Te pāmahana me te wera - ngā raruraru me ngā otinga

Te pāmahana me te wera - ngā raruraru me ngā otinga

1. I runga i te inemahana X, ko te pūwāhi tio o te wai i te -30^o me te pūwāhi koropupū o te wai i te 90^o. 60^OX = … ^oC.

Mōhiotia:

Te pūwāhi tio o te wai = -30^o

Te pūwāhi koropupū o te wai = 90^o

E hiahiatia ana: 60^oX = … ^oC

Rongoā:

I te tauine Fahrenheit, ko te pūwāhi tio o te wai he 32^oF, ā, ko te pūwāhi koropupū o te wai he 212^oF. I waenganui i te pūwāhi tio me te pūwāhi koropupū, 212^o - 32^o = 180^o.

I te tauine Celsius, ko te ira tio o te wai he 0^oC, ā, ko te pūwāhi koropupū o te wai he 100^oC. I waenganui i te pūwāhi tio me te pūwāhi koropupū, 100^o - 0^o = 100^o.

I te tauine X, ko te pūwāhi tio o te wai he -30^oX, ā, ko te pūwāhi koropupū o te wai he 90^oX. I waenganui i te pūwāhi tio me te pūwāhi koropupū, 90^o – (-30^o) = 90^o + 30^o = 120^o.

Hurihia te tauine X ki te tauine Celsius:

Te whakawhānui wera

2. He tokotoko whakarewa kua werahia mai i te 30^oC ki 80^oC. Ko te roa whakamutunga o te tokotoko he 115 cm. Ko te tauwehenga o whakawhanuitanga rārangi is 3.10^{-3 o}C^-1. He aha te roa tīmatanga o te tokotoko whakarewa?

Mōhiotia:

Te pāmahana tuatahi (T₁) = 30^oC

Te pāmahana whakamutunga (T₂) = 80^oC

Te huringa o te pāmahana (ΔT) = 80^oC - 30^oC=50^oC

Te tauwehenga o te whakawhānui raina (α) = 3.10^{-3 o}C^-1

Ko te roa whakamutunga o te konganuku (L) = 115 cm

E hiahiatia ana: Ko te roa tīmatanga o te tokotoko whakarewa (L_o)

Rongoā:

Ko te whārite o te whānui rārangi:

R = R_o + ΔL

R = R_o + α L_o ΔT

R = R_o (1 + α ΔT)

115 = R_o (1 + 3.10^-3.50)

115 = R_o (1 + 150.10^-3)

115 = R_o (1 + 0.15)

115 = R_o (1.15)

L_o = 115/1.15

L_o = 100cm

3. Ko te roa tīmatanga o te tokotoko parahi he 40 cm. I muri i te whakamahana, ko te roa whakamutunga o te parahi he 40.04 cm, ā, ko te pāmahana whakamutunga he 80^oC. Mena ko te tauwehenga whānui rārangi o te parahi he 2.0 x 10^{-5 o}C^-1, he aha te pāmahana tīmatanga o te tokotoko parahi?

Mōhiotia:

Te pāmahana whakamutunga (T₂) = 80^oC

Te roa tuatahi (L_o) = 40 henemita

Ko te roa whakamutunga (L) = 40.04 cm

Te pikinga o te roa (ΔL) = 40.04 cm – 40 cm = 0.04 cm

Te tauwehenga o te whakawhānui raina (α) = 2.0 x 10^{-5 o}C^-1

Rongoā: Te pāmahana tīmatanga (T₁)

Otinga;

Ko te whārite o te whānui rārangi:

R = R_o + α L_o ΔT

L – L_o = α L_o ΔT

ΔL = αL_o ΔT

ΔL = αL_o (T₂ - T₁)

0.04 = (2.0 x 10^-5)(40)(80 – T₁)

0..04 = (80 x 10^-5)(80 – T₁)

0.04 = 0.0008 (80 – T₁)

0.04 = 0.064 – 0.0008 T₁

0..0008 T₁ = 0.064 - 0.040

0.0008 T₁ = 0.024

T₁ = 30^oC

Te kawe wera

4. E rua ngā tokotoko whakarewa he rite te rahi engari he rerekē ngā momo, e whakaaturia ana i te pikitia i raro nei. Ko te kawe wera o te whakarewa I = 4 ngā wā o te kawe wera o te whakarewa II. He aha te pāmahana i waenganui i ngā whakarewa e rua.

Mōhiotia:

He rite tonu te rahi o ngā tokotoko e rua.

Ko te kawe wera o te konganuku I = 4k

Ko te kawe wera o te konganuku II = k

Ko te pāmahana o tētahi pito o te konganuku I = 50⁰ C

Ko te pāmahana o tētahi pito o te konganuku II = 0⁰ C

Hiahia: Te pāmahana i waenganui i ngā tokotoko whakarewa e rua

Rongoā:

Ko te whārite o te kawe wera:

Q/t = te tere o te kawe wera, k = te whakawhitinga taiao, A = te horahanga whakawhiti-wāhanga, T₁-T₂ = te huringa o te pāmahana, l = te roa o te tokotoko.

Te pāmahana i waenganui i ngā tokotoko e rua:

Ko te pāmahana i waenganui i ngā tokotoko whakarewa e rua he 40^oC.

5.

(1) Te kawe i te konganuku

(2) Te rerekētanga o te pāmahana

(3) Te roa o te konganuku

(4) Te taumaha o te konganuku

Ko ngā āhuatanga e whakatau ana i te tere o te kawe wera ki ngā konganuku ko…

Rongoā:

I runga i te whārite o te kawe wera, ko ngā āhuatanga e whakatau ana i te tere o te kawe wera ki runga i ngā konganuku ko te kawe wera o te konganuku (k), te rerekētanga o te pāmahana (T) me te roa o te konganuku (l).

6. E rua ngā tokotoko he rite te rahi engari he rerekē te momo, e whakaaturia ana i te pikitia i raro nei. Ko te kawe wera o te tokotoko P he 2 ngā wā o te kawe wera o te tokotoko Q. He aha te pāmahana i waenganui i ngā tokotoko e rua.

Mōhiotia:

He rite te rahi o ngā tokotoko e rua.

Te kawe wera o te tokotoko P (k)_P) = 2k

Ko te kawe wera o te tokotoko Q (k_Q) = k

Hiahia: Te pāmahana i waenganui i ngā tokotoko e rua

Rongoā:

Ko te whārite o te kawe wera:

Q/t = te tere o te kawe wera, k = te whakawhitinga taiao, A = te horahanga whakawhiti-wāhanga, T₁-T₂ = te huringa o te pāmahana, l = te roa o te tokotoko.

Ko te pāmahana i waenganui i ngā tokotoko e rua:

Kaupapa pango

8. 100 karamu hinu i te 20^oC me te rino 50-karamu i te 75 ^oKa whakanohoia ngā C ki roto i tētahi ipu rino 200-karamu. Ko te pikinga o te pāmahana o te ipu he 5^oC, ā, ko te wera motuhake o te hinu he 0.43 cal/g ^oC. He aha te wera motuhake o te rino?

Mōhiotia:

Taumaha o te ipu rino (m) = 200 karamu

Ko te pāmahana tīmatanga o te ipu rino (T₁) = te pāmahana o te hinu = 20^oC

Ko te pāmahana whakamutunga o te ipu rino (T₂) = 20^oC + 5^oC=25^oC

Taumaha o te hinu (m) = 100 karamu

Ko te wera motuhake o te hinu (c_hinu) = 0.43 karori/karamu ^oC

Te pāmahana tīmatanga o te hinu (T₁) = 20^oC

Te pāmahana whakamutunga o te hinu (T₂) = 20^oC + 5^oC=25^oC

Taumaha o te rino (m) = 50 karamu

Te pāmahana tīmatanga o te hinu (T₁) = 75^oC

Te pāmahana whakamutunga o te hinu (T₂) = 25^oC

E hiahiatia ana: Te wera motuhake o te rino (c rino)

Rongoā:

Te wera i tukuna e te rino:

Q = mc ΔT = (50)(c)(75-25) = (50)(c)(50) = 2500c kaora

Te wera e mimitia ana e te ipu rino:

Q = mc ΔT = (200)(c)(25-20) = (200)(c)(5) = 1000c kaora

Te wera e mimitia ana e te hinu:

Q = mc ΔT = (100)(0.43)(25-20) = (43)(5) = 215 kaora

E mea ana te mātāpono pango, i roto i tētahi pūnaha motuhake, ka mimitia te wera e te mea wera ake, ka mimitia e te mea mātao ake.

Tukunga Q = mimitinga Q

2500c = 1000c + 215

2500c – 1000c = 215

1500c = 215

c = 215/1500

c = 0.143 karori/karamu ^oC

9. He wai 200-karamu i te 20°C kua whakanohoia ki roto i te hukapapa 50-karamu i te -2°C. Mena kei waenganui noa i te wai me te hukapapa te huringa wera, he aha te pāmahana whakamutunga o te ranunga? Ko te wera motuhake o te wai he 1 cal/gr°C, ko te wera motuhake o te hukapapa he 0.5 cal/gr°C, ko te wera o te hanumitanga mō te hukapapa he 80 cal/gr.

Mōhiotia:

Te taumaha o te wai (m_wai) = 200 karamu

Te pāmahana o te wai (T_wai) = 20^oC

Ko te wera motuhake o te wai (c_wai) = 1 karori/gr°C

Te taumaha o te huka (m_tio) = 50 karamu

Te pāmahana o te huka (T_tio) = -2^oC

Ko te wera motuhake o te hukapapa (c_tio) = 0.5 karori/gr°C

Ko te wera o te hanumitanga mō te hukapapa (L) = 80 karori/karamu

Rongoā:

Ka whakanuia te hukapapa e te wera mai i te -2^oC ki 0^oC:

Q = mc ΔT

Q = (50 karamu)(0.5 karori/karamu°C)(0^oC – (-2^oC))

Q = (50)(0.5 karori)(2)

Q = 50 karori

Te wera hei whakarewa i ngā huka katoa:

Q = m L = (50 karamu)(80 karori/karamu) = 4000 karori

Whakamahana hei whakaiti i te pāmahana o te wai katoa mai i te 20^oC ki 0^oC:

Q = mc ΔT

Q = (200 karamu)(1 karori/karamu°C)(0^oC – (20^oC))

Q = (200)(1 karori)(-20)

Q = -4000 kaora

Ko te tohu tāpiri e tohu ana kua tāpirihia te wera, ko te tohu tango e tohu ana kua tukuna te wera.

50-karori o te wera e hiahiatia ana hei whakanui ake i te pāmahana o te hukapapa ki te 0^oC me te 4000-karori e hiahiatia ana hei whakarewa i te hukapapa katoa. Ko te wera katoa = 4050 karori. Ko te wera e tukuna ana e te wai he 4000 karori.

Kāore ētahi o te huka e rewa, nō reira ko te pāmahana whakamutunga o te huka me te wai he 0.^oC.

10. He konumohe 200-karamu i te 20^oC i roto i te 100 karamu wai i te 80^oC i roto i tētahi ipu. Ko te wera motuhake o te konumohe he 0.22 cal/g ^oC, ā, ko te wera motuhake o te wai he 1 cal/g ^oC. He aha te pāmahana whakamutunga o te konumohe?

Mōhiotia:

Taumaha o te konumohe = 200 karamu

Te pāmahana o te konumohe = 20^oC

Taumaha o te wai = 100 karamu

Te pāmahana wai = 80^oC

Ko te wera motuhake o te konumohe = 0.22 karori/karamu ^oC

Ko te wera motuhake o te wai = 1 cal/g ^oC

Hiahia: Te pāmahana whakamutunga o te konumohe

Rongoā:

Kei roto te konumohe me te wai i te taurite wera, nō reira ko te pāmahana whakamutunga o te konumohe = te pāmahana whakamutunga o te wai.

Te wera e tukuna ana e te wai wera (tukunga Q) = te wera e mimitia ana e te konumohe (te mimitia Q)

m_wai c (ΔT) = m_konumohe c (ΔT)

(100)(1)(80 – T) = (200)(0.22)(T – 20)

(100)(80 – T) = (44)(T – 20)

8000 – 100T = 44T – 880

8000 + 880 = 44T + 100T

8880 = 144T

T = 62^oC

11. I whakanohoia he konganuku 50-karamu i te 85 °C ki roto i te wai 50 karamu i te 29.8 °C. Ko te wera motuhake o te wai = 1 cal.g ^-1 .°C^-1Ko te pāmahana whakamutunga he 37 °C. He aha te wera motuhake o te konganuku?

Mōhiotia:

Papatipu o te konganuku (m_whakarewa) = 50 karamu

Te pāmahana o te konganuku = 85^oC

Te taumaha o te wai (m_wai) = 50 karamu

Te pāmahana wai = 29,8^oC

Ko te wera motuhake o te wai (c_wai) = 1 karori ^-1 .°C^-1

Ko te pāmahana whakamutunga o te wai = 37^oC

E hiahiatia ana: Te wera motuhake o te konganuku (c konganuku)

Rongoā:

Te wera e tukuna ana e te konganuku wera (tukunga Q) = te wera e mimitia ana e te wai (te wera e mimitia ana e te Q)

m_whakarewa c (ΔT) = m_wai c (ΔT)

(50)(c)(85 – 37) = (50)(1)(37 – 29.8)

(c)(85 – 37) = (1)(37 – 29.8)

48 c = 7.2

c = 0.15 karori karamu ^-1 .°C^-1

12. He poraka hukapapa he 50 karamu te taumaha i te 0°C me te 200 karamu wai i te 30°C, kua whakanohoia ki roto i tētahi ipu. . Mena ko te wera motuhake o te wai he 1 karori karamu^{- 1} ° C ^-1 ā, ko te wera o te hanumitanga mō te huka he 80 karori karamu ^-1. He aha te pāmahana whakamutunga o te ranunga?

Mōhiotia:

Te taumaha o te huka (m_tio) = 50 karamu

Te pāmahana o te hukapapa = 0°C

Te taumaha o te wai (m_wai) = 200 karamu

Te pāmahana wai = 30^oC

Ko te wera motuhake o te wai (c_wai) = 1 karori^{- 1} ° C ^-1

Ko te wera o te hanumitanga mō te hukapapa (L_tio) = 80 karori ^-1

Hiahia: Te pāmahana whakamutunga

Rongoā:

Whakatauhia te āhua whakamutunga:

Te wera e tukuna ana e te wai hei whakaiti i tōna pāmahana mai i te 30^oC ki 0^oC:

Q_tuku = m_wai c_wai (ΔT) = (200)(1)(30-0) = (200)(30) = 6000

Te wera e hiahiatia ana hei whakarewa i ngā huka katoa:

Q = m_tio L_tio= (50)(80) = 4000

Ko te wera e whakamahia ana hei whakarewa i ngā huka katoa he 4000, ko te wera e tukuna ana e te wai he 6000. Ka taea te whakatau ko te pāmahana whakamutunga o te ranunga kei runga ake i te 0.^oC.

Te mātāpono pango:

Te wera i tukuna e te wai = te wera hei rewa i ngā hukapapa katoa + te wera hei whakanui ake i te pāmahana o te hukapapa.

(m_wai)(c_wai)(ΔT) = (m_tio)(R_tio) + (m_tio)(c_wai)(ΔT)

(200)(1)(30-T) = (50)(80) + (50)(1)(T-0)

(200)(30-T) = (50)(80) + (50)(T-0)

6000 – 200T = 4000 + 50T – 0

6000 – 4000 = 50T + 200T

2000 = 250T

T = 2000/250

T = 8^oC