Mathata a Rarollotsoeng Fisiks ea Motheo

1. Bolelele ba ntlha bo shebaneng le seipone se kobehileng ke 10 cm mme sebaka sa ntho ke 20 cm. Fumana (a) sebaka sa setšoantšo (b) kgolo ya setshwantsho

Tse tsejoang:

Bolelele ba focal (f) = -10 cm

Letšoao la ho tlosa le bontša hore ntlha ea bohlokoa ea seipone se kobehileng ke ea sebele

Sebaka sa ntho ( do _o ) = 20 cm

Tharollo:

Sebopeho sa setšoantšo ka seipone se kobehileng:

Sebaka sa setšoantšo (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

Letšoao la minus le bontša hore setšoantšo ke sa sebele.

Ho holisa setšoantšo:

m = – di _/ do o = -(-6.7)/20 = 6.7/20 = _0.3

m = 0,3 nako e nyane ho feta ntho.

Letšoao la ho eketsa le bontša hore setšoantšo se holimo.

[irp]

2. Ntho e bolelele ba 10 cm e beoa ka pel'a seipone se kobehileng se nang le bolelele ba 20 cm. Fumana bophahamo ba setšoantšo haeba sebaka sa ntho e le (a) 10 cm (b) 30 cm (c) 40 cm (d) 50 cm

Tse tsejoang:

Bolelele ba focus ba seipone se kobehileng (f) = -20 cm

Letšoao la ho tlosa le bontša hore ntlha ea bohlokoa ke ea sebele

Radius ea kobeho ( r ) = 2 f = 2(20) = 40 cm

Bolelele ba ntho (h) = 10 cm

Tharollo:

a) bolelele ba focal (f) = -20 cm le sebaka sa ntho (do _o ) = 10 cm

Sebaka sa setšoantšo (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

Letšoao la minus le bontša hore setšoantšo ke sa sebele kapa setšoantšo se ka mor'a seipone.

Ho holisa setšoantšo ( m ):

m = – di _/ do o = -(-6.7)/10 = 6.7/10 = _0.67

Letšoao la ho eketsa le bontša hore setšoantšo se eme hantle.

Setšoantšo se senyenyane ka 0.67 ho feta ntho.

Bolelele ba setšoantšo (h _i ):

m = h _i / h _o

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

b) bolelele ba focal (f) = -20 cm le sebaka sa ntho ( do _o ) = 30 cm

Sebaka sa setšoantšo ( di _i ):

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

d _i = -60/5 = -12

Letšoao la minus le bontša hore setšoantšo ke sa sebele kapa setšoantšo se ka mor'a seipone.

Ho holisa setšoantšo ( m ):

m = – di / _do o ₌ -(-12)/30 = 12/30 = 0.4

Letšoao la ho eketsa le bontša hore setšoantšo se eme hantle.

Setšoantšo se senyenyane ka makhetlo a 0,4 ho feta ntho.

Bophahamo ba setšoantšo (h _i ):

m = h _i / h _o

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

c) Bolelele ba focal (f) = -20 cm le sebaka sa ntho ( do _o ) = 40 cm

Sebaka sa setšoantšo ( 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

Letšoao la ho tlosa le bontša hore setšoantšo ke sa sebele kapa setšoantšo se ka mor'a seipone se kobehileng.

Ho holisa setšoantšo ( m ):

m = – di / _do o = -(-13.3)/40 = 13.3/40 = _0.3

Letšoao la ho eketsa le bontša hore setšoantšo se eme hantle.

Setšoantšo se senyenyane ka 0.3 ho feta ntho.

Bophahamo ba setšoantšo ( h _{i )} :

m = h _i / h _o

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

d) Bolelele ba fokhase (f) = -20 cm le sebaka sa ntho ( do _o ) = 50 cm

Sebaka sa setšoantšo ( 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

Letšoao la ho tlosa le bontša hore setšoantšo ke sa sebele kapa setšoantšo se ka mor'a seipone se kobehileng.

Ho holisa setšoantšo ( m ):

m = – di _/ do o = -(-14.3)/50 = 14.3/50 = _0.3

Letšoao la ho eketsa le bontša hore setšoantšo se eme hantle.

Setšoantšo se senyenyane ka 0.3 ho feta ntho.

Bolelele ba setšoantšo (h _i ) :

m = h _i / h _o

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

[irp]

3. Nthong e bohōle ba 20 cm ka pel'a seipone se kobehileng . Haeba bophahamo ba setšoantšo bo le 1/5 makhetlo a bophahamo ba ntho, fumana ( a) bolelele ba setšoantšo b) bolelele ba focal c) litšobotsi tsa setšoantšo

Tse tsejoang:

Sebaka sa ntho ( do _o ) = 20 cm

Bolelele ba setšoantšo (h _i ) = 1/5 h = 0.2 h

Bophahamo ba ntho (h) = h

Tharollo:

a) sebaka sa setšoantšo ( di ₎

Foromo ea ho holisa setšoantšo :

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

Letšoao la ho eketsa le bontša hore setšoantšo se eme hantle.

Setšoantšo se senyenyane ka 0.2 ho feta ntho.

Sebaka sa setšoantšo ( di _i ):

– d _i = md _o

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

Letšoao la ho tlosa le bontša hore setšoantšo ke sa sebele kapa setšoantšo se ka mor'a seipone se kobehileng.

b) Bolelele ba fokhase ( f)

Bolelele ba focus (f):

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

f = -20/4 = -5 cm

Letšoao la ho tlosa le bontša hore ntlha ea bohlokoa ke ea sebele.

c) Thepa ea setšoantšo:

– E lokileng

– E nyane

– inthaneteng

4. Leseli le otla seipone se kobehileng se bapileng le mothapo le tla bonahatswa….

A. ho ea sebakeng se ka sehloohong sa seipone

B. ho tloha ntlheng ea mantlha ea seipone

C. ho pholletsa le bohareng ba seipone se kobehileng

D. e otlolohileng ho seipone sa sefofane

tharollo

Bothata bo takiloe setšoantšong se ka tlase.

Karabo e nepahetseng ke B.

5. Mopalami oa baesekele o bona setšoantšo sa sethuthuthu se ka morao ho sona ka makhetlo a 1/6 a boholo ba sona ba pele ha sebaka se pakeng tsa mopalami le sethuthuthu e le limithara tse 30. Fumana radius ea kobeho ea seipone se ka morao…

A. 7.14 m

B. 8.57 m

C. 12.00 m

D. 24.00 m

Tse tsejoang:

Ho holisa setšoantšo (M) = 1/6 makhetlo

Sebaka sa ntho (d) = limithara tse 30

Ho batloa: Radius ea ho kobeha ha seipone se shebileng ka morao (R)

Tharollo:

Bala sebaka sa setšoantšo (d')

Kaha kgolo ya setshwantsho (M) le sebaka (dibaka) sa ntho di se di tsejwa, sebaka sa setshwantsho se ka tsejwa ka ho sebedisa foromo ya kgolo ya setshwantsho:

Letšoao le fosahetseng le bolela hore setšoantšo ke sa sebele. Setšoantšo se limithara tse 5 ka mor'a seipone se kobehileng.

Bala bolelele ba focal (f)

Kaha sebaka sa ntho (d) le sebaka sa setšoantšo (d'), bolelele ba focal bo ka baloa ho sebelisoa foromo ea seipone:

Radius ea kobeho (R)

Radius ea ho kobeha ha seipone se kobehileng e habeli bolelele ba focal ba seipone se kobehileng.
R = 2 f = 2 (limithara tse 6) = limithara tse 12
Radius ea ho kobeha ha seipone se kobehileng ke limithara tse 12.
Karabo e nepahetseng ke C.

6. Seipone se kobehileng se kgethwa e le seipone se shebang ka morao sa sethuthuthu hobane thepa ya setshwantsho se hlahiswang ke seipone ke…

A. ea 'nete, e otlolohileng, e fokolitsoeng

B. ea 'nete, e otlolohileng, e atolositsoeng

C. e hlakileng, e otlolohileng, e fokotsehile

D. ya sebele, e otlolohileng, e hodisitsweng

Tharollo:

Ho latela dipalo tse pedi tse ka hodimo ho ka fihlellwa qeto ya hore thepa ya setshwantsho ke ya sebele, e otlolohileng, e fokoditswe.

Karabo e nepahetseng ke C.

7. Ntho e ka 12 cm ka pel'a seipone se kobehileng se nang le radius ea 6 cm. Thepa ea setšoantšo ke…

A. ea 'nete, e khelohileng bohōle ba 12 cm

B. ea 'nete, e otlolohile bohōle ba 4 cm

C. e hlakileng, e eme hantle hole le 2.4 cm

D. e fumanehang ka ho hlaka, e khelohileng bohōleng ba 6 cm

Tse tsejoang:

Sebaka sa ntho (d) = 12 cm

Radius ea seipone se kobehileng (r) = 6 cm.

Bolelele ba focus ba seipone se kobehileng (f) = 6 cm / 2 = -3 cm

Bolelele ba ntlha ya seipone se kobehileng bo saennwe ke kgaello hobane ke ntho ya sebele. Ntho ya sebele hobane ha e fetiswe ke lesedi.

Ho batloa: Matlotlo a setšoantšo

Tharollo:

Sebaka sa setšoantšo (d'):

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

d' = -12/5 = -2.4 cm

Sebaka sa setšoantšo se saennweng se le mpe se bolela hore setšoantšo ke sa sebele.

Kgodiso ya setshwantsho (m):

m = -d' / d = -(-2.4) / 12 = 2.4 / 12 = makhetlo a 0.2

Ho holisa setšoantšo se saennweng hantle ho bolela hore setšoantšo se eme hantle 'me ho holisa setšoantšo ke 0.2 ho bolela hore boholo ba setšoantšo bo bonyenyane ho feta boholo ba ntho (bo fokotsehile).

Karabo e nepahetseng ke C.

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Bala haholoanyane

1. Ntho e beoa 10 cm ho tloha seiponeng se kobehileng . Bolelele ba fokhase ke 5 cm. Fumana (a) Sebaka sa setšoantšo (b) kholo ea setšoantšo

Tse tsejoang:

Bolelele ba focal (f) = 5 cm

Sebaka sa ntho ( do _o ) = 10 cm

Tharollo :

Sebopeho sa setšoantšo ka seipone se kobehileng:

Sebaka sa setšoantšo:

1/ di ₌ 1/f – 1/ do _o = 1/5 – 1/10 = 2/10 – 1/10 = 1/10

d _i = 10/1 = 10 cm

Sebaka sa setšoantšo ke 10 cm.

Kgodiso:

m = – di _/ do _o = -10/10 = -1

1 e bolela hore setšoantšo se tšoana le ntho.

Letšoao la ho tlosa le bontša hore setšoantšo se khelohile. Haeba letšoao le le ntle, setšoantšo se eme hantle.

[irp]

2. Ntho e bolelele ba 5 cm e beoa ka pel'a seipone se kobehileng se nang le radius ea kobeho ea 20 cm. Fumana bophahamo ba setšoantšo haeba sebaka sa ntho e le 5 cm, 15 cm, 20 cm, 30 cm.

Tse tsejoang:

Radius ea kobeho ( r ) = 20 cm

Bolelele ba focal (f) = R/2 = 20/2 = 10 cm

Bolelele ba ntho (h _o ) = 5 cm

Tharollo:

a) bolelele ba focal (f) = 10 cm le sebaka sa ntho ( do _o ) = 5 cm

Sebopeho sa setšoantšo ka seipone se kobehileng:

Sebaka sa setšoantšo ( 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

Letšoao la minus le bontša hore setšoantšo ke sa sebele kapa setšoantšo se ka mor'a seipone.

Ho holisa setšoantšo ( m ):

m = – di / _do o ₌ -(-10)/5 = 10/5 = 2

Letšoao la ho eketsa le bontša hore setšoantšo se eme hantle.

Bophahamo ba setšoantšo ( h _i ):

m = h _i / h _o

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

Bophahamo ba setšoantšo ke 10 cm.

b) Bolelele ba fokhase (f) = 10 cm le sebaka sa ntho ( do _o ) = 15 cm

Sebopeho sa setšoantšo ka seipone se kobehileng:

Sebaka sa setšoantšo ( 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

Letšoao la ho eketsa le bontša hore setšoantšo ke sa 'nete kapa setšoantšo se bolelele ba 30 cm ka pel'a seipone, ka lehlakoreng le le leng le ntho.

Ho holisa setšoantšo ( m ):

m = – di _/ do _o = -30/15 = -2

Letšoao la ho tlosa le bontša hore setšoantšo se khelohile.

Setšoantšo se seholo ho feta ntho ka makhetlo a mabeli.

Bolelele ba setšoantšo (h _i ):

m = h _i / h _o

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

Bophahamo ba setšoantšo ke 10 cm.

c) Bolelele ba fokhase (f) = 10 cm le sebaka sa ntho ( do _o ) = 20 cm

Sebopeho sa setšoantšo ka seipone se kobehileng:

Sebaka sa setšoantšo (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

Letšoao le letle le bontša hore setšoantšo ke sa 'nete kapa setšoantšo se bohōle ba 20 cm ka pel'a seipone, ka lehlakoreng le le leng le ntho.

Ho holisa setšoantšo ( m ):

m = – di _/ do _o = -20/20 = -1

Letšoao le lebe le bolela hore setšoantšo se khelohile.

Bolelele ba setšoantšo ( hello ):

m = h _i / h _o

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

d) Bolelele ba fokhase (f) = 10 cm le sebaka sa ntho ( do _o ) = 30 cm

Sebaka sa setšoantšo ( 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

Letšoao la ho eketsa le bontša hore setšoantšo ke sa 'nete kapa setšoantšo se bolelele ba 15 cm ka pel'a seipone, ka lehlakoreng le le leng le ntho.

Kgodiso ya setshwantsho ( m) :

m = – di _/ do _o = -15/30 = -0.5

Letšoao la ho tlosa le bontša hore setšoantšo se khelohile.

Setšoantšo se senyenyane ka 0.5 ho feta ntho.

Bolelele ba setšoantšo (h _i ):

m = h _i / h _o

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

[irp]

3. Setšoantšo se entsoeng ke seipone se kobehileng se seholo ho feta ntho ka makhetlo a mane. Haeba radius ea kobeho e le 20 cm, fumana sebaka sa ntho ka pel'a seipone!

Tse tsejoang:

Ho holisa setšoantšo ( m ) = 4

Radius ea kobeho ( r ) = 20 cm

Bolelele ba focal (f) = r /2 = 20/2 = 10 cm

Ho batloa : Sebaka sa ntho ( do _o )

Tharollo:

m = _– ke _/ ke​

4 = _– ke _{/ ke}

– 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

Sebaka sa ntho = 12.5 cm.

[irp]

4. Ntho e bolelele ba 1 cm e beoa 10 cm ho tloha seiponeng se kobehileng se nang le bolelele ba focus, f = 15 cm. Fumana:

A. Sebaka sa setšoantšo?

B. Bolelele ba setšoantšo?

C. Thepa ea setšoantšo se entsoeng ke seipone se kobehileng ke efe?

Tse tsejoang:

Bolelele ba ntho (h) = 1 cm

Sebaka sa ntho (do _o ) = 10 cm

Bolelele ba focus ba seipone se kobehileng (f) = 15 cm

Tharollo:

A. Sebaka sa setšoantšo (d _i )

1/f = 1/do ₊ 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

Letšoao le fosahetseng le bontša hore setšoantšo ke sa sebele kapa setšoantšo se ka mor'a seipone.

B. Bophahamo ba setšoantšo (h _i )

Ho holisa setšoantšo (M):

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

M = -(-30)/10 = 30/10 = makhetlo a 3

Bolelele ba setšoantšo (h _i ):

M = h _i / h _o

3 = h _i / 1 cm

h _i = 3 (1 cm)

h _i = 3 cm

Bophahamo ba setšoantšo ke 3 cm. Letšoao la ho eketsa le bontša hore setšoantšo se holimo.

C. Thepa ea setšoantšo:

'Nete, ho ea holimo, e kholo ho feta ntho

[irp]

5. Ho hodisa setshwantsho, ho ya ka setshwantsho se ka tlase.

Tse tsejoang:

Sebaka sa ntho (do _o ) = 60 cm

Bolelele ba focal (f) = 20 cm

Ho batloa: Ho holisa setšoantšo (M)

Tharollo:

Sebaka sa setšoantšo:

1/f = 1/do ₊ 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

Ho holisa setšoantšo (M):

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

6. Haeba ntho e behiloe 6 cm ho tloha seiponeng se kobehileng, sebaka sa setšoantšo ke 12 cm joalo ka ha ho bontšitsoe setšoantšong se ka tlase. Sebaka sa setšoantšo ke sefe haeba ntho e tlosoa sebakeng sa pele 1 cm hole le seipone.

Tse tsejoang:

Sebaka sa ntho (do _o ) = 6 cm

Sebaka sa setšoantšo (d _i ) = 12 cm

Ho batloa: haeba sebaka sa ntho (do _o ) = 7 cm joale sebaka sa setšoantšo ke …

Tharollo:

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

f = 12/3 = 4 cm

Bolelele ba focus bo botle, ho bolelang hore ntlha e ka sehloohong ke ea 'nete kapa mahlaseli a feta ka har'a ntlha.

Sebaka sa setšoantšo:

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. Ngaka ea meno e sheba le ho hlahloba meno a mokuli a sebelisa seipone se nang le radius ea 8 cm. E le hore lesoba le bonahale hantle ke ngaka, sebaka se pakeng tsa meno a mokuli le seipone ke sefe?

A. ka tlase ho 4 cm ka pel'a seipone se kobehileng

B. ka tlase ho 4 cm ka pel'a seipone se kobehileng

C. ho feta 4 cm ka pel'a seipone se kobehileng

D. ho feta 4 cm ka pel'a seipone se kobehileng

Tse tsejoang:

Radius ea seipone (r) = 8 cm

Bolelele ba focal ba seipone (f) = r / 2 = 8 / 2 = 4 cm

Ho batloa: Sebaka se pakeng tsa meno a mokuli le seipone

Tharollo:

Seipone se sebediswang ke seipone se kobehileng kapa seipone se kobehileng? E le hore lesoba la leino le bonahale hantle ke ngaka, seipone se sebediswang se lokela ho kgona ho hodisa setshwantsho sa leino mme setshwantsho se lokela ho ema. Diipone tse kobehileng kamehla di hlahisa ditshwantsho tse kgutlelang morao mme boholo ba setshwantsho bo bonyenyane ho feta boholo ba ntho. Ka lehlakoreng le leng, seipone se kobehileng se ka hlahisa setshwantsho se otlolohileng haeba sebaka sa ntho (d) se le senyenyane ho feta bolelele ba focus (f). Haeba sebaka sa ntho se le seholo ho feta bolelele ba focus (f) jwale seipone se kobehileng se hlahisa setshwantsho se kobehileng.

Bolelele ba focus (f) ba seipone se kobehileng ke 4 cm, ka hona meno a mokuli a lokela ho ba ka tlase ho 4 cm ka pel'a seipone se kobehileng.

Karabo e nepahetseng ke A.

8. Seipone se kobehileng se na le radius e kobehileng ya 24 cm. Haeba ntho e behilwe 20 cm ka pela seipone, fumana hore na setshwantsho se na le thepa efe.

A. Ea 'nete, e otlolohileng le e atolositsoeng

B. Ea 'nete, e khelohileng le e atolositsoeng

C. E sebetsang ka ho toba, e eme hantle ebile e holisitsoe

D. Virtual, inverted le e nyane

Tse tsejoang:

Radius ea kobeho (r) = 24 cm

Bolelele ba fokase (f) = R/2 = 24/2 = +12 cm

Bolelele ba ntlha e bohareng ba seipone se kobehileng bo botle kapa ba nnete hobane lesedi le feta ka ntlha e bohareng ya seipone.

Sebaka sa ntho (d) = 20 cm

Ho batloa: Matlotlo a setšoantšo

Tharollo:

Setšoantšo ke sa 'nete kapa ke sa sebele? Bala sebaka (s') sa setšoantšo:

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

Sebaka sa setšoantšo se saennweng se bolela hore setšoantšo ke sa nnete hobane se fetisoa ke khanya.

Setšoantšo se holisitsoe? Se otlolohile kapa se khelohile? Qala ka ho bala keketseho ea setšoantšo (M):

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

M > 1 e bolela hore setšoantšo se holisitsoe, M e na le lets'oao le lebe le bolelang setšoantšo se khelohileng. Kahoo litšobotsi tsa setšoantšo ke tsa 'nete, tse khelohileng, tse holisitsoeng.

Karabo e nepahetseng ke B.

9. Seipone se chitja se hlahisa setšoantšo se boholo bo fetang ntho e skrineng ka makhetlo a 5, se bohōle ba limithara tse 5 ho tloha nthong eo. Seipone se…..

A. sekoti se nang le bolelele ba focus ba 25/24 m

B. convex ka bolelele ba focus ba 25/24 m

C. sekoti se nang le bolelele ba focal ba 24/25 m

D. convex e nang le bolelele ba focus ba 24/25 m

Tse tsejoang:

Ho holisa setšoantšo (M) = makhetlo a 5

Sebaka se pakeng tsa ntho le setšoantšo = limithara tse 5

Tharollo:

Boholo ba setšoantšo se hlahisoang ke seipone se kobehileng kamehla bo bonyenyane ho feta boholo ba ntho, ka hona, seipone ke seipone se kobehileng.

Sebaka sa ntho (d) = x

Sebaka sa setšoantšo (d') = x + 5

Kgodiso ya setshwantsho (M) = makgetlo a 5

Mokhoa oa ho holisa setšoantšo:

Foromo ea bolelele ba focal (f):

Karabo e nepahetseng ke A.

[ID ea sephutheloana sa wpdm='858′]

1. Mathata le litharollo tsa seipone se kobehileng
2. Mathata le litharollo tsa seipone se kobehileng
3. Mathata le litharollo tsa lense tse fapanyetsanang
4. Mathata le litharollo tsa lense tse kopanyang
5. Lisebelisoa tsa mahlo le litharollo tsa mahlo a batho
6. Mathata le litharollo tsa lilense tsa mahlo
7. Likhalase tsa mahlo tsa lisebelisoa tsa optical
8. Lisebelisoa tsa optical tse holisang mathata le litharollo tsa khalase
9. Maekroskoupo ea lisebelisoa tsa optical - mathata le litharollo
10. Mathata le litharollo tsa litheleskopu tsa lisebelisoa tsa optical

Bala haholoanyane

1. Metsi a 1 kg ho 100 ^o C a kopantsoe le metsi a 1 kg ho 10 ^o C tsamaisong e arohaneng. Mocheso o itseng wa metsi ke 4200 J/kg ^o C. Fumana mocheso wa ho qetela wa motswako!

Tse tsejoang:

Boima ba metsi a chesang (m ₁ ) = 1 kg

Mocheso oa metsi a chesang (T ₁ ) = 100 ^o C

Boima ba metsi a batang (m2 ₎ = 1 kg

Mocheso oa metsi a batang (T ₂ ) = 10 ^o C

Ho batloa: Thempereichara ea ho qetela (T)

Tharollo:

Ho lahleheloa ke mocheso = Mocheso o fumanoeng (tsamaiso e arohaneng)

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

Mocheso oa ho qetela ke 55 ^o C.

[irp]

2. Boloko ba loto ea 3 kg ho 80^o e beoa ka metsing a 10 kg. Mocheso o itseng oa loto ke 1400 J.kg^-1C^-1 'me mocheso o itseng oa metsi ke 4200 J.kg^-1C^-1Mocheso oa ho qetela oa tekano ea mocheso ke 20^oC. Fumana mocheso oa pele oa metsi!

Tse tsejoang:

Boima ( _m1 ) = 3 kg

Mocheso o itseng oa loto (c ₁ ) = 1400 J.kg ^-1 C ^-1

Mocheso oa loto (T ₁ ) = 80 ^o C

Boima ba metsi (m2 ₎ = 10 kg

Mocheso o itseng oa metsi (c ₂ ) = 4200 J.kg ^-1 C ^-1

Mocheso oa tekano ea mocheso (T) = 20 ^o C

Ho batloa: Thempereichara ea pele ea metsi (T ₂ )

Tharollo:

Mocheso o lahlehileng = Mocheso o fumanoeng

Q lead = Q metsi

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

Mocheso oa pele oa metsi ke 14 ^° C.

[irp]

3. Boloko ba koporo ho 100^oC e beoa ka har'a ligrama tse 128 tsa metsi 30 ^oC. Mocheso o itseng oa metsi ke 1 cal.g^-1oC^-1 'me mocheso o itseng oa koporo ke 0.1 cal.g^-1oC^-1. Haeba mocheso oa tekano ea mocheso o 36 ^oC, fumana boima ba koporo!

Tse tsejoang:

Thempereichara ea koporo (T ₁ ) = 100 ^o C

Mocheso o itseng oa koporo (c ₁ ) = 0.1 c al.g ^-1o C ^-1

Boima ba metsi (m2 ₎ = digrama tse 128

Mocheso oa metsi (T ₂ ) = 30 ^o C

Mocheso o itseng oa metsi (c ₂ ) = 1 kcal al.g ^-1o C ^-1

Mocheso oa tekano ea mocheso (T) = 36 ^o C

Ho batloa: Boima ba koporo (m ₁ )

Tharollo:

Mocheso o lahlehileng = Mocheso o fumanoeng

Koporo ea Q = Metsi a Q

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

Boima ba koporo ke digrama tse 120.

[irp]

4. Leqhoa la M-kg ho 0^oC e beoa ka har'a ligrama tse 340 tsa metsi ho 20^oC ka har'a vase. Haeba mocheso oa ho kopanya bakeng sa metsi = 80 cal g^-1, mocheso o itseng oa metsi ke 1 khalori g^{-1 o}C^-1. Leqhoa lohle lea qhibiliha le mocheso oa tekatekano ea mocheso is 5^oC, fumana boima ba leqhoa!

Tse tsejoang:

Boima ba metsi (m) = digrama tse 340

Thempereichara ea leqhoa ( _{leqhoa la} T ) = 0 ^o C

Thempereichara ea metsi ( _metsi a T ) = 20 ^o C

Mocheso oa tekano ea mocheso (T) = 5 ^o C

Mocheso oa ho kopanya metsi ( L ) = 80 cal g ^-1

Mocheso o itseng oa metsi (c _metsi ) = 1 cal g ^{-1 o} C ^-1

Ho batloa: Boima ba leqhoa (M)

Tharollo:

Mocheso o lahlehileng = Mocheso o fumanoeng

Q metsi = Q leqhoa

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 = digrama tse 60

[ID ea sephutheloana sa wpdm='714′]

1. Ho fetola sekala sa mocheso
2. Katoloso ya mola
3. Katoloso ea sebaka
4. Ho atolosoa ha molumo
5. Heat
6. E lekanang le mocheso ka mechine
7. Mocheso le bokgoni ba mocheso bo ikgethang
8. Mocheso o patehileng, mocheso oa ho kopana, mocheso oa mouoane
9. Paballo ea matla bakeng sa phetisetso ea mocheso

Bala haholoanyane

4 Mocheso o patehileng Mocheso oa ho kopanya Mocheso oa ho fetoha mouoane - Mathata le Litharollo

1. Bala tekanyo ea mocheso o ekelitsoeng ho gram e le 'ngoe ea khauta ho fetola karolo ho tloha ho tiileng ho ea ho mokelikeli. Mocheso oa ho kopanya khauta ke 64.5 x 10 ³ J/kg.

Tse tsejoang:

Boima (m) = gram e le 1 = 1 x 10 ^-3 kg

Mocheso oa ho kopanya (L _F ) = 64.5 x 10 ³ J/kg

Ho Batloa: Mocheso (Q)

Tharollo:

Q = m L _F

Q = (1 x 10 ^-3 kg)(64.5 x 10 ³ J/kg)

Q = 64.5 Joule

[irp]

2. Bala tekanyo ea mocheso o lokolloang ke gram e le 'ngoe ea mercury ho fetola mohato ho tloha ho mokelikeli ho ea ho o tiileng. Mocheso oa ho kopanya mercury ke 11.8 x 10 ³ J/kg.

Tse tsejoang:

Boima (m) = gram e le 1 = 1 x 10 ^-3 kg

Mocheso oa ho kopanya (L _F ) = 11.8 x 10 ³ J/kg

Ho Batloa: Mocheso (Q)

Tharollo:

Q = m L _F

Q = (1 x 10 ^-3 kg)(11.8 x 10 ³ J/kg)

Q = 11.8 Joule

3. Fumana hore na mocheso o monngoa ke metsi a 1 kg ho fetola moedi (mouoane). Mocheso oa mouoane bakeng sa metsi = 2256 x 10 ³ J/kg

Tse tsejoang:

Boima (m) = 1 kg

Mocheso oa mouoane (L _V ) = 2256 x 10 ³ J/kg

Ho Batloa: Mocheso (Q)

Tharollo:

Q = m L _V

Q = (1 kg)( 2256 x 10 ³ J/kg)

Q = 2256 x 10 ³ Joule

[irp]

4. Fumana hore na naetrojene e ntša mocheso o kae ho fetola moedi ho tloha mouoaneng ho ea ho mokelikeli. Mocheso oa mouoane bakeng sa naetrojene = 200 x 10 ³ J/kg

Tse tsejoang:

Boima (m) = gram e le 1 = 1 x 10 ^-3 kg

Mocheso oa mouoane (L _V ) = 200 x 10 ³ J/kg

Tse tsejoang: Mocheso (Q)

Tharollo:

Q = m L _V

Q = (1 x 10 ^-3 kg)( 200 x 10 ³ J/kg)

Q = 200 Joule

1. Ho fetola sekala sa mocheso
2. Katoloso ya mola
3. Katoloso ea sebaka
4. Ho atolosoa ha molumo
5. Heat
6. E lekanang le mocheso ka mechine
7. Mocheso le bokgoni ba mocheso bo ikgethang
8. Mocheso o patehileng, mocheso oa ho kopana, mocheso oa mouoane
9. Paballo ea matla bakeng sa phetisetso ea mocheso

Bala haholoanyane

1. ' Mele o boima ba 2 kg o monya dikhalori tse 100 mochesong ha mocheso oa oona o eketseha ho tloha ho 20 ^o C ho isa ho 70 ^o C. Mocheso o itseng oa 'mele ke ofe ?

Tse tsejoang:

Boima (m) = 2 kg = 2000 gr

Mocheso ( Q) = 100 kcal

Phetoho mochesong ( ΔT ) = 70 ^o C – 20 ^o C = 50 ^o C

Ho batloa: Mocheso o itseng (c)

Tharollo:

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 lik'hilojule gr ^{-1 o} C ^-1

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

Mocheso o itseng oa 'mele ke 10 ^-3 cal/gr ^o C

[irp]

2. Mocheso o itseng oa metsi ke 4180 J/kg Co2 ^. Ke bokae ba mocheso ba metsi a 2 kg…

Tse tsejoang:

Mocheso o itseng (c) = 4180 J/kg C ^o

Boima (m) = 2 kg

Ho batloa: Bokhoni ba mocheso (C)

Tharollo:

C = mc

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

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

C = 8360 J/C ^o

3. Mocheso o itseng oa aluminium ke 900 J/kg Co2 ^. Ke matla a bokae a mocheso a aluminium ea 2 gram…..

Tse tsejoang:

Mocheso o itseng oa aluminium (c) = 900 J/kg C ^o = 9 x 10 ² J/kg C ^o

Boima (m) = 2 dikgerama = 2/1000 kg = 2/10 ³ kg = 2 x 10 ^-3 kg

Ho batloa: Bokhoni ba mocheso (C)

Tharollo:

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

[ID ea sephutheloana sa wpdm='710′]

1. Ho fetola sekala sa mocheso
2. Katoloso ya mola
3. Katoloso ea sebaka
4. Ho atolosoa ha molumo
5. Heat
6. E lekanang le mocheso ka mechine
7. Mocheso le bokgoni ba mocheso bo ikgethang
8. Mocheso o patehileng, mocheso oa ho kopana, mocheso oa mouoane
9. Paballo ea matla bakeng sa phetisetso ea mocheso

Bala haholoanyane

1. 2 kcal (kilograma c khalori e ) = ….. c khalori e?

tharollo

1 kcal = 1000 kcal

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

2. 4 C khalori e = ….. c khalori e?

tharollo

1 Khalori e ( Motse-moholo C ) = 1 k cal = 1000 lik'hilojule e

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

3. 10 c khalori e = ….. Joule?

tharollo

Khalori e le 1 e = 4.186 Joule

10 c khalori e = 10 (4.186 Joule) = 41.86 Joule

[irp]

4. 5 kcal = ….. Joule?

tharollo

1 k cal = 1000 c alorie = 4186 Joules

5 kcal = 5 (4186 Joule) = 20930 Joule

5. Lijoule tse 2000 = ….. k cal?

tharollo

4186 Joule = 1 kcal

Li - joules tse 8372 = 8372 / 4186 = 2 kcal

Li - joules tse 2000 = 2000 / 4186 = 0.4777 kcal

[ID ea sephutheloana sa wpdm='706′]

1. Ho fetola sekala sa mocheso
2. Katoloso ya mola
3. Katoloso ea sebaka
4. Ho atolosoa ha molumo
5. Heat
6. E lekanang le mocheso ka mechine
7. Mocheso le bokgoni ba mocheso bo ikgethang
8. Mocheso o patehileng, mocheso oa ho kopana, mocheso oa mouoane
9. Paballo ea matla bakeng sa phetisetso ea mocheso

Bala haholoanyane

9 Boima ba Mocheso Mocheso o itseng Phetoho mochesong - Mathata le Litharollo

1. Moloto oa boima ba 2 kg o futhumatsoa ho tloha 50^oC ho 100^oC. The mocheso o itseng ea loto ke 130 J.kg^{-1 o}C^-1. Bokae mocheso e monngoa ke loto?

Tse tsejoang:

Boima (m) = 2 kg

Mocheso o itseng (c) = 1 3 0 J.kg ^-1 C ^-1

Phetoho mochesong ( Δ T) = 100 ^o C – 50 ^o C = 50 ^o C

Ho Batloa: Mocheso (Q)

Tharollo:

Q = mc Δ T

Q = mocheso , m = boima, c = mocheso o itseng , Δ T = phetoho mochesong

Mocheso o monngoang ke loto:

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

Q = (100)(1 3 0)

Q = 1 3,000 Joule

Q = 1.3 x ¹⁰⁴ Joule

[irp]

2. Mocheso o itseng oa koporo ke 390 J/k g ^o C, phetoho ea mocheso ke 40 ^o C. Haeba koporo e monya li-Joules tse 40 tsa mocheso, boima ba koporo ke bokae!

Tse tsejoang:

Mocheso o itseng oa koporo (c) = 390 J/k g ^o C

Phetoho mochesong ( ΔT ) = 40 ^o C

Mocheso ( Q) = 40 J

Ho batloa: Boima (m) ba koporo

Tharollo:

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 = digrama tse 26

3. Mocheso oa pele oa ligrama tse 20 tsa metsi ke 30 ^o C. Mocheso o itseng oa metsi ke 1 cal g ^{-1 o} C ^-1 . Haeba metsi a monya lik'hilojule tse 300 tsa mocheso, fumana mocheso oa ho qetela!

Tse tsejoang:

Boima (m) = 20 gr

Mocheso oa pele (T ₁ ) = 30 ^o C

Mocheso o itseng oa metsi (c) = 1 cal gr ^{-1 o} C ^-1

Mocheso (Q) = 300 cal

Ho batloa: Thempereichara ea ho qetela ea metsi

Tharollo:

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

Phetoho ea mocheso ke 45 ^o C - 30 ^o C = 15 ^o C.

 [irp]

4. Tphetoho ea mocheso ea metsi a leoatle is 1^oC ha metsi a monya mocheso oa li-Joule tse 3900. Mocheso o itseng oa metsi a leoatle ke 3.9 × 10³ J/kg°C, boima ba metsi a leoatle ke eng.

Tse tsejoang:

Phetoho mochesong ( ΔT ) = 1 ^o C

Mocheso (Q) = 3900 Joule

Mocheso o itseng oa metsi a leoatle (c) = 3.9 x 10 ³ J/ k g°C = 3900 J/Kg°C

Ho batloa: Boima (m)

Tharollo:

Q = mc Δ T

Q = mocheso , m = boima, c = mocheso o itseng , Δ T = phetoho mochesong

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

5. Koporo ea 2-kg e monya 39,000 J ea mocheso ho 30°C. Haeba mocheso o itseng oa koporo e le 390 J/kg °C, mocheso oa ho qetela oa koporo ke ofe…

Tse tsejoang:

Boima (m) = 2 kg

Mocheso oa pele (T ₁ ) = 30 ^o C

Mocheso (Q) = 39,000 Joule

Mocheso o itseng (c) oa koporo = 390 J/kg ^o C

Ho batloa : Thempereichara ea ho qetela (T ₂ )

Tharollo:

Q = mc ΔT

Q = mocheso , m = boima, c = mocheso o itseng , ΔT = phetoho mochesong

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. Metsi a boima ba 5 kg a futhumatsoa ho tloha ho 15°C ho isa ho 40°C. Mocheso o monngoa ke metsi ke eng. Mocheso o itseng oa metsi ke 4.2 × 10 ³ J/Kg° C.

Tse tsejoang:

Boima (m) = 5 kg

Mocheso oa pele (T ₁ ) = 15°C

Mocheso oa ho qetela (T ₂ ) = 40°C

Mocheso o itseng oa metsi (c) = 4.2 × 10 ³ J/kg° C

Ho Batloa: Mocheso (Q)

Tharollo:

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 Joule

7. Metsi a boima ba 2 kg a futhumatsoa ho tloha ho 24°C ho isa ho 90°C. Mocheso o monngoa ke metsi ke eng. Mocheso o itseng oa metsi ke 4.2 × 10 ³ J/Kg° C.

Tse tsejoang:

Boima (m) = 2 kg

Mocheso oa pele (T ₁ ) = 24°C

Mocheso oa ho qetela (T ₂ ) = 90°C

Mocheso o itseng oa metsi (c) = 4,200 Joules/kg°C

Ho Batloa :: Mocheso (Q)

Tharollo:

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 Joule)

Q = 554,400 Joule

[irp]

8. Metsi a digrama tse 5 a futhumatswa ho tloha ho 10°C ho isa ho 40°C. Mocheso o monngwang ke metsi ke eng. Mocheso o itseng wa metsi ke 1 × 10 ³ cal / g r ° C.

Tse tsejoang:

Boima (m) = digrama tse 5

Mocheso oa pele (T ₁ ) = 10 ^o C

Mocheso oa ho qetela (T ₂ ) = 40 ^o C

Mocheso o itseng oa metsi (c) = 1 c al/ gr°C

Ho Batloa : Mocheso

Tharollo:

Q = mc ΔT

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

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

Q = lik'hilojule tse 150

9. Metsi a 0.2 -kg a monya di-Joules tse 42,000 tsa mocheso ho 25 ^o C. Mocheso o itseng wa metsi ke 4200 J/kg ^o C, mocheso wa ho qetela wa metsi ke ofe.

Tse tsejoang:

Boima ba metsi (m) = 0.2 kg

Mocheso (Q) = 42,000 Joule

Mocheso o itseng oa metsi (c) = 4200 J/kg ^o C

Mocheso oa pele (T ₁ ) = 25 ^o C

Ho batloa: Mocheso oa ho qetela (T ₂ )

Tharollo:

Q = mc ΔT = mc (T ₂ – T ₁ )

Q = mocheso, m = boima, c = mocheso o itseng, ΔT = phetoho ea mocheso, T₁ = mocheso oa pele, T₂ = mocheso oa ho qetela

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. Ho fetola sekala sa mocheso
2. Katoloso ya mola
3. Katoloso ea sebaka
4. Ho atolosoa ha molumo
5. Heat
6. E lekanang le mocheso ka mechine
7. Mocheso le bokgoni ba mocheso bo ikgethang
8. Mocheso o patehileng, mocheso oa ho kopana, mocheso oa mouoane
9. Paballo ea matla bakeng sa phetisetso ea mocheso

Bala haholoanyane

Katoloso e otlolohileng e bonoa ke lintho tse tiileng feela; katoloso ea bophahamo e bonoa ke lintho tsohle, tse tiileng, tse metsi le tse nang le khase. Tekanyo ea katoloso ea bophahamo e tšoana le ekanyo ea katoloso e otlolohileng.

Tlhaloso: Vo _o = Bolumo ba pele, V = Bolumo ba ho qetela, ΔV = V – Vo _o = Phetoho ya bophahamo, To _o = Mocheso wa pele, T = Mocheso wa ho qetela, ΔT = T – To _o = Phetoho ya mocheso, β = coefficient ya katoloso ya bophahamo. Diyuniti tsa β = ( ^Co ) ^-1

[irp]

Tekanyo ea katoloso ea bophahamo ba modumo e kaholimo e sebetsa feela ha liphetoho tsa bophahamo ba modumo tsa lintho (tse tiileng, tse metsi le tse nang le khase) li le nyane ho feta bophahamo ba modumo ba pele ba ntho. Haeba phetoho ea bophahamo ba modumo ea ntho e le kholo ho feta bophahamo ba modumo ba pele ba ntho, equation ea katoloso ea bophahamo ba modumo ha e fane ka liphetho tse nepahetseng. Hangata, liphetoho tsa bophahamo ba modumo tse bonoang ke lintho tse tiileng ha li kholo haholo. Ka lehlakoreng le leng, coefficient ea katoloso ea bophahamo ba modumo ea mokelikeli le khase e kholo. Coefficient ea katoloso ea bophahamo ba modumo bakeng sa lintho tse nang le khase le eona e bonolo ho e fetola haeba mocheso o fetoha. Ka hona foromo e kaholimo e sebelisoa feela bakeng sa katoloso ea lintho tse tiileng.

[irp]

1. Ho 30 ^o C bophahamo ba modumo wa aluminium circle ke 30 cm ^3. Koefficient ya katoloso e otlolohileng ke 24 x 10 ^{-6 o} C ^-1 . Haeba modumo wa ho qetela ke 30.5 cm ³ , mocheso wa ho qetela wa aluminium circle ke ofe?

Tse tsejoang:

Koefficient ea katoloso e otlolohileng ( α ) = 24 x 10 ^{-6 o} C ^-1

Koefficient ea katoloso ea bophahamo ba modumo ( β ) = 3 α = 3 x 24 x 10 ^{-6 o} C ^-1 = 72 x 10 ^{-6 o} C ^-1

Mocheso oa pele (T ₁ ) = 30 ^o C

Bophahamo ba pele (V ₁ ) = 30 cm ³

Bolumo ba ho qetela (V ₂ ) = 30.5 cm ³

Phetoho ea bophahamo ba modumo ( Δ V) = 30.5 cm ³ – 30 cm ³ = 0.5 cm ³

Ho batloa: Thempereichara ea ho qetela (T ₂ )

Tharollo:

Δ V = β (V ₁ )( ΔT )

Δ V = β (V ₁ )(T ₂ – T ₁ )

0.5 cm,³ = (72: x 10^{-6 o}C^-1)(30 cm)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

[irp]

2. Palo e lekanang ea katoloso e otlolohileng ea polaka ea tšepe ke 9 x 10 ^{-6 o} C ^-1 . Bophara ba ka hare ba polaka ea tšepe ho 20 ^o C ke 2.2 cm. Haeba bophara ba ho qetela e le 2.8 cm, mocheso oa ho qetela ke ofe!

Tse tsejoang:

Koefficient ea katoloso e otlolohileng ( α ) = 9 x 10 ^{-6 o} C ^-1

Koefficient ea katoloso ea bophahamo ba modumo ( β) = 3 α = 3 x 9 x 10 ^{-6 o} C ^-1 = 27 x 10 ^{-6 o} C ^-1

Mocheso oa pele (T ₁ ) = 20 ^o C

Bophara ba pele (D ₁ ) = 2.2 cm

Bophara ba ho qetela (D ₂ ) = 2.8 cm

Radius ea pele (r ₁ ) = D ₁ / 2 = 2.2 cm ³ / 2 = 1.1 cm ³

Radius ea ho qetela (r ₂ ) = D ₂ / 2 = 2.8 cm ³ / 2 = 1.4 cm ³

Bolumo ba pele (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

Bolumo ea ho qetela (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

Phetoho ea bophahamo ba modumo ( Δ V) = 11.48 cm ³ – 5.57 cm ³ = 5.91 cm ³

Ho batloa: Thempereichara ea _{ho qetela} ( T2 )

Tharollo:

Δ V = β (V ₁ )( ΔT )

5.91 cm,³ = (27: x 10^{-6 o}C^-1)(5.57 cm,³)(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. 2000-cm³ setshelo sa aluminium, e tletse metsi ho 0^oC. Ebe e futhumatsoa ho fihlela ho 90^oC. Haeba coefficient ea katoloso e otlolohileng bakeng sa aluminium e le 24 x 10^-6 (^oC)^-1 'me coefficient ea katoloso ea bophahamo ba metsi ke 6.3 x 10^-4 (^oC)^-1, fumana bongata ba metsi a tšolohileng.

Tse tsejoang:

Bophahamo ba pele ba setshelo sa aluminium le metsi (Vo _o ) = 2000 cm ³ = 2 x 10 ³ cm ³

Mocheso oa pele oa setshelo sa aluminium le metsi (T ₁ ) = 0 ^o C

Mocheso oa ho qetela oa setshelo sa aluminium le metsi (T2 ₎ = 90 ^o C

Koefficient ea katoloso e otlolohileng bakeng sa aluminium (α) = 24 x 10 ^-6 ( ^o C ) ^-1

Koefficient ea katoloso ea bophahamo ba modumo bakeng sa aluminium (γ) = 3α = 3 (24 x 10 ^-6 ( ^o C ) ^-1 ) = 72 x 10 ^{-6 o} C ^-1

Koefficient ea katoloso ea bophahamo ba modumo bakeng sa metsi (γ) = 6.3 x 10 ^-4 ( ^o C ) ^-1

Ho batloa: Bongata ba metsi a tšolohileng

Tharollo:

Tekanyo ea katoloso ea molumo:

V = Vo _o + γ Vo _o ΔT

V – Vo _o = γ Vo _o ΔT

ΔV = γ Vo _o ΔT

V = bophahamo ba ho qetela, Vo _o = bophahamo ba pele, ΔV = phetoho bophahamong, γ = coefficient ea katoloso ea bophahamo, ΔT = phetoho mochesong

Bala phetoho ea bophahamo ba setshelo sa aluminium:

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

Bala phetoho ea bophahamo ba metsi:

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

Phetoho ea bophahamo ba metsi e kholo ho feta setshelo sa aluminium hoo metsi a mang a tšolohang.

Bala bophahamo ba metsi a tšolohileng:

113.4 cm ³ – 12.960 cm ³ = 100.44 cm ³

[ID ea sephutheloana sa wpdm='702′]

1. Ho fetola sekala sa mocheso
2. Katoloso ya mola
3. Katoloso ea sebaka
4. Ho atolosoa ha molumo
5. Heat
6. E lekanang le mocheso ka mechine
7. Mocheso le bokgoni ba mocheso bo ikgethang
8. Mocheso o patehileng, mocheso oa ho kopana, mocheso oa mouoane
9. Paballo ea matla bakeng sa phetisetso ea mocheso

Bala haholoanyane

1. Ho 20 ^o C, bolelele ba lakane ea tšepe ke 50 cm 'me bophara ke 30 cm. Haeba coefficient ea katoloso e otlolohileng bakeng sa tšepe e le 10 ^{-5 o} C ^-1 , fumana phetoho sebakeng le sebaka sa ho qetela ho 60 ^o C.

Tse tsejoang:

Mocheso oa pele (T ₁ ) = 20 ^o C

Mocheso oa ho qetela (T2 ₎ = 60 ^o C

Phetoho mochesong ( ΔT ) = 60 ^o C – 20 ^o C = 40 ^o C

Sebaka sa pele (A ₁ ) = bolelele x bophara = 50 cm x 30 cm = 1500 cm ²

Koefficient ea katoloso e otlolohileng bakeng sa tšepe ( α) = 10 ^{-5 o} C ^-1

Koefficient ea katoloso ea sebaka bakeng sa tšepe ( β) = 2α = 2 x 10 ^{-5 o} C ^-1

Ho batloa: Phetoho sebakeng ( ΔA )

Tharollo:

Phetoho sebakeng ( 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

Sebaka sa ho qetela ( A2 ₎ :

A ₂ = A ₁ + ΔA

A ₂ = 1500 cm ² + 1. 2 cm ²

A ₂ = 1501. 2 cm ²

[irp]

2. Ho 30 ^o C, sebaka sa lakane ea aluminium ke 40 cm ² mme coefficient ea katoloso e otlolohileng ke 24 x 10 ^-6 / ^o C. Fumana mocheso oa ho qetela haeba sebaka sa ho qetela e le 40.2 cm ².

Tse tsejoang:

Mocheso oa pele (T ₁ ) = 30 ^o C

Koefficient ea katoloso e otlolohileng ( α) = 24 x 10 ^{-6 o} C ^-1

Koefficient ea katoloso ea sebaka ( β) = 2a = 2 x 24 x 10 ^{-6 o} C ^-1 = 48 x 10 ^{-6 o} C ^-1

Sebaka sa pele (A ₁ ) = 40 cm ²

Sebaka sa ho qetela (A ₂ ) = 40.2 cm ²

Phetoho sebakeng ( ΔA) = 40.2 cm ² – 40 cm ² = 0.2 cm ²

Ho batloa: Fumana mocheso oa ho qetela (T ₂ )

Tharollo:

Foromo ea phetoho sebakeng ( ΔA) :

ΔA = β A ₁ Δ T

Mocheso oa ho qetela (T2 ₎ :

ΔA = β A ₁ (T ₂ – T ₁ )

0.2 cm,² = (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

Mocheso oa ho qetela = 130 ^o C

[irp]

3. Radius ea lesale ho 20 ^o C ke 20 cm. Haeba radius ea ho qetela ho 100 ^o C e le 20.5 cm, fumana coefficient ea katoloso ea sebaka le coefficient ea katoloso e otlolohileng…

Tse tsejoang:

Mocheso oa pele (T ₁ ) = 30 ^o C

Mocheso oa ho qetela (T2 ₎ = 100 ^o C

Phetoho mochesong ( ΔT ) = 100 ^o C – 30 ^o C = 70 ^o C

Radius ea pele (r ₁ ) = 20 cm

Radius ea ho qetela (r ₂ ) = 20.5 cm

Ho batloa: Koefficient ea katoloso ea sebaka ( β )

Tharollo:

Sebaka sa pele (A ₁ ) = π r ₁ ² = (3.14)(20 cm) ² = (3.14)(400 cm ² ) = 1256 cm ²

Sebaka sa ho qetela (A ₂ ) = π r ₂ ² = (3.14)(20.5 cm) ² = (3.14)(420.25 cm ² ) = 1319.585 cm ²

Phetoho sebakeng ( ΔA) = 1319.585 cm ² – 1256 cm ² = 63.585 cm ²

Foromo ea phetoho sebakeng ( ΔA) :

ΔA = β A ₁ ΔT

Palo ea katoloso ea sebaka:

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

Koefficient ea katoloso e otlolohileng ( 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

[ID ea sephutheloana sa wpdm='698′]

1. Ho fetola sekala sa mocheso
2. Katoloso ya mola
3. Katoloso ea sebaka
4. Ho atolosoa ha molumo
5. Heat
6. E lekanang le mocheso ka mechine
7. Mocheso le bokgoni ba mocheso bo ikgethang
8. Mocheso o patehileng, mocheso oa ho kopana, mocheso oa mouoane
9. Paballo ea matla bakeng sa phetisetso ea mocheso

Bala haholoanyane