Mavuto Othetsedwa mu Fiziki Yoyambira

1. Utali wa galasi lozungulira ndi 10 cm ndipo mtunda wa chinthucho ndi 20 cm. Dziwani (a) mtunda wa chithunzi (b) kukula kwa chithunzicho

Zodziwika:

Kutalika kwa focal (f) = -10 cm

Chizindikiro chochotsera chimasonyeza kuti malo ofunikira pagalasi lozungulira ndi enieni

Mtunda wa chinthu ( do _o ) = 20 cm

Yankho:

Kupanga chithunzi pogwiritsa ntchito galasi lozungulira:

Mtunda wa chithunzi (di _i ):

1/ di = 1/f – 1/ do _o = -1/10 – 1/20 = -2/20 – 1/20 = _-3/20

d _i = -20/3 = -6.7 cm

Chizindikiro cha minus chikusonyeza kuti chithunzicho ndi cha pa intaneti.

Kukula kwa chithunzi:

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

m = nthawi 0,3 yocheperapo kuposa chinthucho.

Chizindikiro chowonjezera chimasonyeza kuti chithunzicho chili mmwamba.

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2. Chinthu chachitali cha masentimita 10 chimayikidwa patsogolo pa galasi lozungulira lokhala ndi kutalika kwa masentimita 20. Dziwani kutalika kwa chithunzi ngati mtunda wa chinthucho ndi (a) 10 cm (b) 30 cm (c) 40 cm (d) 50 cm

Zodziwika:

Kutalika kwa galasi lozungulira (f) = -20 cm

Chizindikiro chochotsera chikusonyeza kuti malo ofunikira ndi enieni

Utali wa kupindika ( r ) = 2 f = 2(20) = 40 cm

Kutalika kwa chinthu (h) = 10 cm

Yankho:

a) kutalika kwa focal (f) = -20 cm ndi mtunda wa chinthu (do _o ) = 10 cm

Mtunda wa chithunzi (di _i ) :

1/ di = 1/f – 1/ do _o = -1/20 – 1/10 = -1/20 – 2/20 = _-3/20

d _i = -20/3 = -6.7

Chizindikiro chochotsera chimasonyeza kuti chithunzicho ndi cha pa intaneti kapena chithunzicho chili kumbuyo kwa galasi.

Kukula kwa chithunzi ( m ):

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

Chizindikiro chowonjezera chikusonyeza kuti chithunzicho chili choyimirira.

Chithunzicho ndi chaching'ono ndi 0.67 kuposa chinthucho.

Kutalika kwa chithunzi (h _i ):

m = h _i / h _o

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

b) kutalika kwa focal (f) = -20 cm ndi mtunda wa chinthu ( do _o ) = 30 cm

Mtunda wa chithunzi ( di _i ):

1/ di = 1/f – 1/ do _o = -1/20 – 1/30 = -3/60 – 2/60 = _-5/60

d _i = -60/5 = -12

Chizindikiro chochotsera chimasonyeza kuti chithunzicho ndi cha pa intaneti kapena chithunzicho chili kumbuyo kwa galasi.

Kukula kwa chithunzi ( m ):

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

Chizindikiro chowonjezera chikusonyeza kuti chithunzicho chili choyimirira.

Chithunzicho ndi chaching'ono kuwirikiza ka 0,4 kuposa chinthucho.

Kutalika kwa chithunzi (h _i ):

m = h _i / h _o

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

c) Utali wa focal (f) = -20 cm ndi mtunda wa chinthu ( do _o ) = 40 cm

Mtunda wa chithunzi ( di _i ):

1/ di = 1/f – 1/ do _o = -1/20 – 1/40 = -2/40 – 1/40 = _-3/40

d _i = -40/3 = -13.3

Chizindikiro chochotsera chimasonyeza kuti chithunzicho ndi cha pa intaneti kapena chithunzicho chili kumbuyo kwa galasi lozungulira.

Kukula kwa chithunzi ( m ):

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

Chizindikiro chowonjezera chikusonyeza kuti chithunzicho chili choyimirira.

Chithunzicho ndi chaching'ono ndi 0.3 kuposa chinthucho.

Kutalika kwa chithunzi ( h _{i )} :

m = h _i / h _o

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

d) Utali wa focal (f) = -20 cm ndi mtunda wa chinthu ( do _o ) = 50 cm

Mtunda wa chithunzi ( di _i ):

1/ di = 1/f – 1/ do _o = -1/20 – 1/50 = -5/100 – 2/100 = _-7/100

d _i = -100/7 = -14.3

Chizindikiro chochotsera chimasonyeza kuti chithunzicho ndi cha pa intaneti kapena chithunzicho chili kumbuyo kwa galasi lozungulira.

Kukula kwa chithunzi ( m ):

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

Chizindikiro chowonjezera chikusonyeza kuti chithunzicho chili choyimirira.

Chithunzicho ndi chaching'ono ndi 0.3 kuposa chinthucho.

Kutalika kwa chithunzi (h _i ) :

m = h _i / h _o

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

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3. Pa chinthu chili ndi 20 cm patsogolo pa galasi lozungulira . Ngati kutalika kwa chithunzi kuli 1/5 kuchulukitsa kutalika kwa chinthucho, dziwani ( a) kutalika kwa chithunzi b) kutalika kwa focal c) makhalidwe a chithunzicho

Zodziwika:

Mtunda wa chinthu ( do _o ) = 20 cm

Kutalika kwa chithunzi (h _i ) = 1/5 h = 0.2 h

Kutalika kwa chinthu (h) = h

Yankho:

a) mtunda wa chithunzi ( di ₎

Fomula yokulitsa chithunzi :

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

Chizindikiro chowonjezera chikusonyeza kuti chithunzicho chili choyimirira.

Chithunzicho ndi chaching'ono ndi 0.2 kuposa chinthucho.

Mtunda wa chithunzi ( di _i ):

– d _i = md _o

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

Chizindikiro chochotsera chimasonyeza kuti chithunzicho ndi cha pa intaneti kapena chithunzicho chili kumbuyo kwa galasi lozungulira.

b) Utali wa focal ( f)

Utali wa focal (f):

1/f = 1/ do _o + 1/ di = 1/20 – 1/4 = 1/20 – 5/20 = _-4/20

f = -20/4 = -5 cm

Chizindikiro cha minus chimasonyeza kuti malo ofunikira ndi enieni.

c) Makhalidwe a chithunzi:

- Wowongoka

- Kakang'ono

- pa intaneti

4. Kuwala kukagunda galasi lozungulira lomwe likufanana ndi mzere wozungulira lidzawonekera….

A. kulowera ku malo owonekera pagalasi

B. monga momwe zilili pagalasi

C. kudutsa pakati pa kupindika kwa galasi

D. yolunjika ku galasi

Anakonza

Vutoli lawonetsedwa pachithunzi chili pansipa.

Yankho lolondola ndi B.

5. Wokwera njinga yamoto amaona chithunzi cha njinga yamoto kumbuyo kwake 1/6 kuchulukitsa kukula kwake koyambirira pamene mtunda pakati pa wokwera njinga ndi njinga yamoto uli mamita 30. Dziwani kutalika kwa kupindika kwa galasi lowonera kumbuyo…

A. 7.14 m

B. 8.57 m

C. 12.00 m

D. 24.00 m

Zodziwika:

Kukula kwa chithunzi (M) = 1/6 nthawi

Mtunda wa chinthu (d) = mamita 30

Kufunidwa: Utali wozungulira wa galasi lowonera kumbuyo (R)

Yankho:

Werengerani mtunda wa chithunzi (d')

Popeza kukula kwa chithunzi (M) ndi mtunda (s) wa chinthu chadziwika, mtunda wa chithunzi ukhoza kudziwika pogwiritsa ntchito njira yowonjezerera chithunzi:

Chizindikiro chotsutsa chimatanthauza kuti chithunzicho ndi chenicheni. Chithunzicho chili mamita 5 kumbuyo kwa galasi lozungulira.

Werengerani kutalika kwa focal (f)

Popeza mtunda wa chinthu (d) ndi mtunda wa chithunzi (d'), ndiye kuti kutalika kwa focal kumatha kuwerengedwa pogwiritsa ntchito njira ya galasi:

Utali wozungulira wa kupindika (R)

Kutalika kwa galasi lopindika ndi kawiri kutalika kwa galasi lopindika.
R = 2 f = 2 (mamita 6) = mamita 12
Kutalika kwa galasi lopindika ndi mamita 12.
Yankho lolondola ndi C.

6. Galasi lozungulira limasankhidwa ngati galasi lowonera kumbuyo kwa njinga yamoto chifukwa mawonekedwe a chithunzi chopangidwa ndi galasi ndi…

A. yeniyeni, yowongoka, yochepetsedwa

B. yeniyeni, yowongoka, yokulirapo

C. yeniyeni, yowongoka, yochepetsedwa

D. yeniyeni, yowongoka, yokulirapo

Yankho:

Kutengera ndi zithunzi ziwiri zomwe zili pamwambapa, tinganene kuti mawonekedwe a chithunzicho ndi enieni, owongoka, ochepetsedwa.

Yankho lolondola ndi C.

7. Chinthu chili ndi mtunda wa masentimita 12 patsogolo pa galasi lozungulira lokhala ndi utali wa masentimita 6. Makhalidwe a chithunzicho ndi…

A. yeniyeni, yopindika patali pa 12 cm

B. yeniyeni, yowongoka patali ndi 4 cm

C. yeniyeni, yoyimirira patali wa 2.4 cm

D. yeniyeni, yopindika patali pa 6 cm

Zodziwika:

Mtunda wa chinthu (d) = 12 cm

Utali wozungulira wa galasi lopindika (r) = 6 cm.

Kutalika kwa galasi lozungulira (f) = 6 cm / 2 = -3 cm

Utali wa galasi lozungulira umalembedwa kuti ndi woipa chifukwa ndi weniweni. Wapakompyuta chifukwa sudutsa ndi kuwala.

Kufunidwa: Katundu wa chithunzi

Yankho:

Mtunda wa chithunzi (d'):

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

d' = -12/5 = -2.4 cm

Mtunda wa chithunzi womwe wasainidwa ndi negative umatanthauza kuti chithunzicho ndi cha pa intaneti.

Kukula kwa chithunzi (m):

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

Kukula kwa chithunzi chosainidwa bwino kumatanthauza kuti chithunzicho chili choyimirira ndipo kukula kwa chithunzicho ndi 0.2 kumatanthauza kuti kukula kwa chithunzicho ndi kochepa kuposa kukula kwa chinthucho (kochepetsedwa).

Yankho lolondola ndi C.

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1. Mavuto ndi mayankho a galasi lopindika
2. Mavuto ndi mayankho a magalasi ozungulira
3. Mavuto ndi njira zothetsera mavuto a lens
4. Kugwirizanitsa mavuto ndi mayankho a lens
5. Zipangizo zowunikira mavuto a maso a anthu ndi mayankho ake
6. Mavuto ndi mayankho a magalasi olumikizirana ndi zida zamagetsi
7. Magalasi a zida zowunikira
8. Zida zowunikira zokulitsa mavuto a magalasi ndi mayankho
9. Maikulosi ya zida zowunikira - mavuto ndi mayankho
10. Mavuto ndi mayankho a ma telescope a zida zowunikira

Werengani zambiri

1. Chinthu chimayikidwa pa 10 cm kuchokera pagalasi lopindika . Utali wa focal ndi 5 cm. Dziwani (a) Mtunda wa chithunzi (b) kukula kwa chithunzi

Zodziwika:

Kutalika kwa focal (f) = 5 cm

Mtunda wa chinthu ( do _o ) = 10 cm

Yankho :

Kupanga chithunzi pogwiritsa ntchito galasi lozungulira:

Mtunda wa chithunzi:

1/ di = 1/f – 1/ _{do o} = _1/5 – 1/10 = 2/10 – 1/10 = 1/10

d _i = 10/1 = 10 cm

Mtunda wa chithunzi ndi 10 cm.

Kukula:

m = – di _i / do _o = -10/10 = -1

1 imatanthauza kuti chithunzicho ndi chofanana ndi chinthucho.

Chizindikiro chochotsera chimasonyeza kuti chithunzicho chatembenuzidwa. Ngati chizindikirocho chili chabwino ndiye kuti chithunzicho chili choyima.

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2. Chinthu cha kutalika kwa masentimita 5 chimayikidwa patsogolo pa galasi lopindika lomwe lili ndi utali wa masentimita 20. Dziwani kutalika kwa chithunzi ngati mtunda wa chinthucho ndi masentimita 5, masentimita 15, masentimita 20, masentimita 30.

Zodziwika:

Utali wozungulira wa kupindika ( r ) = 20 cm

Kutalika kwa focal (f) = R/2 = 20/2 = 10 cm

Kutalika kwa chinthu (h _o ) = 5 cm

Yankho:

a) kutalika kwa focal (f) = 10 cm ndi mtunda wa chinthu ( do _o ) = 5 cm

Kupanga chithunzi pogwiritsa ntchito galasi lozungulira:

Mtunda wa chithunzi ( di _i ):

1/ di = 1/f – 1/ do _{o = 1/10 – 1/5} = 1/10 – 2/10 = -1/10

d _i = -10/1 = -10 cm

Chizindikiro chochotsera chimasonyeza kuti chithunzicho ndi cha pa intaneti kapena chithunzicho chili kumbuyo kwa galasi.

Kukula kwa chithunzi ( m ):

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

Chizindikiro chowonjezera chikusonyeza kuti chithunzicho chili choyimirira.

Kutalika kwa chithunzi ( h _i ):

m = h _i / h _o

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

Kutalika kwa chithunzi ndi 10 cm.

b) Utali wa focal (f) = 10 cm ndi mtunda wa chinthu ( do _o ) = 15 cm

Kupanga chithunzi pogwiritsa ntchito galasi lozungulira:

Mtunda wa chithunzi ( di _i ):

1/ di = 1/ _f – 1/ do _o = 1/10 – 1/15 = 3/30 – 2/30 = 1/30

d _i = 30/1 = 30 cm

Chizindikiro chowonjezera chimasonyeza kuti chithunzicho ndi chenicheni kapena chithunzicho chili pa 30 cm patsogolo pa galasi, mbali yomweyo ndi chinthucho.

Kukula kwa chithunzi ( m ):

m = – di _i / do _o = -30/15 = -2

Chizindikiro chochotsera chimasonyeza kuti chithunzicho chatembenuzidwa.

Chithunzicho ndi chachikulu kawiri kuposa chinthucho.

Kutalika kwa chithunzi (h _i ):

m = h _i / h _o

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

Kutalika kwa chithunzi ndi 10 cm.

c) Utali wa focal (f) = 10 cm ndi mtunda wa chinthu ( do _o ) = 20 cm

Kupanga chithunzi pogwiritsa ntchito galasi lozungulira:

Mtunda wa chithunzi (di _i ):

1/ di = 1/ _f – 1/ do _o = 1/10 – 1/20 = 2/20 – 1/20 = 1/20

d _i = 20/1 = 20 cm

Chizindikiro chabwino chimasonyeza kuti chithunzicho ndi chenicheni kapena chithunzicho chili pa 20 cm patsogolo pa galasi, mbali yomweyo ndi chinthucho.

Kukula kwa chithunzi ( m ):

m = – di _i / do _o = -20/20 = -1

Chizindikiro chotsutsa chimatanthauza kuti chithunzicho chatembenuzidwa.

Kutalika kwa chithunzi ( moni ):

m = h _i / h _o

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

d) Utali wa focal (f) = 10 cm ndi mtunda wa chinthu ( do _o ) = 30 cm

Mtunda wa chithunzi ( di _i ):

1/ di = 1/ _f – 1/ do _o = 1/10 – 1/30 = 3/30 – 1/30 = 2/30

d _i = 30/2 = 15 cm

Chizindikiro chowonjezera chimasonyeza kuti chithunzicho ndi chenicheni kapena chithunzicho chili pa 15 cm patsogolo pa galasi, mbali yomweyo ndi chinthucho.

Kukula kwa chithunzi ( m) :

m = – di _i / do _o = -15/30 = -0.5

Chizindikiro chochotsera chimasonyeza kuti chithunzicho chatembenuzidwa.

Chithunzicho ndi chaching'ono ndi 0.5 kuposa chinthucho.

Kutalika kwa chithunzi (h _i ):

m = h _i / h _o

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

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3. Chithunzi chopangidwa ndi galasi lopindika chimakhala chachikulu kuwirikiza kanayi kuposa chinthucho. Ngati utali wa kupindika ndi masentimita 20, dziwani mtunda wa chinthucho patsogolo pa galasi!

Zodziwika:

Kukula kwa chithunzi ( m ) = 4

Utali wozungulira wa kupindika ( r ) = 20 cm

Kutalika kwa focal (f) = r /2 = 20/2 = 10 cm

Kufunidwa : Mtunda wa chinthu ( do _o )

Yankho:

m = _– di _/ do o

₄ = – di _{/ do} o

– d _i = 4 do _o

d _i = – 4 do _o

1/f = 1/ do _o + 1/ di _i

1/10 = 1/ do _o + 1/4 do _o

4/40 = 4/4 do _o + 1/4 do _o

4/40 = 5/4 do _o

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

16 do ₌ 200

do _o = 12.5 cm

Mtunda wa chinthucho = 12.5 cm.

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4. Chinthu cha kutalika kwa 1 cm chimayikidwa 10 cm kuchokera pagalasi lopindika ndi kutalika kwa focal, f = 15 cm. Dziwani:

A. Mtunda wa chithunzi?

B. Kutalika kwa chithunzi?

C. Kodi chithunzi chopangidwa ndi galasi lopindika ndi chiyani?

Zodziwika:

Kutalika kwa chinthu (h) = 1 cm

Mtunda wa chinthu (do _o ) = 10 cm

Kutalika kwa galasi lopindika (f) = 15 cm

Yankho:

A. Mtunda wa chithunzi (d _i )

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

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

d _i = -30/1 = -30 cm

Chizindikiro chotsutsa chimasonyeza kuti chithunzicho ndi cha pa intaneti kapena chithunzicho chili kumbuyo kwa galasi.

B. Kutalika kwa chithunzi (h _i )

Kukula kwa chithunzi (M):

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

M = -(-30)/10 = 30/10 = katatu

Kutalika kwa chithunzi (h _i ):

M = h _i / h _o

3 = h _i / 1 cm

h _i = 3 (1 cm)

h _i = 3 cm

Kutalika kwa chithunzi ndi 3 cm. Chizindikiro chowonjezera chimasonyeza kuti chithunzicho chili mmwamba.

C. Makhalidwe a chithunzicho:

Zenizeni, mmwamba, zazikulu kuposa chinthu

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5. Kukula kwa chithunzicho, malinga ndi chithunzi chomwe chili pansipa.

Zodziwika:

Mtunda wa chinthu (do _o ) = 60 cm

Kutalika kwa focal (f) = 20 cm

Kufunidwa: Kukula kwa chithunzi (M)

Yankho:

Mtunda wa chithunzi:

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

1/di _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

Kukula kwa chithunzi (M):

M = di _i / do _o = 30 cm / 60 cm = 1/2 nthawi

6. Ngati chinthucho chayikidwa pa 6 cm kuchokera pagalasi lopindika, mtunda wa chithunzicho ndi 12 cm monga momwe chithunzi chili pansipa chikusonyezera. Kodi mtunda wa chithunzicho ndi wotani ngati chinthucho chasunthidwa kuchokera pamalo oyamba pa 1 cm kuchokera pagalasi?

Zodziwika:

Mtunda wa chinthu (do _o ) = 6 cm

Mtunda wa chithunzi (d _i ) = 12 cm

Chifunidwa: ngati mtunda wa chinthu (do _o ) = 7 cm ndiye kuti mtunda wa chithunzi ndi …

Yankho:

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

f = 12/3 = 4 cm

Kutalika kwa focal ndi kwabwino, kutanthauza kuti focal point ndi yeniyeni kapena kuwala kumadutsa mu point.

Mtunda wa chithunzi:

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

d _i = 28/3 = 9.3 cm

7. Dokotala wa mano amaona ndi kuyang'ana mano a wodwalayo pogwiritsa ntchito galasi lokhala ndi utali wa masentimita 8. Kuti dzenjelo liwoneke bwino kwa dokotala, kodi mtunda pakati pa mano a wodwalayo ndi galasi ndi wotani?

A. zosakwana 4 cm patsogolo pa galasi lopindika

B. zosakwana 4 cm patsogolo pa galasi lozungulira

C. kuposa 4 cm patsogolo pa galasi lopindika

D. kuposa 4 cm patsogolo pa galasi lozungulira

Zodziwika:

Utali wa galasi (r) = 8 cm

Utali wa galasi (f) = r / 2 = 8 / 2 = 4 cm

Kufunidwa: Mtunda pakati pa mano a wodwalayo ndi galasi

Yankho:

Galasi lomwe limagwiritsidwa ntchito ndi galasi lopindika kapena galasi lopindika? Kuti dzenje la dzino liwonekere bwino kwa dokotala, galasi lomwe likugwiritsidwa ntchito liyenera kukhala lotha kukulitsa chithunzi cha dzino ndipo chithunzicho chiyenera kukhala choyima. Magalasi opindika nthawi zonse amapanga zithunzi zopindika ndipo kukula kwa chithunzicho kumakhala kochepa kuposa kukula kwa chinthucho. Mosiyana ndi zimenezi, galasi lopindika limatha kupanga chithunzi choyima ngati mtunda wa chinthu (d) ndi wocheperako kuposa kutalika kwa focal (f). Ngati mtunda wa chinthucho ndi waukulu kuposa kutalika kwa focal (f) ndiye kuti galasi lopindika limapanga chithunzi chopindika.

Utali wa focal (f) wa galasi lopindika ndi 4 cm, choncho mano a wodwalayo ayenera kukhala ochepera 4 cm kutsogolo kwa galasi lopindika.

Yankho lolondola ndi A.

8. Galasi lopindika lili ndi utali wozungulira wa masentimita 24. Ngati chinthucho chayikidwa patsogolo pa galasi pa masentimita 20, ndiye kuti mudziwe momwe chithunzicho chilili.

A. Zenizeni, zowongoka komanso zokulirapo

B. Zenizeni, zopotoka komanso zokulitsidwa

C. Wowoneka bwino, wowongoka komanso wokulirapo

D. Pakompyuta, yozungulira komanso yaying'ono

Zodziwika:

Utali wozungulira wa kupindika (r) = 24 cm

Kutalika kwa focal (f) = R/2 = 24/2 = +12 cm

Kutalika kwa galasi lozungulira ndi kwabwino kapena kwenikweni chifukwa kuwala kumadutsa pamalo ozungulira galasi.

Mtunda wa chinthu (d) = 20 cm

Kufunidwa: Katundu wa chithunzi

Yankho:

Chithunzi ndi chenicheni kapena chenicheni? Werengani mtunda wa chithunzi:

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

Kutalika kwa chithunzi komwe kwalembedwa kuti ndi chabwino kumatanthauza kuti chithunzicho ndi chenicheni chifukwa chadutsa ndi kuwala.

Chithunzi chokulitsidwa? Chowongoka kapena chopotoka? Choyamba werengerani kukula kwa chithunzi (M):

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

M > 1 amatanthauza kuti chithunzi chakulitsidwa, M ali ndi chizindikiro chotsutsa amatanthauza chithunzi chosinthidwa. Chifukwa chake mawonekedwe a chithunzicho ndi enieni, osinthidwa, okulirapo.

Yankho lolondola ndi B.

9. Galasi lozungulira limapanga chithunzi chokhala ndi kukula kowirikiza kasanu kuposa chinthu chomwe chili pazenera, mamita asanu kutali ndi chinthucho. Galasi ili…..

A. concave yokhala ndi kutalika kwa focal kwa 25/24 m

B. convex yokhala ndi kutalika kwa focal kwa 25/24 m

C. concave yokhala ndi kutalika kwa focal kwa 24/25 m

D. convex yokhala ndi kutalika kwa focal kwa 24/25 m

Zodziwika:

Kukula kwa chithunzi (M) = nthawi 5

Mtunda pakati pa chinthu ndi chithunzi = mamita 5

Yankho:

Kukula kwa chithunzi chopangidwa ndi galasi lopindika nthawi zonse kumakhala kochepa kuposa kukula kwa chinthucho, chifukwa chake, galasilo ndi galasi lopindika.

Mtunda wa chinthu (d) = x

Mtunda wa chithunzi (d') = x + 5

Kukula kwa chithunzi (M) = nthawi 5

Fomula yokulitsa chithunzi:

Fomula ya kutalika kwa focal (f):

Yankho lolondola ndi A.

[wpdm_package id='858′]

1. Mavuto ndi mayankho a galasi lopindika
2. Mavuto ndi mayankho a magalasi ozungulira
3. Mavuto ndi njira zothetsera mavuto a lens
4. Kugwirizanitsa mavuto ndi mayankho a lens
5. Zipangizo zowunikira mavuto a maso a anthu ndi mayankho ake
6. Mavuto ndi mayankho a magalasi olumikizirana ndi zida zamagetsi
7. Magalasi a zida zowunikira
8. Zida zowunikira zokulitsa mavuto a magalasi ndi mayankho
9. Maikulosi ya zida zowunikira - mavuto ndi mayankho
10. Mavuto ndi mayankho a ma telescope a zida zowunikira

Werengani zambiri

1. Madzi a 1 kg pa 100 ^o C osakanizidwa ndi madzi a 1 kg pa 10 ^o C mu dongosolo losiyana. Kutentha kwa madzi ndi 4200 J/kg ^o C. Dziwani kutentha komaliza kwa chisakanizocho!

Zodziwika:

Unyinji wa madzi otentha (m ₁ ) = 1 kg

Kutentha kwa madzi otentha (T ₁ ) = 100 ^o C

Madzi ozizira (m2 ₎ = 1 kg

Kutentha kwa madzi ozizira (T2 ₎ = 10 ^o C

Kufunidwa: Kutentha komaliza (T)

Yankho:

Kutentha kotayika = Kutentha kopezeka (dongosolo lodzipatula)

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

Kutentha komaliza ndi 55 ^o C.

[irp]

2. Buluki ya lead yolemera makilogalamu atatu pa 80^o imayikidwa mu 10 kg ya madzi. Kutentha kwapadera kwa lead ndi 1400 J.kg^-1C^-1 ndipo kutentha kwa madzi ndi 4200 J.kg^-1C^-1Kutentha komaliza mu mgwirizano wa kutentha ndi 20^oC. Dziwani kutentha koyambirira kwa madzi!

Zodziwika:

Kulemera (m1 ₎ = 3 kg

Kutentha kwapadera kwa lead (c ₁ ) = 1400 J.kg ^-1 C ^-1

Kutentha kwa lead (T ₁ ) = 80 ^o C

Unyinji wa madzi (m2 ₎ = 10 kg

Kutentha kwa madzi enieni (c ₂ ) = 4200 J.kg ^-1 C ^-1

Kutentha kwa kutentha koyenera (T) = 20 ^o C

Kufunidwa: Kutentha koyambirira kwa madzi ( _T2 )

Yankho:

Kutentha kwatayika = Kutentha kwapezeka

Q lead = Q madzi

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

Kutentha koyamba kwa madzi ndi 14 ^o C.

[irp]

3. Bulu la mkuwa pa 100^oC imayikidwa mu magalamu 128 a madzi pa 30 ^oC. Kutentha kwa madzi kwenikweni ndi 1 cal.g^-1oC^-1 ndipo kutentha kwapadera kwa mkuwa ndi 0.1 cal.g^-1oC^-1. Ngati kutentha kwa kutentha kuli kofanana 36 ^oC, kudziwa kulemera kwa mkuwa!

Zodziwika:

Kutentha kwa mkuwa (T ₁ ) = 100 ^o C

Kutentha kwapadera kwa mkuwa (c ₁ ) = 0.1 c al.g ^-1o C ^-1

Unyinji wa madzi (m2 ₎ = 128 magalamu

Kutentha kwa madzi (T ₂ ) = 30 ^o C

Kutentha kwa madzi enieni (c ₂ ) = 1 c al.g ^-1o C ^-1

Kutentha kwa kutentha koyenera (T) = 36 ^o C

Kufunidwa: Unyinji wa mkuwa (m ₁ )

Yankho:

Kutentha kwatayika = Kutentha kwapezeka

Q mkuwa = Q madzi

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

Kulemera kwa mkuwa ndi magalamu 120.

[irp]

4. Chipolopolo cha ayezi cha M-kg pa 0^oC imayikidwa mu magalamu 340 a madzi pa 20^oC mu chidebe. Ngati kutentha kwa fusion kwa madzi = 80 cal g^-1, kutentha kwa madzi enieni ndi 1 calories g^{-1 o}C^-1. Chipale chonse chimasungunuka ndi kutentha kwa kutentha koyenera is 5^oC, dziwani kuchuluka kwa ayezi!

Zodziwika:

Unyinji wa madzi (m) = 340 magalamu

Kutentha kwa ayezi (T _ayezi ) = 0 ^o C

Kutentha kwa madzi ( _madzi a T ) = 20 ^o C

Kutentha kwa kutentha koyenera (T) = 5 ^o C

Kutentha kwa kusakanikirana kwa madzi ( L ) = 80 kcal g ^-1

Kutentha kwa madzi enieni (c _madzi ) = 1 cal g ^{-1 o} C ^-1

Kufunidwa: Unyinji wa ayezi (M)

Yankho:

Kutentha kwatayika = Kutentha kwapezeka

Madzi a Q = ayezi a Q

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 = magalamu 60

[wpdm_package id='714′]

1. Kusintha miyeso ya kutentha
2. Kukula kwa mzere
3. Kukula kwa dera
4. Kukula kwa voliyumu
5. kutentha
6. Kutentha kofanana ndi makina
7. Kutentha ndi mphamvu ya kutentha yeniyeni
8. Kutentha kobisika, kutentha kwa fusion, kutentha kwa nthunzi
9. Kusunga mphamvu potumiza kutentha

Werengani zambiri

4 Kutentha kobisika Kutentha kwa fusion Kutentha kwa nthunzi - Mavuto ndi Mayankho

1. Werengani kuchuluka kwa kutentha komwe kwawonjezeredwa ku gramu imodzi ya golide kuti musinthe gawo kuchokera ku cholimba kupita ku chamadzimadzi. Kutentha kwa fusion ya golide ndi 64.5 x 10 ³ J/kg.

Zodziwika:

Kulemera (m) = 1 gramu = 1 x 10 ^-3 kg

Kutentha kwa kusakanikirana (L _F ) = 64.5 x 10 ³ J/kg

Kufunidwa: Kutentha (Q)

Yankho:

Q = m L _F

Q = (1 x 10 ^-3 kg)(64.5 x 10 ³ J/kg)

Q = 64.5 Joules

[irp]

2. Werengani kuchuluka kwa kutentha komwe kumatulutsidwa ndi gramu imodzi ya mercury kuti musinthe gawo kuchokera ku madzi kupita ku cholimba. Kutentha kwa fusion ya mercury ndi 11.8 x 10 ³ J/kg.

Zodziwika:

Kulemera (m) = 1 gramu = 1 x 10 ^-3 kg

Kutentha kwa kusakanikirana (L _F ) = 11.8 x 10 ³ J/kg

Kufunidwa: Kutentha (Q)

Yankho:

Q = m L _F

Q = (1 x 10 ^-3 kg)(11.8 x 10 ³ J/kg)

Q = 11.8 Joules

3. Dziwani kuchuluka kwa kutentha komwe madzi okwana 1 kg amayamwa kuti asinthe gawo kuchokera ku madzi kupita ku nthunzi (nthunzi). Kutentha kwa nthunzi ya madzi = 2256 x 10 ³ J/kg

Zodziwika:

Kulemera (m) = 1 kg

Kutentha kwa nthunzi (L _V ) = 2256 x 10 ³ J/kg

Kufunidwa: Kutentha (Q)

Yankho:

Q = m L _V

Q = (1 kg)( 2256 x 10 ³ J/kg)

Q = 2256 x 10 ³ Joule

[irp]

4. Dziwani kuchuluka kwa kutentha komwe nayitrogeni imatulutsa kuti isinthe gawo kuchokera ku nthunzi kupita ku madzi. Kutentha kwa nthunzi ya nayitrogeni = 200 x 10 ³ J/kg

Zodziwika:

Kulemera (m) = 1 gramu = 1 x 10 ^-3 kg

Kutentha kwa nthunzi (L _V ) = 200 x 10 ³ J/kg

Kudziwika: Kutentha (Q)

Yankho:

Q = m L _V

Q = (1 x 10 ^-3 kg)( 200 x 10 ³ J/kg)

Q = 200 Joules

1. Kusintha miyeso ya kutentha
2. Kukula kwa mzere
3. Kukula kwa dera
4. Kukula kwa voliyumu
5. kutentha
6. Kutentha kofanana ndi makina
7. Kutentha ndi mphamvu ya kutentha yeniyeni
8. Kutentha kobisika, kutentha kwa fusion, kutentha kwa nthunzi
9. Kusunga mphamvu potumiza kutentha

Werengani zambiri

1. Thupi lolemera makilogalamu awiri limayamwa kutentha kwa ma calories 100 kutentha kwake kukakwera kuchoka pa 20 ^o C mpaka 70 ^o C. Kodi kutentha kwenikweni kwa thupi ndi kotani ?

Zodziwika:

Kulemera (m) = 2 kg = 2000 gr

Kutentha ( Q) = 100 kcal

Kusintha kwa kutentha ( ΔT ) = 70 ^o C – 20 ^o C = 50 ^o C

Kufunidwa: Kutentha kwapadera (c)

Yankho:

c = Q / m Δ T

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

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

c = 10 ² cal / 10 ⁵ gr ^o C

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

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

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

Kutentha kwa thupi ndi 10 ^-3 cal/gr ^o C

[irp]

2. Kutentha kwa madzi ndi 4180 J/kg Co. ^Kodi mphamvu ya kutentha ya madzi a 2 kg ndi yotani?

Zodziwika:

Kutentha kwenikweni (c) = 4180 J/kg C ^o

Kulemera (m) = 2 kg

Kufunika: Kutentha (C)

Yankho:

C = mc

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

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

C = 8360 J/C ^o

3. Kutentha kwa aluminiyamu ndi 900 J/kg Co2 ^. Kuchuluka kwa kutentha kwa aluminiyamu ya magalamu awiri…..

Zodziwika:

Kutentha kwa aluminiyamu (c) = 900 J/kg C ^o = 9 x 10 ² J/kg C ^o

Kulemera (m) = magalamu awiri = 2/1000 kg = 2/10 ³ kg = 2 x 10 ^-3 kg

Kufunika: Kutentha (C)

Yankho:

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. Kusintha miyeso ya kutentha
2. Kukula kwa mzere
3. Kukula kwa dera
4. Kukula kwa voliyumu
5. kutentha
6. Kutentha kofanana ndi makina
7. Kutentha ndi mphamvu ya kutentha yeniyeni
8. Kutentha kobisika, kutentha kwa fusion, kutentha kwa nthunzi
9. Kusunga mphamvu potumiza kutentha

Werengani zambiri

1. 2 kcal ( kilo c calorie e ) = ….. c calorie e?

Anakonza

1 kcal = 1000 kcal

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

2. 4 C calorie e = ….. c calories e?

Anakonza

1 Kalori e ( Capital C ) = 1 kcal = 1000 calories e

4 C calories e = 4 (1000 c calorie e ) = 4000 c calorie e

3. 10 c calorie e = ….. Joule?

Anakonza

Kalori imodzi e = 4.186 Joules

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

[irp]

4. 5 kcal = ….. Joule ?

Anakonza

1 kcal = 1000 c alorie = 4186 Joules

5 kcal = 5 (4186 Joules) = 20930 Joules

5. Ma Joules 2000 = ….. k cal?

Anakonza

4186 Joules = 1 kcal

Ma Joules 8372 = 8372 / 4186 = 2 kcal

Ma Joules 2000 = 2000 / 4186 = 0.4777 kcal

[wpdm_package id='706′]

1. Kusintha miyeso ya kutentha
2. Kukula kwa mzere
3. Kukula kwa dera
4. Kukula kwa voliyumu
5. kutentha
6. Kutentha kofanana ndi makina
7. Kutentha ndi mphamvu ya kutentha yeniyeni
8. Kutentha kobisika, kutentha kwa fusion, kutentha kwa nthunzi
9. Kusunga mphamvu potumiza kutentha

Werengani zambiri

9 Kutentha Kwambiri Kutentha Kwapadera Kusintha kwa kutentha - Mavuto ndi Mayankho

1. Chitoliro cha 2 kg chimatenthedwa kuchokera 50^oC kuti 100^oC. The kutentha kwapadera cha kutsogolera ndi 130 J.kg^{-1 o}C^-1. Zingati kutentha imatengedwa ndi lead?

Zodziwika:

Kulemera (m) = 2 kg

Kutentha kwenikweni (c) = 1 3 0 J.kg ^-1 C ^-1

Kusintha kwa kutentha ( Δ T) = 100 ^o C – 50 ^o C = 50 ^o C

Kufunidwa: Kutentha (Q)

Yankho:

Q = mc Δ T

Q = kutentha , m = kulemera, c = kutentha kwenikweni , Δ T = kusintha kwa kutentha

Kutentha komwe kumatengedwa ndi lead:

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

Q = (100)(1 3 0)

Q = 1 3,000 Joules

Q = 1.3 x ¹⁰⁴ Joules

[irp]

2. Kutentha kwapadera kwa mkuwa ndi 390 J/k g ^o C, kusintha kwa kutentha ndi 40 ^o C. Ngati mkuwa umatenga kutentha kwa ma Joules 40, kodi kulemera kwa mkuwa ndi kotani!

Zodziwika:

Kutentha kwapadera kwa mkuwa (c) = 390 J/k g ^o C

Kusintha kwa kutentha ( ΔT ) = 40 ^o C

Kutentha ( Q) = 40 J

Kufunidwa: Kulemera (m) kwa mkuwa

Yankho:

Q = mc Δ T

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

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

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

40 = (m)( 1560/kg )

m = 40 / 1560

m = 0.026 kg

m = magalamu 26

3. Kutentha koyambirira kwa magalamu 20 a madzi ndi 30 ^o C. Kutentha kwapadera kwa madzi ndi 1 cal g ^{-1 o} C ^-1 . Ngati madzi amatenga ma calories 300 a kutentha, dziwani kutentha komaliza!

Zodziwika:

Kulemera (m) = 20 gr

Kutentha koyambirira (T1 ₎ = 30 ^o C

Kutentha kwa madzi enieni (c) = 1 cal gr ^{-1 o} C ^-1

Kutentha (Q) = 300 cal

Kufunidwa: Kutentha komaliza kwa madzi

Yankho:

Q = mc ΔT

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

300 = (20)(1)( T ₂ -30)

300 = 20 ( T ₂ -30 )

300 = 20 T ₂ - 600

300 + 600 = 20T ₂

900 = 20T ₂

T ₂ = 900 / 20

T ₂ = 45

Kusintha kwa kutentha ndi 45 ^o C - 30 ^o C = 15 ^o C.

 [irp]

4. Tkusintha kwa kutentha madzi a m'nyanja is 1^oC pamene madzi amatenga kutentha kwa ma Joules 3900. Kutentha kwapadera kwa madzi a m'nyanja ndi 3.9 × 10³ J/kg°C, kuchuluka kwa madzi a m'nyanja ndi kotani.

Zodziwika:

Kusintha kwa kutentha ( ΔT ) = 1 ^o C

Kutentha (Q) = 3900 Joule

Kutentha kwapadera kwa madzi a m'nyanja (c) = 3.9 x 10 ³ J/ k g°C = 3900 J/Kg°C

Kufunidwa: Misa (m)

Yankho:

Q = mc Δ T

Q = kutentha , m = kulemera, c = kutentha kwapadera , Δ T = kusintha kwa kutentha

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

5. Mkuwa wa makilogalamu awiri umayamwa kutentha kwa 39,000 J pa 30°C. Ngati kutentha kwa mkuwa ndi 390 J/kg °C, kodi kutentha komaliza kwa mkuwa ndi kotani?

Zodziwika:

Kulemera (m) = 2 kg

Kutentha koyambirira (T ₁ ) = 30 ^o C

Kutentha (Q) = 39,000 Joule

Kutentha kwapadera (c) kwa mkuwa = 390 J/kg ^o C

Kufunidwa : Kutentha komaliza ( _T2 )

Yankho:

Q = mc ΔT

Q = kutentha , m = kulemera, c = kutentha kwapadera , ΔT = kusintha kwa kutentha

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

T ₂ = 50 + 30

T ₂ = 80 ^o C

[irp]

6. Madzi okwana makilogalamu awiri amatenthedwa kuyambira 15°C mpaka 40°C. Kutentha kwake kumatengedwa ndi madzi. Kutentha kwapadera kwa madzi ndi 4.2 × 10 ³ J/Kg° C.

Zodziwika:

Kulemera (m) = 5 kg

Kutentha koyambirira (T1 ₎ = 15°C

Kutentha komaliza (T2 ₎ = 40°C

Kutentha kwa madzi enieni (c) = 4.2 × 10 ³ J/kg° C

Kufunidwa: Kutentha (Q)

Yankho:

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 = 525,000 Joules

7. Madzi okwana makilogalamu awiri amatenthedwa kuyambira 24°C mpaka 90°C. Kutentha kwake kumatengedwa ndi madzi. Kutentha kwapadera kwa madzi ndi 4.2 × 10 ³ J/Kg° C.

Zodziwika:

Kulemera (m) = 2 kg

Kutentha koyambirira (T1 ₎ = 24°C

Kutentha komaliza (T2 ₎ = 90°C

Kutentha kwa madzi enieni (c) = 4,200 Joules/kg°C

Kufunidwa :: Kutentha (Q)

Yankho:

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)( 4,200 Joules)

Q = 554,400 Joules

[irp]

8. Madzi a magalamu 5 amatenthedwa kuyambira 10°C mpaka 40°C. Kutentha komwe kumayamwa ndi madzi ndi chiyani. Kutentha kwapadera kwa madzi ndi 1 × 10 ³ cal /g r ° C.

Zodziwika:

Kulemera (m) = magalamu 5

Kutentha koyambirira (T ₁ ) = 10 ^o C

Kutentha komaliza (T2 ₎ = 40 ^o C

Kutentha kwa madzi enieni (c) = 1 c al/ gr°C

Kufunidwa : Kutentha

Yankho:

Q = mc ΔT

Q = (5 magalamu)( 1 cal/ gr°C)(40 ^o C – 10 ^o C)

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

Q = ma calories 150

9. Madzi a 0.2 -kg amayamwa kutentha kwa ma Joules 42,000 pa 25 ^o C. Kutentha kwapadera kwa madzi ndi 4200 J/kg ^o C, kutentha komaliza kwa madzi ndi kotani.

Zodziwika:

Kulemera kwa madzi (m) = 0.2 kg

Kutentha (Q) = 42,000 Joule

Kutentha kwa madzi enieni (c) = 4200 J/kg ^o C

Kutentha koyambirira (T ₁ ) = 25 ^o C

Kufunidwa: Kutentha komaliza ( _T2 )

Yankho:

Q = mc ΔT = mc (T ₂ – T ₁ )

Q= kutentha, m = kulemera, c = kutentha kwapadera, ΔT = kusintha kwa kutentha, T₁ = kutentha koyambirira, T₂ = kutentha komaliza

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. Kusintha miyeso ya kutentha
2. Kukula kwa mzere
3. Kukula kwa dera
4. Kukula kwa voliyumu
5. kutentha
6. Kutentha kofanana ndi makina
7. Kutentha ndi mphamvu ya kutentha yeniyeni
8. Kutentha kobisika, kutentha kwa fusion, kutentha kwa nthunzi
9. Kusunga mphamvu potumiza kutentha

Werengani zambiri

Kukula kwa mzere kumachitika ndi zinthu zolimba zokha; kukula kwa voliyumu kumachitika ndi zinthu zonse, zolimba, zamadzimadzi, ndi mpweya. Kuchuluka kwa kuchuluka kwa voliyumu kumafanana ndi kuchuluka kwa kukula kwa mzere.

Kufotokozera: Vo ₌ Voliyumu yoyambirira, V = Voliyumu yomaliza, ΔV = V – Vo ₌ Kusintha kwa voliyumu, To _o = Kutentha koyambirira, T = Kutentha komaliza, ΔT = T – To _o = Kusintha kwa kutentha, β = coefficient of voliyumu expansion. Mayunitsi a β = ( ^Co ) ^-1

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Chiyerekezo cha kukulitsa voliyumu chomwe chili pamwambapa chimagwira ntchito pokhapokha ngati kusintha kwa voliyumu ya zinthu (zonse zolimba, zamadzimadzi, ndi mpweya) kuli kochepa kuposa voliyumu yoyambirira ya chinthucho. Ngati kusintha kwa voliyumu ya chinthu kuli kwakukulu kuposa voliyumu yoyambirira ya chinthucho, chiyerekezo cha kukulitsa voliyumu sichipereka zotsatira zoyenera. Nthawi zambiri, kusintha kwa voliyumu komwe kumachitika ndi zinthu zolimba sikuli kwakukulu kwambiri. Kumbali inayi, kukulitsa kwa voliyumu kwa madzi ndi mpweya kumakhala kwakukulu. Kukulitsa kwa voliyumu kwa zinthu za gasi ndikosavuta kusintha ngati kutentha kwasintha. Chifukwa chake fomula yomwe ili pamwambapa imagwiritsidwa ntchito kokha pakukulitsa kwa zinthu zolimba.

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1. Pa 30 ^o C voliyumu ya aluminiyamu ndi 30 cm ^3. Chiwerengero cha kukula kwa mzere ndi 24 x 10 ^{-6 o} C ^-1 . Ngati voliyumu yomaliza ndi 30.5 cm ³ , kutentha komaliza kwa aluminiyamu ndi kotani?

Zodziwika:

Chiŵerengero cha kukula kolunjika ( α ) = 24 x 10 ^{-6 o} C ^-1

Chiŵerengero cha kukula kwa voliyumu ( β ) = 3 α = 3 x 24 x 10 ^{-6 o} C ^-1 = 72 x 10 ^{-6 o} C ^-1

Kutentha koyambirira (T1 ₎ = 30 ^o C

Kuchuluka koyambirira (V ₁ ) = 30 cm ³

Voliyumu yomaliza (V ₂ ) = 30.5 cm ³

Kusintha kwa voliyumu ( Δ V) = 30.5 cm ³ – 30 cm ³ = 0.5 cm ³

Kufunidwa: Kutentha komaliza ( _T2 )

Yankho:

Δ V = β (V ₁ )( ΔT )

Δ V = β (V ₁ )(T ₂ – T ₁ )

0.5 masentimita³ = (72 × 10^{-6 o}C^-1)(30cm)³)(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 = T ₂

T ₂ = 260 ^o C

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2. Chiwerengero cha kukula kwa mzere wa chitsulo ndi 9 x 10 ^{-6 o} C ^-1 . M'mimba mwake wa chitsulo pa 20 ^o C ndi 2.2 cm. Ngati m'mimba mwake womaliza ndi 2.8 cm, kutentha komaliza ndi kotani!

Zodziwika:

Chiŵerengero cha kukula kolunjika ( α ) = 9 x 10 ^{-6 o} C ^-1

Chiŵerengero cha kukula kwa voliyumu ( β) = 3 α = 3 x 9 x 10 ^{-6 o} C ^-1 = 27 x 10 ^{-6 o} C ^-1

Kutentha koyambirira (T1 ₎ = 20 ^o C

Chidutswa choyamba cha m'mimba mwake (D ₁ ) = 2.2 cm

Chidutswa chomaliza cha m'mimba mwake (D ₂ ) = 2.8 cm

Ulalo woyambira (r ₁ ) = D ₁ / 2 = 2.2 cm ³ / 2 = 1.1 cm ³

Ulalo womaliza (r ₂ ) = D ₂ / 2 = 2.8 cm ³ / 2 = 1.4 cm ³

Voliyumu yoyambirira (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

Voliyumu yomaliza (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

Kusintha kwa voliyumu ( Δ V) = 11.48 cm ³ – 5.57 cm ³ = 5.91 cm ³

Kufunidwa: Kutentha _komaliza ( T2 )

Yankho:

Δ V = β (V ₁ )( ΔT )

5.91 masentimita³ = (27 × 10^{-6 o}C^-1)(5.57 masentimita³)(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 = T ₂

T ₂ = 39,020 ^o C

3. A 2000-cm³ chotengera cha aluminiyamu, wodzazidwa ndi madzi pa 0^oC. Kenako kutentha kufika madigiri 90^oC. Ngati coefficient ya linear expansion ya aluminiyamu ndi 24 x 10^-6 (^oC)^-1 ndipo kuchuluka kwa kuchuluka kwa madzi ndi 6.3 x 10^-4 (^oC)^-1, kudziwa kuchuluka kwa madzi omwe atayika.

Zodziwika:

Kuchuluka koyambirira kwa chidebe cha aluminiyamu ndi madzi (Vo ₎ = 2000 cm ³ = 2 x 10 ³ cm ³

Kutentha koyambirira kwa chidebe cha aluminiyamu ndi madzi (T ₁ ) = 0 ^o C

Kutentha komaliza kwa chidebe cha aluminiyamu ndi madzi (T2 ₎ = 90 ^o C

Kuchuluka kwa kukula kwa aluminiyamu (α) = 24 x 10 ^-6 ( ^o C ) ^-1

Kuchuluka kwa kuchuluka kwa aluminiyamu (γ) = 3α = 3 (24 x 10 ^-6 ( ^o C ) ^-1 ) = 72 x 10 ^{-6 o} C ^-1

Kuchuluka kwa kuchuluka kwa madzi (γ) = 6.3 x 10 ^-4 ( ^o C ) ^-1

Kufunidwa: Kuchuluka kwa madzi otayika

Yankho:

Chiyerekezo cha kukula kwa voliyumu:

V = Vo _o + γ Vo _o ΔT

V – Vo _o = γ Vo _o ΔT

ΔV = γ Vo _o ΔT

V = voliyumu yomaliza, Vo ₌ voliyumu yoyambirira, ΔV = kusintha kwa voliyumu, γ = coefficient ya kukula kwa voliyumu, ΔT = kusintha kwa kutentha

Werengani kusintha kwa voliyumu ya chidebe cha aluminiyamu:

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

Werengerani kusintha kwa kuchuluka kwa madzi:

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

Kusintha kwa kuchuluka kwa madzi kumakhala kwakukulu kuposa chidebe cha aluminiyamu kotero kuti madzi ena amatuluka.

Werengani kuchuluka kwa madzi otayika:

113.4 cm ³ – 12.960 cm ³ = 100.44 cm ³

[wpdm_package id='702′]

1. Kusintha miyeso ya kutentha
2. Kukula kwa mzere
3. Kukula kwa dera
4. Kukula kwa voliyumu
5. kutentha
6. Kutentha kofanana ndi makina
7. Kutentha ndi mphamvu ya kutentha yeniyeni
8. Kutentha kobisika, kutentha kwa fusion, kutentha kwa nthunzi
9. Kusunga mphamvu potumiza kutentha

Werengani zambiri

1. Pa 20 ^o C, kutalika kwa pepala lachitsulo ndi 50 cm ndipo m'lifupi ndi 30 cm. Ngati coefficient of linear expansion ya chitsulo ndi 10 ^{-5 o} C ^-1 , dziwani kusintha kwa dera ndi dera lomaliza pa 60 ^o C.

Zodziwika:

Kutentha koyambirira (T1 ₎ = 20 ^o C

Kutentha komaliza (T2 ₎ = 60 ^o C

Kusintha kwa kutentha ( ΔT ) = 60 ^o C – 20 ^o C = 40 ^o C

Malo oyamba (A ₁ ) = kutalika x m'lifupi = 50 cm x 30 cm = 1500 cm ²

Chiŵerengero cha kukula kwa mzere wachitsulo ( α) = 10 ^{-5 o} C ^-1

Chiŵerengero cha kukula kwa dera la chitsulo ( β) = 2α = 2 x 10 ^{-5 o} C ^-1

Kufunidwa: Kusintha kwa dera ( ΔA )

Yankho:

Kusintha kwa dera ( ΔA ):

ΔA = β A 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

Gawo lomaliza ( _A2 ) :

A ₂ = A ₁ + ΔA

A ₂ = 1500 cm ² + 1. 2 cm ²

A ₂ = 1501 . 2 cm ²

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2. Pa 30 ^o C, dera la pepala la aluminiyamu ndi 40 cm ² ndipo coefficient of linear expansion ndi 24 x 10 ^-6 / ^o C. Dziwani kutentha komaliza ngati dera lomaliza ndi 40.2 cm ².

Zodziwika:

Kutentha koyambirira (T1 ₎ = 30 ^o C

Chiŵerengero cha kukula kolunjika ( α) = 24 x 10 ^{-6 o} C ^-1

Chiŵerengero cha kukula kwa dera ( β) = 2a = 2 x 24 x 10 ^{-6 o} C ^-1 = 48 x 10 ^{-6 o} C ^-1

Malo oyamba (A ₁ ) = 40 cm ²

Malo omaliza (A ₂ ) = 40.2 cm ²

Kusintha kwa dera ( ΔA) = 40.2 cm ² – 40 cm ² = 0.2 cm ²

Kufunidwa: Dziwani kutentha komaliza ( _T2 )

Yankho:

Fomula ya kusintha kwa dera ( ΔA) :

ΔA = β A ₁ Δ T

Kutentha komaliza (T2 ₎ :

ΔA = β A ₁ (T ₂ – T ₁ )

0.2 masentimita² = (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 = T ₂

T ₂ = 130

Kutentha komaliza = 130 ^o C

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3. Utali wa mphete pa 20 ^o C ndi 20 cm. Ngati utali womaliza pa 100 ^o C ndi 20.5 cm, dziwani kuchuluka kwa kukula kwa dera ndi kuchuluka kwa kukula kwa mzere…

Zodziwika:

Kutentha koyambirira (T1 ₎ = 30 ^o C

Kutentha komaliza (T2 ₎ = 100 ^o C

Kusintha kwa kutentha ( ΔT ) = 100 ^o C – 30 ^o C = 70 ^o C

Utali woyambira (r ₁ ) = 20 cm

Ulalo womaliza (r ₂ ) = 20.5 cm

Kufunidwa: Chiwerengero cha kukula kwa dera ( β )

Yankho:

Malo oyamba (A ₁ ) = π r ₁ ² = (3.14)(20 cm) ² = (3.14)(400 cm ² ) = 1256 cm ²

Malo omaliza (A ₂ ) = π r ₂ ² = (3.14)(20.5 cm) ² = (3.14)(420.25 cm ² ) = 1319.585 cm ²

Kusintha kwa dera ( ΔA) = 1319.585 cm ² – 1256 cm ² = 63.585 cm ²

Fomula ya kusintha kwa dera ( ΔA) :

ΔA = β A ₁ ΔT

Chiwerengero cha kukula kwa dera:

ΔA = β A 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 ^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

Chiŵerengero cha kukula kolunjika ( 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. Kusintha miyeso ya kutentha
2. Kukula kwa mzere
3. Kukula kwa dera
4. Kukula kwa voliyumu
5. kutentha
6. Kutentha kofanana ndi makina
7. Kutentha ndi mphamvu ya kutentha yeniyeni
8. Kutentha kobisika, kutentha kwa fusion, kutentha kwa nthunzi
9. Kusunga mphamvu potumiza kutentha

Werengani zambiri