Ngā tauira pātai mō te Mātāpono Pango

15 Ngā Tauira o Ngā Pātai Mātāpono a Black

1. Ka konatunatua he hukapapa he 0,2 kg te taumaha ki te tī mahana he 0,2 kg te taumaha. Ko te pāmahana o te hukapapa = – 10 ^° C, ko te pāmahana o te tī mahana = 40 ^° C. Ko te wera motuhake o te hukapapa = 2100 J/kg C₂o ^, ko te wera motuhake o te wai = 4200 J/kg C₂o ^, ko te wera o te hanumitanga o te wai = 334.000 J/kg. Mena ka konatunatua te hukapapa me te tī mahana ki roto i tētahi pūnaha motuhake, katia, tātaihia te pāmahana whakamutunga o te ranunga.

Kōrero
E mōhiotia ana :
Taumaha o te huka (m es) = 0,2 kg
Taumaha o te wai tī mahana (m tī) = 0,2 kg
Te wera motuhake o te wai (c wai) = 4180 J/kg C^o
Te wera motuhake o te hukapapa (c es) = 2100 J/kg C^o
Te wera o te hanumitanga o te wai (L)_f wai) = 334.000 J/kg
Te pāmahana hukapapa (T es) = -10^oC
Te pāmahana wai tī mahana (T tī) = 40^oC
I pātaihia : te pāmahana whakamutunga o te ranunga (T ranunga) ?
Whakautu :
Ko te taahiraa tuatahi, whakatau tata i te āhua whakamutunga.
Ko te wera me tuku e te wai hei whakaheke i te pāmahana o te 0,2 kg o te tī mahana mai i te 40^oC ki te 0^oC:
Ko te wera i mimitia e te 0,2 kg o te hukapapa hei whakapiki i tōna pāmahana mai i te -10^oC ki te 0^oC:
Te wera e mimitia ana hei whakarewa i te 0,2 kg o te hukapapa (te wera e hiahiatia ana hei huri i te hukapapa katoa hei wai):
I runga i ngā tātaitanga i runga ake nei, i puta mai ngā hua e whai ake nei:
Q i tukuna = 33,444 kJ
Q i whiwhi = 4,2 kJ
Q rewa = 66,8 kJ

Ina tukuna te 33,44 kJ o te wera e te tī wera, ka huri te pāmahana o te tī wera mai i te 40°C ki te 0°C. Ko tētahi o te wera i tukuna (tata ki te 4,2 kJ) ka whakamahia hei whakaara ake i te pāmahana o te hukapapa mai i te -10°C ^ki te 0°C ^. 33,44 kJ – 4,2 kJ = 29,24 kJ. Hei whakarewa i te hukapapa katoa ki roto i te wai, e hiahiatia ana te 66,8 kJ o te wera. Ko te wera e toe ana ko te 29,24 kJ.

Ka taea te whakatau ko te wera e tukuna ana e te tī wera ka whakamahia hei whakaara ake i te pāmahana o te hukapapa mai i te -10 ^° C ki te 0 ^° C, hei whakarewa hoki i ētahi o ngā hukapapa. Kua huri ētahi o ngā hukapapa hei wai, ko ētahi kāore. I te tukanga o te huri mai i te totoka ki te wai, kāore te pāmahana e rerekē. Nō reira, ko te pāmahana whakamutunga o te ranunga he 0 ^° C.

2. Te taumaha o te tī wera = 0,4 kg, te taumaha o te hukapapa = 0,2 kg, te pāmahana o ngā poraka hukapapa = -10^oC, te pāmahana tī wera = 90^oC. Mena ka konatunatua ngā mea e rua, he aha te pāmahana whakamutunga o te ranunga?
Kōrero
Hipanga tuatahi: whakatau tata i te āhua whakamutunga
Ko te wera me tuku e te wai hei whakaheke i te pāmahana o te 0,4 kg o te wai tī wera mai i te 90^oC ki te 0^oC:
Ko te wera i riro i te 0,2 kg o te hukapapa hei whakapiki i tōna pāmahana mai i te -10^oC ki te 0^oC:
Te wera e hiahiatia ana hei whakarewa i te 0,2 kg o te hukapapa (te wera e hiahiatia ana hei huri i te hukapapa katoa hei wai):
I runga i ngā tātaitanga i runga ake nei, i puta mai ngā hua e whai ake nei:
Q i tukuna = 150,48 kJ
Q i whiwhi = 4,2 kJ
Q rewa = 66,8 kJ
Ina tukuna te 150,48 kJ o te wera e te tī wera, ka huri te pāmahana o te tī wera mai i te 90°C ki te 0°C. Ko tētahi o te wera i tukuna (4,2 J) ka whakamahia hei whakaara ake i te pāmahana o te hukapapa mai i te -10°C ki te 0°C. 150,48 kJ – 4,8 kJ = 146,28 kJ. Ko te wera e toe ana = 146,28 kJ.
Ko te wera e hiahiatia ana hei whakarewa i te hukapapa katoa ki roto i te wai he 66,8 kJ anake. 146,28 kJ – 66,8 kJ = 79,48 kJ. Kāore e hiahiatia ana e te tī wera te tuku i tōna wera katoa kia heke rā anō tōna pāmahana ki te 0.^oC. Hei whakamutunga, me nui ake te pāmahana whakamutunga o te ranunga i te 0^oC.

Hipanga tuarua: whakatau i te pāmahana whakamutunga (T)
Te wera e hiahiatia ana hei whakaara ake i te pāmahana o te hukapapa mai i te -10^oC ki te 0^oKo C ko 4200 J.
Ko te wera e hiahiatia ana hei whakarewa i te hukapapa katoa ki roto i te wai (wera huna) = 66.800 J
Ko te wera e hiahiatia ana hei whakaara ake i te pāmahana o te wai (te wai e puta mai ana i te rewa o te hukapapa katoa) mai i te 0^oC ki T^oC = (papatipu hukapapa)(wera motuhake o te wai)(T – 0) = (0,2)(4180)(T) = 836 T
Ko te wera i tukuna e te tī mahana hei whakaheke i tōna pāmahana mai i te 90°C ki te T = (kiato o te wai)(90-T) = (0,4)(4180)(90 – T) = 1672 (90-T) = 150.480 – 1672 T

 

3. E 60 karamu o te wai i te pāmahana o te 90 ^° C (te wera motuhake o te wai = 1 cal.g ^-1 .o ^{C -1} ) ka konatunatua ki te 40 karamu o te wai ōrite i te pāmahana o te 25 ^° C . Mēnā kāore he āhuatanga kē atu e pā ana ki tēnei tukanga, ko te pāmahana whakamutunga o te ranunga ko...

A. 15,4 ^oC
B. 23,0 ^oC
C. 46,0 ^oC
D. 64,0 ^oC
E. 77,0 ^oC

Kōrero
E mōhiotia ana :
Taumaha o te wai 1 (m₁) = 60 karamu
Te pāmahana wai 1 (T₁) = 90^oC
Taumaha o te wai 2 (m₂) = 40 karamu
Te pāmahana wai 2 (T₂) = 25^oC
Te wera motuhake wai (c) = 1 karori^-1.^oC^-1
I pātaihia : te pāmahana ranunga whakamutunga
Whakautu :
Te wera e tukuna ana e te wai pāmahana teitei (Q e tukuna ana) = te wera e mimitihia ana e te wai pāmahana iti (Q e mimitihia ana)
m₁ c (ΔT) = m₂ c (ΔT)
(60)(1)(90 – T) = (40)(1)(T – 25)
(60)(90 – T) = (40)(T – 25)
5400 – 60T = 40T – 1000
5400 + 1000 = 40T + 60T
6400 = 100T
T = 6400/100
T = 64^oC
Ko te whakautu tika ko D.

4. He 500 karamu te taumaha o tētahi wahi konumohe, ā, he 30 te pāmahana ^oKa makahia he wai C ki roto i tētahi oko kei roto he wai e 200 karamu te taumaha, ā, e 90 te pāmahana. ^oC. Mena e mōhiotia ana ko te wera motuhake o te konumohe he 0,22 cal/g C^o ā, ko te wera motuhake o te wai he 1 cal/g C^o, kātahi ko te pāmahana whakamutunga o te wai me te konumohe ko...
A. 20,3 ^oC
B. 42,2 ^oC
C. 68,7 ^oC
D. 80,5 ^oC
E. 100 ^oC
Kōrero:
Kāore e hiahiatia te huri i te waeine o te papatipu, karamu (g) ​​ki kirokaramu (kg) nā te mea ko te wera motuhake o te konumohe me te wera motuhake o te wai e whakaatuhia ana i roto i te cal/g C.^o.
E mōhiotia ana :
m konumohe = 500 karamu
konumohe = 0,22 karori/gC^o
T konumohe = 30 ^oC
m wai = 200 karamu
wai = 1 karori/karamu^o
T wai = 90 ^oC
I pātaihia :
Te pāmahana whakamutunga (T) o te wai me te konumohe?
Whakautu :

Tātai wera : Q = (m)(c)(delta T)

Q wai = = (200 karamu)(1 karori/karamu^o)(90 ^oC – T)
Q konumohe = (500 karamu)(0,22 karori/gC^o)(T– 30 ^oC)

Te tātai taketake a Black : Q _{i tukuna} = Q _{i mimitia}

He teitei ake te pāmahana tīmatanga o te wai (90 ^oC) kia tukuna ai te wera e te wai, he iti ake te pāmahana tīmatanga o te konumohe (30 ^oC) kia mimiti ai te wera e te konumohe. Me iti iho te pāmahana whakamutunga o te ranunga wai me te konumohe i te pāmahana tīmatanga o te wai, me teitei ake i te pāmahana tīmatanga o te konumohe.
(200 karamu)(1 karori/karamu^o)(90 ^oC – T) = (500 karamu)(0,22 karori/karamu C^o)(T– 30 ^oC)
(200)(1)(90-T) = (500)(0,22)(T-30)
(200)(90-T) = (110)(T-30)
18000 – 200 T = 110 T – 3300
18000 + 3300 = 110 T + 200 T
21300 = 310 T
T = 68,7 ^oC
Ko te pāmahana whakamutunga o te ranunga o te wai me te konumohe he 68,7 ^oC.
Ko te whakautu tika ko C.

5. He konganuku he 300 karamu te taumaha i te pāmahana o te 80 ^oC i tōia ki roto i te 200 karamu wai i te 40 ^oC. Te wera motuhake o te wai = 1 karori/karamu C^o. Mēnā ko te pāmahana whakamutunga o te ranunga o te konganuku me te wai he 50^o C, ā, kāore te ipu e mimiti i te wera, ko te wera motuhake o te konganuku he…
A. 0,15 karori/karamu C^o
B. 0,22 karori/karamu C^o
C. 1,50 karori/karamu C^o
D. 4,8 karori/karamu C^o
E. 7,2 karori/karamu C^o
Kōrero:
E mōhiotia ana :
m te konganuku = 300 karamu
T konganuku = 80 ^oC
m wai = 200 karamu
T wai = 40 ^oC
wai = 1 karori/karamu C^o
T te ranunga whakamutunga o te konganuku me te wai = 50 ^oC
I pātaihia :
c whakarewa?
Whakautu :
Q konganuku = (m)(c)(delta T) = (300 karamu)(c konganuku)(80^oC - 50^oC) = (300 karamu)(c konganuku)(30 C^o)
Q wai = (m)(c)(delta T) = (200 karamu)(1 karori/karamu C^o)(60^oC - 50^oC) = (200 karamu)(1 karori/karamu C^o)(10 C^o)

Te tātai taketake a Black : Q _{i tukuna} = Q _{i mimitia}

He teitei ake te pāmahana tīmatanga o te konganuku (80 ^oC) kia tukuna ai te wera e te konganuku, ka iti ake te pāmahana tīmatanga o te wai (40 ^oC) kia mimiti ai te wera e te wai.
(300 karamu)(c konganuku)(30 C^o) = (200 karamu)(1 karori/karamu C^o)(10 C^o)
(300)(c)(30) = (200)(1)(10)
9000 c = 2000
c = 2000 / 9000
c = 0,22 karori/karamu C^o
Ko te wera motuhake o te konganuku he 0,22 karori/karamu C^o.
Ko te whakautu tika ko B.

6. E rua ngā pōro ōrite, he ōrite te pāmahana, arā, 40 ^oC, he 10 karamu te taumaha o ngā pōro e rua, he 40 karamu te taumaha. Ka whakanohoia ngā pōro e rua ki roto i tētahi wai, kia piki ai te pāmahana o ngā pōro e rua ki te 60^oC. Mena ko te wera motuhake o te pōro he 2 karori/karamu C^o ā, ko te 1 karori = 4,2 Joules, kātahi ko te rerekētanga o te wera e mimitihia ana e ia pōro ko...
A. 5,04 x 10³ Joule
B. 7,50 x 10³ Joule
C. 10,6 x 10³ Joule
D. 40 x 10³ Joule
E. 42 x 10³ Joule
Kōrero:
E mōhiotia ana :
m₁ = 10 karamu
m₂ = 40 karamu
T₁ =T₂ = 40 ^oC
T _mutunga = 60 ^oC
pōro c = 2 karori/karamu C^o
I pātaihia :
He aha te rerekētanga o te wera e mimitihia ana e ia pōro?
Whakautu :
Ka piki ake te pāmahana o ngā pōro e rua nā te mea me mimiti te wera e ngā pōro e rua.
Q₁ = (10 karamu)(2 karori/karamu C^o)(60^oC–40^oC) = (10 karamu)(2 karori/karamu C^o)(20 C^o) = 400 kara = (400)(4,2 J) = 1680 Joules
Q₂ = (40 karamu)(2 karori/karamu C^o)(60^oC–40^oC) = (40 karamu)(2 karori/karamu C^o)(20 C^o) = 1600 kara = (1600)(4,2 J) = 6720 Joules
Te rerekētanga o te wera e mimitihia ana e ia pōro:
6720 J – 1680 J = 5040 J = 5,04 x 10³ J
Ko te whakautu tika ko A.

7. Ka konatunatua te wai he 200 karamu te taumaha i te pāmahana o te 30°C ki te wai kohua he 100 karamu te taumaha me te pāmahana o te 90°C. (Te wera motuhake o te wai = 1 karori karamu ^-1 °C ^-1 ). Ko te pāmahana o te wai i konatunatua i te wā o te taurite wera ko….

A. 10°C

B. 30°C

C. 50°C

D. 75°C

E. 150°C

Kōrero

E mōhiotia ana :

Taumaha o te wai 1 (m ₁ ) = 200 karamu

Te pāmahana wai 1 (T ₁ ) = 30 ^° C

Taumaha o te wai 2 (m ₂ ) = 100 karamu

Te pāmahana wai 2 (T ₂ ) = 90 ^° C

Te wera motuhake o te wai (c) = 1 karori.karamu ⁻¹ °C ⁻¹

I pātaihia : te pāmahana whakamutunga o te ranunga

Whakautu :

Te wera e tukuna ana e te wai pāmahana teitei (Q e tukuna ana) = te wera e mimitihia ana e te wai pāmahana iti (Q e mimitihia ana)

Ko te whakautu tika ko C.

8. E 60 karamu o te wai i te pāmahana o te 90 ^° C (te wera motuhake o te wai = 1 cal.g ^-1 .o ^{C -1} ) ka konatunatua ki te 40 karamu o te wai ōrite i te pāmahana o te 25 ^° C . Mēnā kāore he āhuatanga kē atu e pā ana ki tēnei tukanga, ko te pāmahana whakamutunga o te ranunga ko...

A. 15,4 ^° C

B. 23,0 ^o C

C. 46,0 ^o C

D. 64,0 ^o C

E. 77,0 ^o C

Kōrero

E mōhiotia ana :

Taumaha o te wai 1 (m ₁ ) = 60 karamu

Te pāmahana wai 1 (T ₁ ) = 90 ^° C

Taumaha o te wai 2 (m ₂ ) = 40 karamu

Te pāmahana wai 2 (T ₂ ) = 25 ^° C

Te wera motuhake o te wai (c) = 1 cal.g ^-1 . ^o C ^-1

I pātaihia : te pāmahana whakamutunga o te ranunga

Whakautu :

Te wera e tukuna ana e te wai pāmahana teitei (Q e tukuna ana) = te wera e mimitihia ana e te wai pāmahana iti (Q e mimitihia ana)

Ko te whakautu tika ko D.

9. Ka makahia he hukapapa he M karamu te taumaha i te pāmahana o te 0 ^° C ki roto i te wai he 340 karamu te taumaha i te pāmahana o te 20 ^° C, ka whakanohoia ki roto i tētahi oko motuhake. Me kī kāore te oko e mimiti/tuku i te wera. Mēnā ko te L _hukapapa = 80 karori karamu ^-1 , c _wai = 1 karori karamu ^{-1 o} C ^-1 , ka rewa katoa ngā hukapapa, ā, ka eke ki te taurite wera i te pāmahana o te 5 ^° C, ko te taumaha o te hukapapa (M) ko...

A. 60 karamu

B. 68 karamu

C. 75 karamu

D. 80 karamu

E. 170 karamu

Kōrero

E mōhiotia ana :

Taumaha o te wai (m) = 340 karamu

Te pāmahana hukapapa (T _es ) = 0 ^o C

Te pāmahana wai (T _wai ) = 20 ^° C

Te pāmahana taurite wera (T) = 5 ^o C

Te wera o te huka rewa (L _hukapapa ) = 80 karori karamu ^-1

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

Pātai : Te papatipu o te huka (M)

Whakautu :

E ai ki te mātāpono a Black , i roto i tētahi pūnaha kati motuhake, ko te wera e tukuna ana e tētahi mea pāmahana-tiketike he ōrite ki te wera e mimitihia ana e tētahi mea pāmahana-iti.

Te wera i tukuna e te wai (Q i tukuna) = te wera i mimitia e te hukapapa (Q i mimitia)

Ko te whakautu tika ko A.

Tuhipoka:

Ki te kīia kei te 0 ^°C te pāmahana o te hukapapa , he totoka tonu te wai. Ki te kīia kei te 0 ^° C te pāmahana o te wai, he wai te āhua o te wai. Wehewehea te whakamahinga o ngā kupu hukapapa me te wai. Nā te mea kei te totoka tonu te wai, te hukapapa rānei, ka whakamahia tuatahitia te wera e mimitihia ana hei whakarewa i ngā hukapapa katoa ki roto i te wai, nō reira, i te taha matau o te whārite i runga ake nei, ka tāpirihia he tātai hei tatau i te nui o te wera hei whakarewa i te hukapapa (m _es L _es ). I muri i te rewa o ngā hukapapa katoa ki roto i te wai, ka whakamahia he wera tāpiri hei whakaara ake i te pāmahana o te hukapapa mai i te 0 ^° C ki te 5 ^° C.

10. Ka tāpirihia he konganuku parahi ki roto i te wai i te pāmahana o te 100 ^° C, ko tōna taumaha he 128 karamu, ā, ko tōna pāmahana he 30 ^° C. Ko te wera motuhake o te wai he 1 cal.g ^-1 °C ^-1 , ā, ko te wera motuhake o te parahi he 0,1 cal.g ^-1° C ^-1 . Mena ka puta te taurite wera i te pāmahana o te 36 ^° C, ko te taumaha o te konganuku he….

A. 140 karamu

B. 120 karamu

C. 100 karamu

D. 80 karamu

E. 75 karamu

Kōrero

E mōhiotia ana:

Te pāmahana parahi (T ₁ ) = 100 ^o C

Te wera motuhake o te parahi (c ₁ ) = 0,1 cal.g ^-1o C ^-1

Taumaha o te wai (m2 ₎ = 128 karamu

Te pāmahana wai (T ₂ ) = 30 ^° C

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

Te pāmahana taurite wera (T) = 36 ^o C

Pātai: Te taumaha o te parahi ( _m1 )

Whakautu:

E ai ki te mātāpono a Black, ko te wera e tukuna ana e te mea pāmahana teitei = te wera e whiwhi ana i te mea pāmahana iti.

Ko te whakautu tika ko B.

11. E toru kirokaramu o te tokotoko mata pango me te wera motuhake o te 1400 J.kg ^-1 C ^-1 i te pāmahana o te 80 ^° C ka toua ki roto i te 10 kg o te wai me te wera motuhake o te 4200 J.kg ^-1 C ^-1 . I muri i te taurite wera, ko te pāmahana whakamutunga o te ranunga he 20 ^° C. Ko te pāmahana tīmatanga o te wai ko….

A. 20 ^° C

B. 18 ^o C

C. 14 ^o C

D. 12 ^o C

E. 10 ^o C

Kōrero

E mōhiotia ana:

Taumaha o te mata (m1 ₎ = 3 kg

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

Te pāmahana tine (T ₁ ) = 80 ^° C

Taumaha o te wai (m2 ₎ = 10 kg

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

Te pāmahana taurite wera (T) = 20 ^o C

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

Whakautu:

Ko te whakautu tika ko C.

12. Ka whakamahanahia he moni 50 karamu ki te pāmahana o te 85 ^° C, kātahi ka toua ki roto i tētahi oko kei roto te 50 karamu wai i te pāmahana o te 29,8 ^° C (te wera motuhake o te wai = 1 cal.g ^-1 . ^o C ^-1 ). Mena ko te pāmahana whakamutunga o te pūnaha he 37 ^° C, ā, ki te whakaarohia kāore he huringa o te wera i roto i te oko, ko te wera motuhake o te konganuku ko...

A. 0,12 karori karamu ^-1 . ^o C ^-1

B. 0,30 karori karamu ^-1 . ^o C ^-1

C. 1,50 karori karamu ^-1 . ^o C ^-1

D. 4,8 karori karamu ^-1 . ^o C ^-1

E. 7,2 karori karamu ^-1 . ^o C ^-1

Kōrero

E mōhiotia ana:

Te taumaha o te moni (m) = 50 karamu

Te pāmahana tīmatanga o te moni (T ₁ ) = 85 ^° C

Taumaha o te wai (m) = 50 karamu

Te pāmahana wai tīmatanga (T ₂ ) = 29,8 ^o C

Te wera motuhake o te wai = 1 cal.g ^-1 . ^o C ^-1

Te pāmahana pūnaha whakamutunga (T) = 37 ^o C

Pātai: Te wera motuhake o te konganuku (c)

Whakautu:

E ai ki te mātāpono a Black, ko te wera e tukuna ana = ko te wera e mimitia ana. Ka tukuna te wera e te moni, ka mimitia hoki te wera e te wai, kia tae rā anō ki te taurite wera.

Ka whakaatuhia ngā waeine katoa i roto i te karamu, nō reira kāore he take ki te huri i ngā waeine.

Q _{i tukuna} = Q i _mimitia

m _whakarewa c ΔT = m _wai c ΔT

(50)(c)(85-37) = (50)(1)(37-29,8)

(50)(c)(48) = (50)(7,2)

(50)(c)(48) = (50)(7,2)

(c)(48) = 7,2

c = 7,2 / 48

c = 0,15 karori ^-1 . ^o C ^-1

13. Ka tāpirihia he konganuku parahi ki roto i te wai i te pāmahana o te 100 ^{° C, ko tōna taumaha he 128 karamu, ā, ko tōna pāmahana he 30 °} C. Ko te wera motuhake o te wai he 1 cal.g ^-1° C ^-1 , ā, ko te wera motuhake o te parahi he 0,1 cal.g ^{-1 °} C ^-1 . Mena ka puta te taurite wera i te pāmahana o te 36 ^° C, ko te taumaha o te konganuku he….

A. 140 karamu
B. 120 karamu
C. 100 karamu
D. 80 karamu
E. 75 karamu

Kōrero
E mōhiotia ana:
Te pāmahana parahi (T₁) = 100 ^oC
Te wera motuhake o te parahi (c₁) = 0,1 karori^{-1 o}C^-1

Papatipu wai (m₂) = 128 karamu
Te pāmahana wai (T₂) = 30 ^oC
Te wera motuhake o te wai (c₂) = 1 karori^{-1 o}C^-1

Te pāmahana taurite wera (T) = 36 ^oC
Pātai: Te taumaha o te parahi (m₁)
Whakautu:

E ai ki te mātāpono a Black, ko te wera e tukuna ana e te mea pāmahana teitei = te wera e whiwhi ana i te mea pāmahana iti.
Q parahi = Q wai
m₁ c₁ ΔT = m₂ c₂ ΔT
(m₁)(0,1)(100-36) = (128)(1)(36-30)
(m₁)(0,1)(64) = (128)(1)(6)
(m₁)(6,4) = 768
m₁ = 768/6,4
m₁ = 120
Ko te taumaha o te parahi he 120 karamu.
Ko te whakautu tika ko B.

14. E toru kirokaramu o te tokotoko mata pango me te wera motuhake o te 1400 J.kg ^-1 C ^-1 i te pāmahana o te 80 ^° C ka toua ki roto i te 10 kg o te wai me te wera motuhake o te 4200 J.kg ^-1 C ^-1 . I muri i te taurite wera, ko te pāmahana whakamutunga o te ranunga he 20 ^° C. Ko te pāmahana tīmatanga o te wai ko….

A. 20 ^oC
B. 18 ^oC
C. 14 ^oC
D. 12 ^oC
E. 10 ^oC

Kōrero
E mōhiotia ana:
Te taumaha o te mata (m₁) = 3 kirokaramu
Te wera motuhake o te tine (c₁) = 1400 J.kg^-1 C^-1
Te pāmahana tine (T₁) = 80 ^oC

Papatipu wai (m₂) = 10 kirokaramu
Te wera motuhake o te wai (c₂) = 4200 J.kg^-1 C^-1

Te pāmahana taurite wera (T) = 20 ^oC
E hiahiatia ana: Te pāmahana wai tīmatanga (T₂)
Whakautu:
Q i tukuna = Q i whiwhi
Q tine = Q wai
m₁ c₁ ΔT = m₂ c₂ ΔT
(3)(1.400)(80-20) = (10)(4.200)(20-T)
(4.200)(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 wai tuatahi he 14^oC.
Ko te whakautu tika ko C.

15. Ka makahia he hukapapa he M karamu te taumaha i te pāmahana o te 0 ^° C ki roto i te wai he 340 karamu te taumaha i te pāmahana o te 20 ^° C, ka whakanohoia ki roto i tētahi oko motuhake. Me kī kāore te oko e mimiti/tuku i te wera. Mēnā ko te L _hukapapa = 80 karori karamu ^-1 , c _wai = 1 karori karamu ^{-1 o} C ^-1 , ka rewa katoa ngā hukapapa, ā, ka tutuki te taurite wera i te pāmahana o te 5 ^° C, ko te taumaha o te hukapapa (M) ko...

A. 60 karamu
B. 68 karamu
C. 75 karamu
D. 80 karamu
E. 170 karamu

Kōrero
E mōhiotia ana :
Taumaha o te wai (m) = 340 karamu
Te pāmahana hukapapa (T_es) = 0^oC
Suhu wai (T_rangi) = 20^oC
Te pāmahana taurite wera (T) = 5^oC
Te wera o te hanumitanga o te huka (L)_es) = 80 karori karamu^-1
Te wera motuhake o te wai (c_rangi) = 1 karori karamu^{-1 o}C^-1
I pātaihia Te taumaha o te huka (M)
Whakautu :

Te Kaupapa Pango e kī ana i roto i tētahi pūnaha kati motuhake, ko te wera e tukuna ana e tētahi mea pāmahana teitei he rite ki te wera e mimitihia ana e tētahi mea pāmahana iti.
Te wera i tukuna e te wai (Q i tukuna) = te wera i mimitia e te hukapapa (Q i mimitia)
m_rangi c_rangi (T) = m_es L_es +m_es c_rangi (T)
(340)(1)(20-5) = M (80) + M (1)(5-0)
(340)(15) = 80M + 5M
5100 = 85M
M = 5100/85
M = 60 karamu
Ko te whakautu tika ko A.

Tuhipoka:
Mena ka kīia he 0 te pāmahana o te hukapapa^o kei te totoka tonu te wai. Mēnā ka kīia ko te pāmahana o te wai he 0^oC, kātahi ka wai te āhua. Wehewehea te whakamahinga o ngā kupu hukapapa me te wai. Nā te mea kei te totoka tonu te wai, kei te hukapapa rānei, ko te wera e mimitihia ana ka whakamahia tuatahi hei whakarewa i te hukapapa katoa ki roto i te wai, nō reira, i te taha matau o te whārite i runga ake nei, ka tāpirihia he tātai hei tatau i te nui o te wera hei whakarewa i te hukapapa (m_es L_esKia rewa katoa te hukapapa hei wai, ka whakamahia he wera anō hei whakaara ake i te pāmahana o te hukapapa mai i te 0^oKa huri a C hei 5^oC.

Pūtake pātai:

Ngā Pātai Ahupūngao Whakamātautau ā-Motu mō te Kura Tuarua/Kura Tuarua Mahi-ā-ringa