Ngā Raru Whakaoti i roto i te Ahupūngao Taketake

1. Ko te roa arotahi o te whakaata pūkohu he 10 cm, ā, ko te tawhiti o te mea he 20 cm. Whakatauhia (a) te tawhiti o te ahua (b) te whakanui o te ahua

Mōhiotia:

Ko te roa o te arotahi (f) = -10 cm

Ko te tohu tango e tohu ana he mariko te pūwāhi arotahi o te whakaata pūkohu.

Ko te tawhiti o te mea ( d _o ) = 20 cm

Rongoā:

Te hanganga o te ahua mā te whakaata kōpiko:

Te tawhiti o te ahua (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

Ko te tohu tango e tohu ana he mariko te ahua.

Te whakanui i te ahua:

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

m = 0,3 te wā iti iho i te mea.

Ko te tohu tāpiri e tohu ana kei runga te ahua.

[irp]

2. Ka whakatakotoria tētahi mea 10-cm te teitei ki mua i tētahi whakaata pūkohu me te roa arotahi o te 20 cm. Tātaihia te teitei o te ahua mēnā ko te tawhiti o te mea ko (a) 10 cm (b) 30 cm (c) 40 cm (d) 50 cm

Mōhiotia:

Ko te roa arotahi o te whakaata pūkohu (f) = -20 cm

Ko te tohu tango e tohu ana he mariko te pūwāhi arotahi

Ko te pūtoro o te piko ( r ) = 2 f = 2(20) = 40 cm

Te teitei o te mea (h) = 10 cm

Rongoā:

a) ko te roa arotahi (f) = -20 cm me te tawhiti o te mea (d _o ) = 10 cm

Te tawhiti o te ahua (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

Ko te tohu tango e tohu ana he mariko te ahua, kei muri rānei i te whakaata te ahua.

Te whakanui i te ahua ( m ):

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

Ko te tohu tāpiri e tohu ana kei te poutū te ahua.

He 0.67 te iti iho o te ahua i te mea.

Te teitei o te ahua (h _i ):

m = h _i / h _o

teitei ₌ teitei = (10 henimita )(0.67) = 6.7 _henimita

b) te roa arotahi (f) = -20 cm me te tawhiti o te mea ( d _o ) = 30 cm

Te tawhiti o te ahua ( 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

Ko te tohu tango e tohu ana he mariko te ahua, kei muri rānei i te whakaata te ahua.

Te whakanui i te ahua ( m ):

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

Ko te tohu tāpiri e tohu ana kei te poutū te ahua.

He 0,4 ngā wā te iti ake o te ahua i te mea.

Te teitei o te ahua (h _i ):

m = h _i / h _o

teitei ₌ teitei = (10 henimita )(0.4) = 4 _henimita

c) Ko te roa arotahi (f) = -20 cm me te tawhiti o te mea ( d _o ) = 40 cm

Te tawhiti o te ahua ( 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

Ko te tohu tango e tohu ana he mariko te ahua, kei muri rānei i te whakaata pūkohu te ahua.

Te whakanui i te ahua ( m ):

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

Ko te tohu tāpiri e tohu ana kei te poutū te ahua.

He 0.3 te iti iho o te ahua i te mea.

Te teitei o te ahua ( h _{i )} :

m = h _i / h _o

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

d) Ko te roa arotahi (f) = -20 cm me te tawhiti o te mea ( d _o ) = 50 cm

Te tawhiti o te ahua ( 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

Ko te tohu tango e tohu ana he mariko te ahua, kei muri rānei i te whakaata pūkohu te ahua.

Te whakanui i te ahua ( m ):

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

Ko te tohu tāpiri e tohu ana kei te poutū te ahua.

He 0.3 te iti iho o te ahua i te mea.

Te teitei o te ahua (h _i ) :

m = h _i / h _o

teitei ₌ teitei = (10 henimita)(0.3) = 3 _henimita

[irp]

3. Kei runga i te mea kei te 20 cm te tawhiti i mua i te whakaata pūkohu . Mena he 1/5 te teitei o te ahua i te teitei o te mea, tautuhia ( a) te roa o te ahua b) te roa arotahi c) ngā āhuatanga o te ahua

Mōhiotia:

Ko te tawhiti o te mea ( d _o ) = 20 cm

Te teitei o te ahua (h _i ) = 1/5 h = 0.2 h

Ko te teitei o te mea (h) = h

Rongoā:

a) te tawhiti o te ahua ( d _i )

Te tātai mō te whakanui i te ahua :

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

Ko te tohu tāpiri e tohu ana kei te poutū te ahua.

He 0.2 te iti iho o te ahua i te mea.

Te tawhiti o te ahua ( d _i ):

– d _i = md _o

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

Ko te tohu tango e tohu ana he mariko te ahua, kei muri rānei i te whakaata pūkohu te ahua.

b) Te roa o te arotahi ( f)

Te roa o te arotahi (f):

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

f = -20/4 = -5 henemita

Ko te tohu tango e tohu ana he mariko te pūwāhi arotahi.

c) Ngā āhuatanga o te ahua:

– Tū tika

– Iti ake

– mariko

4. Ka whakaatahia te mārama ki te whakaata pūkohu e whakarara ana ki te tuaka….

A. ki te pūwāhi arotahi o te whakaata

B. mai i te pūwāhi arotahi o te whakaata

C. mā waenganui o te piko o te whakaata

D. poutū ki te papa whakaata

otinga

Kei te pikitia i raro nei te āhua o te raruraru.

Ko te whakautu tika ko B.

5. Ka kite te kaieke pahikara i te ahua o te motopaika i muri i a ia, 1/6 o tōna rahi taketake ina 30 mita te tawhiti i waenganui i te kaieke me te motopaika. Tātaihia te pūtoro piko o te whakaata tirohanga whakamuri…

A. 7.14 mita

B. 8.57 mita

C. 12.00 mita

D. 24.00 mita

Mōhiotia:

Te whakanui i te ahua (M) = 1/6 ngā wā

Te tawhiti o te mea (d) = 30 mita

E hiahiatia ana: Te pūtoro o te piko o te whakaata tirohanga whakamuri (R)

Rongoā:

Tātaihia te tawhiti o te ahua (d')

Nā te mea kua mōhiotia te whakanui o te ahua (M) me te tawhiti o te mea (s), ka taea te mōhio ki te tawhiti o te ahua mā te whakamahi i te tātai whakanui o te ahua:

Ko te tohu kino he tohu mariko te ahua. E 5 mita te tawhiti o te ahua i muri i te whakaata pūkohu.

Tātaihia te roa arotahi (f)

Nā te mea ko te tawhiti o te mea (d) me te tawhiti o te ahua (d'), ka taea te tatau i te roa o te arotahi mā te whakamahi i te tātai o te whakaata:

Te pūtoro o te piko (R)

Ko te pūtoro o te piko o te whakaata pūkohu e rua te roa o te arotahi o te whakaata pūkohu.
R = 2 f = 2 (6 mita) = 12 mita
Ko te radius o te piko o te whakaata pūkohu he 12 mita.
Ko te whakautu tika ko C.

6. I whiriwhiria te whakaata pūkohu hei whakaata tirohanga whakamuri mō te motopaika nā te mea ko ngā āhuatanga o te ahua i puta mai i te whakaata ko…

A. tūturu, poutū, whakaititia

B. tūturu, poutū, whakanuia

C. mariko, poutū, whakaititia

D. mariko, poutū, whakanuia

Rongoā:

I runga i ngā whakaahua e rua i runga ake nei, ka taea te whakatau ko ngā āhuatanga o te ahua he mariko, he poutū, he whakaiti.

Ko te whakautu tika ko C.

7. Kei mua i te whakaata pūkohu te mea he 12 cm te tawhiti, ā, he 6 cm te whānui o tōna whānui. Ko ngā āhuatanga o te ahua ko…

A. tūturu, hurihia i te tawhiti o te 12 cm

B. tūturu, poutū i te tawhiti o te 4 cm

C. mariko, poutū i te tawhiti o te 2.4 cm

D. mariko, hurihia i te tawhiti o te 6 cm

Mōhiotia:

Te tawhiti o te mea (d) = 12 cm

Ko te whānui o te whakaata pūkohu (r) = 6 cm.

Ko te roa arotahi o te whakaata pūkohu (f) = 6 cm / 2 = -3 cm

Ko te roa arotahi o te whakaata pūkohu he tohu kino nā te mea he mariko. He mariko nā te mea kāore te mārama e whiti atu.

E hiahiatia ana: Ngā āhuatanga o te ahua

Rongoā:

Te tawhiti o te ahua (d'):

1/rā' = 1/w – 1/rā = -1/3 – 1/12 = -4/12 – 1/12 = -5/12

d' = -12/5 = -2.4 henimita

Ko te tawhiti o te ahua kua tohua ki te kino e tohu ana he mariko te ahua.

Te whakanui i te ahua (m):

m = -d' / d = -(-2.4) / 12 = 2.4 / 12 = 0.2 ngā wā

Ko te whakanui o te ahua he tohu pai ko te tikanga he poutū te ahua, ā, ko te whakanui o te ahua he 0.2 ko te tikanga he iti ake te rahi o te ahua i te rahi o te mea (kua whakaitihia).

Ko te whakautu tika ko C.

[wpdm_package id='860′]

1. Ngā raruraru me ngā otinga o te whakaata kōpiko
2. Ngā raruraru me ngā otinga o te whakaata pūkohu
3. Ngā raruraru me ngā otinga o te arotahi wehewehe
4. Ngā raruraru me ngā otinga o ngā karāhe arotahi
5. Ngā taputapu whatu Ngā raruraru kanohi tangata me ngā otinga
6. Ngā raruraru me ngā otinga mō ngā karaihe whakapā o ngā taputapu whatu
7. Ngā mōhiti taputapu whatu
8. Ngā raruraru me ngā otinga mō ngā taputapu whatu mō te karāhe whakanui
9. Te karu hikohiko taputapu whatu – ngā raruraru me ngā otinga
10. Ngā raruraru me ngā otinga o ngā karu tirohanga whatu

Pānuitia atu

1. Ka whakatakotoria tētahi mea ki te 10 cm mai i tētahi whakaata kōpiko . Ko te roa arotahi he 5 cm. Whakatauhia (a) Te tawhiti o te ahua (b) te whakanui o te ahua

Mōhiotia:

Ko te roa o te arotahi (f) = 5 cm

Ko te tawhiti o te mea ( d _o ) = 10 cm

Otinga :

Te hanganga o te ahua mā te whakaata kōpiko:

Te tawhiti o te ahua:

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

d _i = 10/1 = 10 cm

Ko te tawhiti o te ahua he 10 henemita.

Te whakanui:

m = – d _i / d _o = -10/10 = -1

Ko te tikanga o te 1 he rite tonu te ahua ki te mea.

Ko te tohu tango e tohu ana kua hurihia te ahua. Ki te mea he pai te tohu, he poutū te ahua.

[irp]

2. Ka whakatakotoria tētahi mea 5-cm te teitei ki mua i tētahi whakaata kōpiko, ā, ko te radius o te piko he 20 cm. Tātaihia te teitei o te ahua mēnā ko te tawhiti o te mea he 5 cm, 15 cm, 20 cm, 30 cm.

Mōhiotia:

Ko te pūtoro o te piko ( r ) = 20 cm

Te roa arotahi (f) = R/2 = 20/2 = 10 cm

Ko te teitei o te mea (h _o ) = 5 cm

Rongoā:

a) ko te roa arotahi (f) = 10 cm me te tawhiti o te mea ( d _o ) = 5 cm

Te hanganga o te ahua mā te whakaata kōpiko:

Te tawhiti o te ahua ( 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

Ko te tohu tango e tohu ana he mariko te ahua , kei muri rānei i te whakaata te ahua.

Te whakanui i te ahua ( m ):

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

Ko te tohu tāpiri e tohu ana kei te poutū te ahua.

Te teitei o te ahua ( h _i ):

m = h _i / h _o

teitei ₌ teitei = (5 henimita)(2) = 10 _henimita

Tekau henemita te teitei o te ahua.

b) Ko te roa arotahi (f) = 10 cm me te tawhiti o te mea ( d _o ) = 15 cm

Te hanganga o te ahua mā te whakaata kōpiko:

Te tawhiti o te ahua ( 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

Ko te tohu tāpiri e tohu ana he tūturu te ahua, kei te 30 henemita rānei te ahua i mua i te whakaata, i te taha kotahi me te mea.

Te whakanui i te ahua ( m ):

m = – d _i / d _o = -30/15 = -2

Ko te tohu tango e tohu ana kua hurihia te ahua.

E rua ngā wā e nui ake ai te ahua i te mea.

Te teitei o te ahua (h _i ):

m = h _i / h _o

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

Tekau henemita te teitei o te ahua.

c) Ko te roa arotahi (f) = 10 cm me te tawhiti o te mea ( d _o ) = 20 cm

Te hanganga o te ahua mā te whakaata kōpiko:

Te tawhiti o te ahua (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

Ko te tohu pai e tohu ana he tūturu te ahua, kei te 20 henemita rānei te ahua i mua i te whakaata, i te taha kotahi me te mea.

Te whakanui i te ahua ( m ):

m = – d _i / d _o = -20/20 = -1

Ko te tohu kino e tohu ana kua hurihia te ahua.

Te teitei o te ahua ( hi ):

m = h _i / h _o

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

d) Ko te roa arotahi (f) = 10 cm me te tawhiti o te mea ( d _o ) = 30 cm

Te tawhiti o te ahua ( 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

Ko te tohu tāpiri e tohu ana he tūturu te ahua, kei te 15 henemita rānei te ahua i mua i te whakaata, i te taha kotahi me te mea.

Te whakanui i te ahua ( m) :

m = – d _i / d _o = -15/30 = -0.5

Ko te tohu tango e tohu ana kua hurihia te ahua.

He 0.5 te iti iho o te ahua i te mea.

Te teitei o te ahua (h _i ):

m = h _i / h _o

teitei ₌ teitei = (5 henimita)(0.5) = 2.5 _henimita

[irp]

3. E whā ngā wā te rahi ake o te ahua i hangaia e te whakaata piko i te mea. Mena he 20 cm te pūtoro o te piko, tātaihia te tawhiti o te mea i mua i te whakaata!

Mōhiotia:

Te whakanui i te ahua ( m ) = 4

Ko te pūtoro o te piko ( r ) = 20 cm

Te roa arotahi (f) = r /2 = 20/2 = 10 cm

E hiahiatia ana : Te tawhiti o te mea ( d _o )

Rongoā:

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

16 d _o = 200

d _o = 12.5 cm

Ko te tawhiti o te mea = 12.5 cm.

[irp]

4. Kei te 10 cm te tawhiti o tētahi mea, 1 cm te teitei, mai i tētahi whakaata kōpiko, ā, ko te roa arotahi, f = 15 cm. Whakatauhia:

A. Te tawhiti o te ahua?

B. Te teitei o te ahua?

C. Ngā āhuatanga o te ahua i hangaia e te whakaata kōpiko?

Mōhiotia:

Te teitei o te mea (h) = 1 cm

Ko te tawhiti o te mea (d _o ) = 10 cm

Ko te roa arotahi o te whakaata kōpiko (f) = 15 cm

Rongoā:

A. Te tawhiti o te ahua (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

Ko te tohu kino e tohu ana he mariko te ahua, kei muri rānei i te whakaata te ahua.

B. Te teitei o te ahua (h _i )

Te whakanui o te ahua (M):

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

M = -(-30)/10 = 30/10 = 3 ngā wā

Te teitei o te ahua (h _i ):

M = h _i / h _o

3 = teitei _/ 1 henimita

h _i = 3 (1 henimita)

h _i = 3 cm

E 3 henemita te teitei o te ahua. Ko te tohu tāpiri e tohu ana kei runga te ahua.

C. Ngā āhuatanga o te ahua:

Mariko, whakarunga, nui atu i te mea

[irp]

5. Te whakanui i te ahua, e ai ki te ahua i raro nei.

Mōhiotia:

Ko te tawhiti o te mea (d _o ) = 60 cm

Ko te roa o te arotahi (f) = 20 cm

E hiahiatia ana: Te whakanui i te ahua (M)

Rongoā:

Te tawhiti o te ahua:

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 henimita = 30 henimita

Te whakanui o te ahua (M):

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

6. Mena ka whakatakotoria te mea ki te 6 cm mai i te whakaata kōpiko, ko te tawhiti o te ahua he 12 cm e whakaaturia ana i te pikitia i raro nei. He aha te tawhiti o te ahua mena ka nekehia te mea mai i te tūranga taketake ki te 1 cm te tawhiti atu i te whakaata?

Mōhiotia:

Ko te tawhiti o te mea (d _o ) = 6 cm

Ko te tawhiti o te ahua (d _i ) = 12 cm

E hiahiatia ana: mēnā ko te tawhiti o te mea (d _o ) = 7 cm, ko te tawhiti o te ahua ko …

Rongoā:

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

f = 12/3 = 4 henemita

He pai te roa o te arotahi, arā, he tūturu te pūwāhi arotahi, he tika rānei ngā hihi e haere ana mā roto i te pūwāhi.

Te tawhiti o te ahua:

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. Ka tirotirohia, ka tirohia hoki e te tākuta niho ngā niho o te tūroro mā te whakamahi i tētahi whakaata he 8 henemita te whānui. Kia mārama ai te kite a te tākuta i te kōhao, he aha te tawhiti i waenganui i ngā niho o te tūroro me te whakaata?

A. iti iho i te 4 cm i mua i te whakaata kōpiko

B. iti iho i te 4 cm i mua i te whakaata pūkohu

C. neke atu i te 4 cm i mua i te whakaata kōpiko

D. neke atu i te 4 cm i mua i te whakaata pūkohu

Mōhiotia:

Te whānui o te whakaata (r) = 8 cm

Ko te roa o te arotahi o te whakaata (f) = r / 2 = 8 / 2 = 4 cm

E hiahiatia ana: Te tawhiti i waenganui i ngā niho o te tūroro me te whakaata

Rongoā:

He whakaata piko, he whakaata pūkohu rānei te whakaata e whakamahia ana? Kia mārama ai te kitea o te kōhao niho e te tākuta, me kaha te whakaata e whakamahia ana ki te whakanui i te ahua o te niho, ā, me poutū te ahua. Ka puta tonu i ngā whakaata pūkohu ngā ahua hurihuri, ā, he iti ake te rahi o te ahua i te rahi o te mea. I tua atu, ka taea e te whakaata piko te whakaputa i tētahi ahua poutū mēnā he iti ake te tawhiti o te mea (d) i te roa arotahi (f). Mēnā he nui ake te tawhiti o te mea i te roa arotahi (f), ka puta he ahua hurihuri i te whakaata piko.

Ko te roa arotahi (f) o te whakaata kōpiko he 4 cm, nō reira me iti iho i te 4 cm te tawhiti o ngā niho o te tūroro ki mua i te whakaata kōpiko.

Ko te whakautu tika ko A.

8. Ko te radius piko o te whakaata kōpiko he 24 cm. Mena ka whakatakotoria te mea ki mua i te whakaata he 20 cm te tawhiti, whakatauhia ngā āhuatanga o te ahua.

A. Tūturu, poutū, me te whakanui

B. Tūturu, hurihia, me te whakanuia

C. Mariko, poutū, me te whakanui

D. Mariko, hurihia, me te iti ake

Mōhiotia:

Te whānui o te piko (r) = 24 cm

Roanga arotahi (f) = R/2 = 24/2 = +12 cm

He pai, he tūturu rānei te roa arotahi o te whakaata kōpiko nā te mea ka haere te mārama mā te pūwāhi arotahi o te whakaata.

Te tawhiti o te mea (d) = 20 cm

E hiahiatia ana: Ngā āhuatanga o te ahua

Rongoā:

He mariko, he tūturu rānei te ahua? Tātaihia te tawhiti (s') o te ahua:

1/rā + 1/rā' = 1/w

1/rā' = 1/whā – 1/rā

1/rā' = 1/12 – 1/20

1/rā' = 5/60 – 3/60

1/rā' = 2/60

d' = 60/2

d' = 30 henemita

Ko te tawhiti o te ahua kua tohua he pai te tikanga he tūturu te ahua nā te mea ka whiti te mārama i a ia.

Whakaahua kua whakanuia? Tū tika, huripokitia rānei? Tātaihia te whakanui o te whakaahua (M):

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

M > 1 te tikanga kua whakanuia te ahua, ko te tohu kino o M te tikanga he ahua huripokitia. Nō reira, ko ngā āhuatanga o te ahua he tūturu, he huripokitia, he whakanuia.

Ko te whakautu tika ko B.

9. Ka whakaputahia e te whakaata porowhita he ahua e 5 ngā wā te rahi atu i te mea kei runga i te mata, e 5 mita te tawhiti atu i te mea. Ko te whakaata he…..

A. piko me te roa arotahi o te 25/24 m

B. pūkohu me te roa arotahi o te 25/24 m

C. piko me te roa arotahi o te 24/25 m

D. pūkohu me te roa arotahi o te 24/25 m

Mōhiotia:

Te whakanui i te ahua (M) = 5 ngā wā

Ko te tawhiti i waenganui i te mea me te ahua = 5 mita

Rongoā:

He iti iho te rahi o te ahua i hangaia e te whakaata pūkohu i te rahi o te mea, nō reira, he whakaata pūkohu te whakaata.

Te tawhiti o te mea (d) = x

Te tawhiti o te ahua (d') = x + 5

Whakanuia o te ahua (M) = 5 ngā wā

Ko te tātai mō te whakanui i te ahua:

Ko te tātai o te roa arotahi (f):

Ko te whakautu tika ko A.

[wpdm_package id='858′]

1. Ngā raruraru me ngā otinga o te whakaata kōpiko
2. Ngā raruraru me ngā otinga o te whakaata pūkohu
3. Ngā raruraru me ngā otinga o te arotahi wehewehe
4. Ngā raruraru me ngā otinga o ngā karāhe arotahi
5. Ngā taputapu whatu Ngā raruraru kanohi tangata me ngā otinga
6. Ngā raruraru me ngā otinga mō ngā karaihe whakapā o ngā taputapu whatu
7. Ngā mōhiti taputapu whatu
8. Ngā raruraru me ngā otinga mō ngā taputapu whatu mō te karāhe whakanui
9. Te karu hikohiko taputapu whatu – ngā raruraru me ngā otinga
10. Ngā raruraru me ngā otinga o ngā karu tirohanga whatu

Pānuitia atu

1. 1-kg wai i te 100 ^° C i konatunatua ki te 1-kg wai i te 10 ^° C i roto i tētahi pūnaha motuhake. Ko te wera motuhake o te wai ko 4200 J/kg ^oC . Tātaihia te pāmahana whakamutunga o te ranunga!

Mōhiotia:

Taumaha o te wai wera (m1 ₎ = 1 kg

Te pāmahana o te wai wera (T ₁ ) = 100 ^° C

Taumaha o te wai matao (m2 ₎ = 1 kg

Te pāmahana o te wai matao (T ₂ ) = 10 ^o C

E hiahiatia ana: Te pāmahana whakamutunga (T)

Rongoā:

Te wera i ngaro = Te wera i whiwhi (pūnaha motuhake)

mc ΔT = mc ΔT​​​

m ΔT = m ΔT

m1 ₍ T1 – _T ) = m2 ₍ T – _T2 )

(1)(100 – T) = (1)(T – 10)

100 – T = T – 10

100 + 10 = T + T

110 = 2T

T = 110 / 2

T = 55

Ko te pāmahana whakamutunga he 55 ^° C.

[irp]

2. He poraka mata 3 kg te taumaha i te 80^o whakatakotoria ki roto i te 10 kg o te wai. Ko te wera motuhake o te mata he 1400 J.kg^-1C^-1 ā, ko te wera motuhake o te wai he 4200 J.kg^-1C^-1Ko te pāmahana whakamutunga i roto i te taurite wera ko 20^oC. Tātaitia te pāmahana tīmatanga o te wai!

Mōhiotia:

Taumaha ( _m1 ) = 3 kg

Ko te wera motuhake o te mata (c ₁ ) = 1400 J.kg ^-1 C ^-1

Ko te pāmahana o te mata (T ₁ ) = 80 ^° C

Taumaha o te wai (m2 ₎ = 10 kg

Ko te wera motuhake o te wai (c ₂ ) = 4200 J.kg ^-1 C ^-1

Ko te pāmahana o te taurite wera (T) = 20 ^° C

E hiahiatia ana: Te pāmahana tīmatanga o te wai (T ₂ )

Rongoā:

Wera i ngaro = Wera i whiwhi

Q mata = Q wai

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

Ko te pāmahana tīmatanga o te wai he 14 ^° C.

[irp]

3. He poraka parahi i 100^oC i roto i te 128 karamu o te wai 30 ^oC. Ko te wera motuhake o te wai ko 1 cal.g^-1oC^-1 ā, ko te wera motuhake o te parahi he 0.1 cal.g^-1oC^-1. Mena ko te pāmahana o te taurite wera he 36 ^oC, whakatauria te taumaha o te parahi!

Mōhiotia:

Ko te pāmahana o te parahi (T ₁ ) = 100 ^° C

Ko te wera motuhake o te parahi (c ₁ ) = 0.1 c al.g ^-1o C ^-1

Taumaha o te wai (m2 ₎ = 128 karamu

Te pāmahana o te wai (T ₂ ) = 30 ^° C

Ko te wera motuhake o te wai (c ₂ ) = 1 c al.g ^-1o C ^-1

Ko te pāmahana o te taurite wera (T) = 36 ^° C

E hiahiatia ana: Taumaha o te parahi ( _m1 )

Rongoā:

Wera i ngaro = Wera i whiwhi

Q parahi = Q wai

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

m1 = ₇₆₈ / 6.4

m1 = ₁₂₀

Ko te taumaha o te parahi he 120 karamu.

[irp]

4. He poraka hukapapa M-kg i 0^oC ringihia ki roto i te 340 karamu o te wai 20^oC i roto i te oko. Mena te te wera o te hanumitanga mo te wai = 80 karori karamu^-1, ko te wera motuhake o te wai 1 karori karamu^{-1 o}C^-1. Ka rewa katoa te hukapapa, ā, ka pāmahana hoki taurite wera is 5^oC, whakatauria te papatipu o te huka!

Mōhiotia:

Taumaha o te wai (m) = 340 karamu

Ko te pāmahana o te hukapapa (T _hukapapa ) = 0 ^° C

Te pāmahana o te wai (T _wai ) = 20 ^° C

Ko te pāmahana o te taurite wera (T) = 5 ^o C

Ko te wera o te hanumitanga mō te wai ( L ) = 80 karori karori ^-1

Ko te wera motuhake o te wai (c _wai ) = 1 karori karamu ^{-1 o} C ^-1

E hiahiatia ana: Taumaha o te hukapapa (M)

Rongoā:

Wera i ngaro = Wera i whiwhi

Q wai = Q hukapapa

m c ( ΔT) = m _e 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 = 60 karamu

[wpdm_package id='714′]

1. Te huri i ngā tauine pāmahana
2. Whānuitanga rārangi
3. Te whakawhānui ake i te rohe
4. Whakawhanuitanga rōrahi
5. Heat
6. Te ōrite ā-pūkaha o te wera
7. Te wera motuhake me te kaha wera
8. Te wera huna, te wera o te hanumi, te wera o te mimiti
9. Te tiaki pūngao mō te whakawhiti wera

Pānuitia atu

4 Te wera huna Te wera o te hanumi Te wera o te mimiti – Ngā raruraru me ngā otinga

1. Tātaihia te nui o te wera i tāpirihia ki te 1 karamu o te koura hei huri i te āhua mai i te totoka ki te wai. Ko te wera o te hanumi mō te koura he 64.5 x 103 ^J /kg.

Mōhiotia:

Taumaha (m) = 1 karamu = 1 x 10 ^-3 kg

Te wera o te hanumitanga (L _F ) = 64.5 x 103 ^J /kg

E hiahiatia ana: Wera (Q)

Rongoā:

Q = m L _F

Q = (1 x 10 ^-3 kg)(64.5 x 10 ³ J/kg)

Q = 64.5 Joule

[irp]

2. Tātaihia te nui o te wera e tukuna ana e te 1 karamu o te konukōre hei huri i te āhua mai i te wai ki te totoka. Ko te wera o te hanumitanga mō te konukōre he 11.8 x 103 ^J /kg.

Mōhiotia:

Taumaha (m) = 1 karamu = 1 x 10 ^-3 kg

Te wera o te hanumitanga (L _F ) = 11.8 x 103 ^J /kg

E hiahiatia ana: Wera (Q)

Rongoā:

Q = m L _F

Q = (1 x 10 ^-3 kg)(11.8 x 10 ³ J/kg)

Q = 11.8 Joule

3. Tātaihia te nui o te wera e mimitihia ana e te 1 kg wai hei huri i te āhua mai i te wai ki te mamaoa (korohū). Te wera o te mimiti mō te wai = 2256 x 103 ^J /kg

Mōhiotia:

Taumaha (m) = 1 kg

Te wera o te mimiti (L _V ) = 2256 x 103 ^J /kg

E hiahiatia ana: Wera (Q)

Rongoā:

Q = m L _V

Q = (1 kg)( 2256 x 103 ^J /kg)

Q = 2256 x 10 ³ Joules

[irp]

4. Tātaihia te nui o te wera e tukuna ana e te hauota hei huri i te āhua mai i te kohu ki te wai. Te wera o te kohu mō te hauota = 200 x 103 ^J /kg

Mōhiotia:

Taumaha (m) = 1 karamu = 1 x 10 ^-3 kg

Te wera o te mimiti (L _V ) = 200 x 103 ^J /kg

Mōhiotia: Wera (Q)

Rongoā:

Q = m L _V

Q = (1 x 10 ^-3 kg)( 200 x 10 ³ J/kg)

Q = 200 Joule

1. Te huri i ngā tauine pāmahana
2. Whānuitanga rārangi
3. Te whakawhānui ake i te rohe
4. Whakawhanuitanga rōrahi
5. Heat
6. Te ōrite ā-pūkaha o te wera
7. Te wera motuhake me te kaha wera
8. Te wera huna, te wera o te hanumi, te wera o te mimiti
9. Te tiaki pūngao mō te whakawhiti wera

Pānuitia atu

1. Ka mimiti te tinana he 2 kg te taumaha i te wera 100 karori ina piki te pāmahana mai i te 20 ^° C ki te 70 ^° C. He aha te wera motuhake o te tinana?

Mōhiotia:

Taumaha (m) = 2 kg = 2000 karamu

Wera ( Q) = 100 karori

Ko te huringa o te pāmahana ( ΔT ) = 70 ^° C – 20 ^° C = 50 ^° C

E hiahiatia ana: Te wera motuhake (c)

Rongoā:

c = Q / m ΔT

c = 100 karori / (2000 karamu)(50 ^° C)

c = 100 karori / 100,000 karamu ^o C

c = 10 ² karori / 10 ⁵ karamu ^o C

c = (10 ² karori)( 10 ^-5 karamu ^{-1 o} C ^-1 )

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

c = 10 -3 ^karori / karamu ^C

Ko te wera motuhake o te tinana he 10 ^-3 karori/karamu ^o C

[irp]

2. Ko te wera motuhake o te wai he 4180 J/kg C ^o . E hia te kaha wera o te 2 kg wai …

Mōhiotia:

Ko te wera motuhake (c) = 4180 J/kg C ^o

Taumaha (m) = 2 kg

E hiahiatia ana: Te kaha wera (C)

Rongoā:

C = mc

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

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

C = 8360 J/C ^o

3. Ko te wera motuhake o te konumohe he 900 J/kg C ^o . E hia te kaha wera o te 2 karamu o te konumohe…..

Mōhiotia:

Ko te wera motuhake o te konumohe (c) = 900 J/kg C ^o = 9 x 102 ^J /kg C ^o

Taumaha (m) = 2 karamu = 2/1000 kg = 2/10 ³ kg = 2 x 10 ^-3 kg

E hiahiatia ana: Te kaha wera (C)

Rongoā:

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. Te huri i ngā tauine pāmahana
2. Whānuitanga rārangi
3. Te whakawhānui ake i te rohe
4. Whakawhanuitanga rōrahi
5. Heat
6. Te ōrite ā-pūkaha o te wera
7. Te wera motuhake me te kaha wera
8. Te wera huna, te wera o te hanumi, te wera o te mimiti
9. Te tiaki pūngao mō te whakawhiti wera

Pānuitia atu

1. 2 karamu karori ( kiro karori e ) = ….. karori e?

otinga

1 kcal = 1000 kcal

2 karori = 2 (1000 karori e ) = 2000 karori e

2. 4 C pūngoi e = ….. c pūngoi e?

otinga

1 Calori e ( a Capital C ) = 1 k cal = 1000 calori e

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

3. 10 c pūngoi e = ….. Joule?

otinga

1 karori e = 4.186 Joules

10 karori e = 10 (4.186 Joule ) = 41.86 Joule

[irp]

4. 5 kcal = ….. Joule ?

otinga

1 k cal = 1000 c alorie = 4186 Joules

5 karori = 5 (4186 Joule) = 20930 Joule

5. 2000 Joule = ….. karori?

otinga

4186 Joule = 1 kcal

8372 Joule = 8372 / 4186 = 2 k karori

2000 Joule = 2000 / 4186 = 0.4777 k karori

[wpdm_package id='706′]

1. Te huri i ngā tauine pāmahana
2. Whānuitanga rārangi
3. Te whakawhānui ake i te rohe
4. Whakawhanuitanga rōrahi
5. Heat
6. Te ōrite ā-pūkaha o te wera
7. Te wera motuhake me te kaha wera
8. Te wera huna, te wera o te hanumi, te wera o te mimiti
9. Te tiaki pūngao mō te whakawhiti wera

Pānuitia atu

9 Te Papatipu Wera Te wera motuhake Te huringa o te pāmahana – Ngā Raru me ngā Otinga

1. Ka whakamahanahia he mata 2 kg te taumaha mai i 50^oC ki 100^oC. Te wera wera o te mata 130 J.kg^{-1 o te ata}C^-1. Kia pehea te nui wera ka mimitia e te mata?

Mōhiotia:

Taumaha (m) = 2 kg

Ko te wera motuhake (c) = 1 3 0 J.kg ^-1 C ^-1

Te huringa o te pāmahana ( ΔT ) = 100 ^° C – 50 ^° C = 50 ^° C

E hiahiatia ana: Wera (Q)

Rongoā:

Q = mcΔT

Q = wera , m = papatipu , c = te wera motuhake , ΔT = te huringa o te pāmahana

Te wera e mimitia ana e te mata:

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. Ko te wera motuhake o te parahi he 390 J/k g ^o C, ko te huringa pāmahana he 40 ^o C. Mena ka mimiti te parahi i te 40 Joule o te wera, he aha te taumaha o te parahi!

Mōhiotia:

Ko te wera motuhake o te parahi (c) = 390 J/k g ^o C

Ko te huringa o te pāmahana ( ΔT ) = 40 ^° C

Te wera ( Q) = 40 J

E hiahiatia ana: Taumaha (m) o te parahi

Rongoā:

Q = mcΔT

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

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

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

40 = (m)( 1560 /kg )

m = 40 / 1560

m = 0.026 kg

m = 26 karamu

3. Ko te pāmahana tīmatanga o te 20 karamu o te wai he 30 ^° C. Ko te wera motuhake o te wai he 1 karori karamu ^{-1 °} C ^-1 . Mena ka mimiti te wai i te 300 karori o te wera, tautuhia te pāmahana whakamutunga!

Mōhiotia:

Taumaha (m) = 20 karamu

Ko te pāmahana tīmatanga (T ₁ ) = 30 ^° C

Ko te wera motuhake o te wai (c) = 1 cal gr ^{-1 o} C ^-1

Wera (Q) = 300 karori

E hiahiatia ana: Te pāmahana whakamutunga o te wai

Rongoā:

Q = mc ΔT

300 karori = (20 karamu)( 1 karori karori ^{-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

T2 = ₄₅

Ko te huringa o te pāmahana he 45 ^° C – 30 ^° C = 15 ^° C.

 [irp]

4. Tte huringa o te pāmahana o te wai moana is 1^oC ina mimiti te wai i te 3900 Joule o te wera. Ko te wera motuhake o te wai moana ko 3.9 × 10³ J/kkaramu°C, he aha te taumaha o te wai moana?

Mōhiotia:

Ko te huringa o te pāmahana ( ΔT ) = 1 ^° C

Wera (Q) = 3900 Joule

Ko te wera motuhake o te wai moana (c) = 3.9 x 103 ^J / k g°C = 3900 J/Kg°C

E hiahiatia ana: Taumaha (m)

Rongoā:

Q = mcΔT

Q = wera , m = papatipu , c = wera motuhake , Δ T = te huringa o te pāmahana

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

5. Ka mimiti te parahi 2-kg i te 39,000 J o te wera i te 30°C. Mena ko te wera motuhake o te parahi he 390 J/kg °C, he aha te pāmahana whakamutunga o te parahi…

Mōhiotia:

Taumaha (m) = 2 kg

Te pāmahana tīmatanga (T ₁ ) = 30 ^° C

Wera (Q) = 39,000 Joule

Te wera motuhake (c) o te parahi = 390 J/kg ^o C

E hiahiatia ana : Te pāmahana whakamutunga (T ₂ )

Rongoā:

Q = mc ΔT

Q = wera , m = papatipu , c = wera motuhake , ΔT = te huringa o te pāmahana

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 ^° C

[irp]

6. Ka whakamahanahia he wai 5-kg te taumaha mai i te 15°C ki te 40°C. Ko te wera ka mimitia e te wai. Ko te wera motuhake o te wai ko 4.2 × 103 ^J /Kg° C.

Mōhiotia:

Taumaha (m) = 5 kg

Te pāmahana tīmatanga (T ₁ ) = 15°C

Te pāmahana whakamutunga (T ₂ ) = 40°C

Te wera motuhake o te wai (c) = 4.2 × 103 ^J /kg° C

E hiahiatia ana: Wera (Q)

Rongoā:

Q = mc ΔT

Q = (5 kg)( 4.2 × 103 ^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. Ka whakamahanahia he wai 2-kg te taumaha mai i te 24°C ki te 90°C. Ko te wera ka mimitia e te wai. Ko te wera motuhake o te wai ko 4.2 × 103 ^J /Kg° C.

Mōhiotia:

Taumaha (m) = 2 kg

Te pāmahana tīmatanga (T ₁ ) = 24°C

Te pāmahana whakamutunga (T ₂ ) = 90°C

Te wera motuhake o te wai (c) = 4,200 Joules/kg°C

E hiahiatia ana :: Wera (Q)

Rongoā:

Q = mc ΔT

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

Q = (2 kg)( 4,200 Joule/kg°C)(66°C)

Q = (132)( 4,200 Joule)

Q = 554,400 Joule

[irp]

8. Ka whakamahanahia he wai 5-karamu mai i te 10°C ki te 40°C. Ko te wera ka mimitia e te wai. Ko te wera motuhake o te wai ko 1 × 10⁻¹ ^karori / karamu r⁻¹ °C.

Mōhiotia:

Papatipu (m) = 5 karamu

Te pāmahana tīmatanga (T ₁ ) = 10 ^° C

Te pāmahana whakamutunga (T ₂ ) = 40 ^° C

Te wera motuhake o te wai (c) = 1 c al/ gr°C

E hiahiatia ana : Te wera

Rongoā:

Q = mc ΔT

Q = (5 karamu)( 1 karori/ karamu°C)(40 ^° C – 10 ^° C)

Q = (5)( 1 karāhe )(30)

Q = 150 karori

9. Ka mimiti te wai 0.2-kg i te 42,000 Joule o te wera i te 25 ° ^C . Ko te wera motuhake o te wai ko 4200 J/kg ^° C, he aha te pāmahana whakamutunga o te wai.

Mōhiotia:

Taumaha o te wai (m) = 0.2 kg

Wera (Q) = 42,000 Joule

Te wera motuhake o te wai (c) = 4200 J/kg ^o C

Te pāmahana tīmatanga (T ₁ ) = 25 ^° C

E hiahiatia ana: Te pāmahana whakamutunga (T ₂ )

Rongoā:

Q = mc ΔT = mc (T ₂ – T ₁ )

Q = wera, m = papatipu, c = wera wera, ΔT = te huringa o te pāmahana, T₁ = te pāmahana tuatahi, T₂ = te pāmahana whakamutunga

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 ^° C

1. Te huri i ngā tauine pāmahana
2. Whānuitanga rārangi
3. Te whakawhānui ake i te rohe
4. Whakawhanuitanga rōrahi
5. Heat
6. Te ōrite ā-pūkaha o te wera
7. Te wera motuhake me te kaha wera
8. Te wera huna, te wera o te hanumi, te wera o te mimiti
9. Te tiaki pūngao mō te whakawhiti wera

Pānuitia atu

Ko ngā mea totoka anake ka pāngia e te whānui rārangi; ko ngā mea katoa ka pāngia e te whānui rōrahi, te totoka, te wai, me te hau. He rite te whārite o te whānui rōrahi ki te whārite o te whānui rārangi.

Whakaahuatanga: V _o = Te rōrahi tīmatanga, V = Te rōrahi whakamutunga, ΔV = V – V _o = Te huringa o te rōrahi, T _o = Te pāmahana tīmatanga, T = Te pāmahana whakamutunga, ΔT = T – T _o = Te huringa o te pāmahana, β = te tauwehenga o te whakawhānui rōrahi. Ngā waeine o β = (C ^o ) ^-1

[irp]

Ka pā te whārite whānui rōrahi i runga ake nei ina iti iho ngā huringa o te rōrahi o ngā mea (totoka, wai, me te hau) i te rōrahi taketake o te mea. Mena he nui ake te huringa o te rōrahi o tētahi mea i te rōrahi tīmatanga o te mea, kāore te whārite o te whānui rōrahi e homai i ngā hua tika. I te nuinga o te wā, kāore i te nui rawa ngā huringa o te rōrahi e pāngia ana e ngā mea totoka. I tētahi atu taha, he nui te tauwehenga whānui rōrahi o te wai me te hau. He ngāwari hoki te whakarerekē i te tauwehenga whānui rōrahi mō ngā matū hau mena ka rerekē te pāmahana. Nō reira, ka whakamahia te tātai i runga ake nei mō te whānui o ngā mea totoka anake.

[irp]

1. I te 30 ^° C, ko te rōrahi o tētahi porowhita konumohe he 30 cm³ ^. Ko te tauwehenga whānui rārangi he 24 x 10−6 ^° C ⁻¹ . Mena ko te rōrahi whakamutunga he 30.5 cm³ ^, he aha te pāmahana whakamutunga o te porowhita konumohe?

Mōhiotia:

Ko te tauwehenga whānui rārangi ( α ) = 24 x 10 ^{-6 o} C ^-1

Ko te tauwehenga o te whakawhanuitanga rōrahi ( β ) = 3 α = 3 x 24 x 10 ^{-6 o} C ^-1 = 72 x 10 ^{-6 o} C ^-1

Ko te pāmahana tīmatanga (T ₁ ) = 30 ^° C

Ko te rōrahi tīmatanga (V ₁ ) = 30 cm ³

Ko te rōrahi whakamutunga (V ₂ ) = 30.5 cm ³

Ko te panonitanga o te rōrahi ( Δ V) = 30.5 cm ³ – 30 cm ³ = 0.5 cm ³

E hiahiatia ana: Te pāmahana whakamutunga (T ₂ )

Rongoā:

ΔV = β (V1 ₎ ( ΔT )

Δ V = β (V ₁ )(T ₂ – T ₁ )

0.5 cm³ = ((72 x 10^{-6 o te ata}C^-1)(30cm³)(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 ^° C

[irp]

2. Ko te tauwehenga whānui rārangi o tētahi porowhita whakarewa he 9 x 10 ^{-6 o} C ^-1 . Ko te whānui o roto o te porowhita whakarewa i te 20 ^o C he 2.2 cm. Mena ko te whānui whakamutunga he 2.8 cm, he aha te pāmahana whakamutunga!

Mōhiotia:

Ko te tauwehenga whānui rārangi ( α ) = 9 x 10 ^{-6 o} C ^-1

Ko te tauwehenga o te whakawhanuitanga rōrahi ( β) = 3 α = 3 x 9 x 10 ^{-6 o} C ^-1 = 27 x 10 ^{-6 o} C ^-1

Ko te pāmahana tīmatanga (T ₁ ) = 20 ^° C

Ko te whānui tīmatanga (D ₁ ) = 2.2 cm

Ko te whānui whakamutunga (D ₂ ) = 2.8 cm

Ko te pūtoro tīmatanga (r ₁ ) = D ₁ / 2 = 2.2 cm ³ / 2 = 1.1 cm ³

Ko te pūtoro whakamutunga (r ₂ ) = D ₂ / 2 = 2.8 cm ³ / 2 = 1.4 cm ³

Ko te rōrahi tīmatanga (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

Ko te rōrahi whakamutunga (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

Ko te panonitanga o te rōrahi ( Δ V) = 11.48 cm³ ^– 5.57 cm³ ⁼ 5.91 ^cm³

E hiahiatia ana: Te pāmahana _whakamutunga ( T2 )

Rongoā:

ΔV = β (V1 ₎ ( ΔT )

5.91 cm³ = ((27 x 10^{-6 o te ata}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 = T ₂

T ₂ = 39,020 ^° C

3. He 2000-cm³ ipu konumohe, kī tonu i te wai i te 0^oC. Kātahi ka whakamahanatia ki te 90^oC. Mena ko te tauwehenga whānui rārangi mō te konumohe he 24 x 10^-6 (^oC)^-1 ā, ko te tauwehenga whakawhanui rōrahi mō te wai he 6.3 x 10^-4 (^oC)^-1, whakatau i te rahinga o te wai i maringi.

Mōhiotia:

Ko te rōrahi tīmatanga o te ipu konumohe me te wai (V _o ) = 2000 cm ³ = 2 x 10 ³ cm ³

Ko te pāmahana tīmatanga o te ipu konumohe me te wai (T ₁ ) = 0 ^° C

Ko te pāmahana whakamutunga o te ipu konumohe me te wai (T ₂ ) = 90 ^° C

Ko te tauwehenga whānui rārangi mō te konumohe (α) = 24 x 10 ^-6 ( ^o C ) ^-1

Ko te tauwehenga whakawhanui rōrahi mō te konumohe (γ) = 3α = 3 (24 x 10 ^-6 ( ^o C ) ^-1 ) = 72 x 10 ^{-6 o} C ^-1

Ko te tauwehenga whānui o te rōrahi mō te wai (γ) = 6.3 x 10 ^-4 ( ^o C ) ^-1

E hiahiatia ana: Te rahinga o te wai i maringi

Rongoā:

Ko te whārite o te whakawhanuitanga rōrahi:

V = V _o + γ V _o ΔT

V – V _o = γ V _o ΔT

ΔV = γV _o ΔT

V = rōrahi whakamutunga, V _o = rōrahi tīmatanga, ΔV = te huringa o te rōrahi, γ = te tauwehenga o te whakawhānui rōrahi, ΔT = te huringa o te pāmahana

Tātaihia te huringa o te rōrahi o te ipu konumohe:

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

Tātaihia te huringa o te rōrahi o te wai:

ΔV = γ V _o ΔT = (6.3 x 10 ^-4 )(2 x 10 ³ )(90) = 1134 x 10 ^-1 = 113.4 cm ³

He nui ake te panonitanga o te rōrahi o te wai i te ipu konumohe, nō reira i maringi ai ētahi wai.

Tātaihia te nui o te wai i maringi:

113.4 henimita ³ – 12.960 henimita ³ = 100.44 henimita ³

[wpdm_package id='702′]

1. Te huri i ngā tauine pāmahana
2. Whānuitanga rārangi
3. Te whakawhānui ake i te rohe
4. Whakawhanuitanga rōrahi
5. Heat
6. Te ōrite ā-pūkaha o te wera
7. Te wera motuhake me te kaha wera
8. Te wera huna, te wera o te hanumi, te wera o te mimiti
9. Te tiaki pūngao mō te whakawhiti wera

Pānuitia atu

1. I te 20 ^° C, ko te roa o tētahi rau maitai he 50 cm, ā, ko te whānui he 30 cm. Mena ko te tauwehenga whānui rārangi mō te maitai he 10 ^{-5 °} C ^-1 , tātaihia te huringa horahanga me te horahanga whakamutunga i te 60 ^° C.

Mōhiotia:

Ko te pāmahana tīmatanga (T ₁ ) = 20 ^° C

Ko te pāmahana whakamutunga (T ₂ ) = 60 ^° C

Ko te huringa o te pāmahana ( ΔT ) = 60 ^° C – 20 ^° C = 40 ^° C

Ko te horahanga tīmatanga (A ₁ ) = te roa x te whānui = 50 cm x 30 cm = 1500 cm ²

Ko te tauwehenga whānui rārangi mō te maitai ( α) = 10 ^{-5 o} C ^-1

Ko te tauwehenga whānui o te horahanga mō te maitai ( β) = 2α = 2 x 10 ^{-5 o} C ^-1

E hiahiatia ana: Te huringa o te horahanga ( ΔA )

Rongoā:

Te huringa o te horahanga ( 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 cm²

Ko te horahanga whakamutunga ( A ₂ ):

A ₂ = A ₁ + ΔA

A ₂ = 1500 cm ² + 1. 2 cm ²

A ₂ = 1501. 2 cm ²

[irp]

2. I te 30 ^° C, ko te horahanga o tētahi rau konumohe he 40 cm² ^, ā, ko te tauwehenga whānui rārangi he 24 x 10⁻¹ ^-6 / ^⁻¹ . Tātaihia te pāmahana whakamutunga mēnā ko te horahanga whakamutunga he 40.2 ^cm².

Mōhiotia:

Ko te pāmahana tīmatanga (T ₁ ) = 30 ^° C

Ko te tauwehenga whānui rārangi ( α) = 24 x 10 ^{-6 o} C ^-1

Ko te tauwehenga whānui o te horahanga ( β) = 2a = 2 x 24 x 10 ^{-6 o} C ^-1 = 48 x 10 ^{-6 o} C ^-1

Ko te horahanga tīmatanga (A ₁ ) = 40 cm ²

Ko te horahanga whakamutunga (A ₂ ) = 40.2 cm ²

Ko te panonitanga o te horahanga ( ΔA) = 40.2 cm² ^– 40 cm² ⁼ 0.2 ^cm²

E hiahiatia ana: Whakatauhia te pāmahana whakamutunga (T ₂ )

Rongoā:

Te tātai o te huringa horahanga ( ΔA) :

ΔA = βA ₁ ΔT

Te pāmahana whakamutunga (T ₂ ):

ΔA = βA1 ( _T2 – _T1 )​_​

0.2 cm² = (48 x 10^{-6 o}C^-1)(40 henimita²)(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

T2 = ₁₃₀

Ko te pāmahana whakamutunga = 130 ^° C

[irp]

3. Ko te radius o te mowhiti i te 20 ^° C he 20 cm. Mena ko te radius whakamutunga i te 100 ^° C he 20.5 cm, tautuhia te tauwehenga whānui o te horahanga me te tauwehenga whānui rārangi…

Mōhiotia:

Ko te pāmahana tīmatanga (T ₁ ) = 30 ^° C

Ko te pāmahana whakamutunga (T ₂ ) = 100 ^° C

Ko te huringa o te pāmahana ( ΔT ) = 100 ^° C – 30 ^° C = 70 ^° C

Ko te pūtoro tīmatanga (r ₁ ) = 20 cm

Ko te radius whakamutunga (r ₂ ) = 20.5 cm

E hiahiatia ana: Te tauwehenga whānui o te horahanga ( β )

Rongoā:

Ko te horahanga tīmatanga (A ₁ ) = π r ₁ ² = (3.14)(20 cm) ² = (3.14)(400 cm ² ) = 1256 cm ²

Ko te horahanga whakamutunga (A ₂ ) = π r ₂ ² = (3.14)(20.5 cm) ² = (3.14)(420.25 cm ² ) = 1319.585 cm ²

Ko te panonitanga o te horahanga ( ΔA) = 1319.585 cm² ^– 1256 cm² ⁼ 63.585 ^cm²

Te tātai o te huringa horahanga ( ΔA) :

ΔA = βA ₁ ΔT

Te tauwehenga o te whakawhānui rohe:

ΔA = βA ₁ ΔT

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

63.585 = b ( 87,920 ^° C)

β = 63.585 / 87,920 ^° C

β = 0.00072 / ^o C

β = 7.2 x 10 ^-4 / ^o C

β = 7.2 x 10 ^{-4 o} C ^-1

Te tauwehenga o te whakawhānui raina ( α ):

β = 2 α

α = β / 2

α = (7.2 x 1 0 ^-4 ) / 2

α = 3.6 x 10 ^{-4 o} C ^-1

[wpdm_package id='698′]

1. Te huri i ngā tauine pāmahana
2. Whānuitanga rārangi
3. Te whakawhānui ake i te rohe
4. Whakawhanuitanga rōrahi
5. Heat
6. Te ōrite ā-pūkaha o te wera
7. Te wera motuhake me te kaha wera
8. Te wera huna, te wera o te hanumi, te wera o te mimiti
9. Te tiaki pūngao mō te whakawhiti wera

Pānuitia atu