ⁾ = 72 x 10 ^{-6 o} C ^-1

Ma'aunin faɗaɗa girma na ruwa (γ) = 6.3 x 10 ^-4 ( ^oC ) ^-1

Ana so: Yawan ruwan da ya zube

Magani:

Daidaiton faɗaɗa girma:

V = _Vo + γ Vo _o ΔT

V – V _o = γ V _o ΔT

ΔV = γ V _o ΔT

V = ƙarar ƙarshe, V _o = ƙarar farko, ΔV = canjin girma, γ = ma'aunin faɗaɗa girma, ΔT = canjin zafin jiki

Lissafa canjin girma na akwatin aluminum:

ΔV = γ V _o ΔT = (72 x 10 ^-6 )(2 x 10 ³ )(90) = 12960 x 10 ^-3 = 12.960 cm ³

Lissafa canjin da ke cikin ƙarar ruwan:

ΔV = γ V _o ΔT = (6. 3 x 10 ^-4 )(2 x 10 ³ )(90) = 1134 x 10 ^-1 = 113.4 cm ³

Sauyin da ake samu a cikin ruwan ya fi na kwantenar aluminum girma, don haka sai ruwa ya zube.

Lissafa yawan ruwan da ya zube:

113.4 cm ³ – 12.960 cm ³ = 100.44 cm ³

[wpdm_package id='702′]

1. Canza ma'aunin zafin jiki
2. Fadada layin layi
3. Faɗaɗa yanki
4. Fadada ƙara
5. Heat
6. Daidaiton zafi na inji
7. Ƙarfin zafi da zafi na musamman
8. Zafin da ke ɓoye, zafin haɗuwa, zafin tururi
9. Ajiye makamashi don canja wurin zafi

Karin bayani

1. A digiri 20 ^na Celsius, tsawon takardar ƙarfe shine 50 cm kuma faɗin shine 30 cm. Idan ma'aunin faɗaɗa layi na ƙarfe shine 10 ^{-5 o} C ^-1 , ƙayyade canjin yankin da yankin ƙarshe a 60 ^o C.

An sani:

Zafin farko (T1 ₎ = 20 ^oC

Zafin ƙarshe (T2 ) ₌ 60 ^oC

Canjin zafin jiki ( ΔT ) = 60 ^o C – 20 ^o C = 40 ^o C

Yankin farko (A ₁ ) = tsayi x faɗi = 50 cm x 30 cm = 1500 cm ²

Ma'aunin faɗaɗa layi na ƙarfe ( α) = 10 ^{-5 o} C ^-1

Ma'aunin faɗaɗa yanki na ƙarfe ( β) = 2α = 2 x 10 ^{-5 o} C ^-1

Ana so: Canjin yanki ( ΔA )

Magani:

Canjin yanki ( ΔA ):

ΔA = βA ₁ ΔT

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

Yankin ƙarshe ( A ₂ ):

A ₂ = A ₁ + ΔA

A ₂ = 1500 cm ² + 1. 2 cm ²

A ₂ = 1501. 2 cm ²

[irp]

2. A zafin digiri 30 na ^Celsius , yankin takardar aluminum shine 40 cm ² kuma ma'aunin faɗaɗa layi shine 24 x 10 ^-6 / ^o C. Ƙayyade zafin jiki na ƙarshe idan yankin ƙarshe shine 40.2 cm ².

An sani:

Zafin farko (T1 ) ₌ 30 ^oC

Ma'aunin faɗaɗa layi ( α) = 24 x 10 ^{-6 o} C ^-1

Ma'aunin faɗaɗa yanki ( β) = 2a = 2 x 24 x 10 ^{-6 o} C ^-1 = 48 x 10 ^{-6 o} C ^-1

Yankin farko (A ₁ ) = 40 cm ²

Yankin ƙarshe (A ₂ ) = 40.2 cm ²

Canjin yanki ( ΔA) = 40.2 cm ² – 40 cm ² = 0.2 cm ²

Ana so: Ƙayyade zafin jiki na ƙarshe ( _T2 )

Magani:

Tsarin canjin yanki ( ΔA) :

ΔA = βA ₁ ΔT

Zafin ƙarshe (T2 ₎ :

ΔA = βA 1 (T ₂ – T _{1 )}

0.2 cm² = (48 x 10^{-6 o}C^-1)(40 cm²)(T₂ - 30^oC)

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 = _T2

T2 = ₁₃₀

Zafin ƙarshe = 130 ^oC

[irp]

3. Radius na zobe a 20 ^oC shine 20 cm. Idan radius na ƙarshe a 100 ^oC shine 20.5 cm, ƙayyade ma'aunin faɗaɗa yanki da ma'aunin faɗaɗa layi…

An sani:

Zafin farko (T1 ) ₌ 30 ^oC

Zafin ƙarshe (T2 ) ₌ 100 ^oC

Canjin zafin jiki ( ΔT ) = 100 ^o C – 30 ^o C = 70 ^o C

Radius na farko (r1 ₎ = 20 cm

Radius na ƙarshe (r2 ₎ = 20.5 cm

Ana so: Ma'aunin faɗaɗa yanki ( β )

Magani:

Yankin farko (A ₁ ) = π r ₁ ² = (3.14)(20 cm) ² = (3.14)(400 cm ² ) = 1256 cm ²

Yankin ƙarshe (A ₂ ) = π r ₂ ² = (3.14)(20.5 cm) ² = (3.14)(420.25 cm ² ) = 1319.585 cm ²

Sauyin yanki ( ΔA) = 1319.585 cm ² – 1256 cm ² = 63.585 cm ²

Tsarin canjin yanki ( ΔA) :

ΔA = βA ₁ ΔT

Ma'aunin faɗaɗa yanki:

ΔA = βA ₁ ΔT

63.585 cm ² = b (1 256 cm ² )(70 ^o C)

63.585 = b ( 87,920 ^o C)

β = 63.585 / 87,920 ^oC

β = 0.00072 / ^oC

β = 7.2 x 1 0 ^-4 / ^o C

β = 7.2 x 1 0 ^{-4 o} C ^-1

Ma'aunin faɗaɗa layi ( 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

[wpdm_package id='698′]

1. Canza ma'aunin zafin jiki
2. Fadada layin layi
3. Faɗaɗa yanki
4. Fadada ƙara
5. Heat
6. Daidaiton zafi na inji
7. Ƙarfin zafi da zafi na musamman
8. Zafin da ke ɓoye, zafin haɗuwa, zafin tururi
9. Ajiye makamashi don canja wurin zafi

Karin bayani