1. Te Whakamāramatanga o te Mātāpono Pango
Ki te whakaranua e tātou te wai wera me te wai matao ki roto i tētahi ipu tuwhera (hei tauira, he peere), ka whakawhitia te wera mai i te wai wera ki te wai matao. Nā te mea he tuwhera te ipu, ka nekehia ētahi wera ki te hau. Ka mahana ake hoki te ipu. Ehara i te mea ka mimitia te wera e tukuna ana e te wai wera e te wai matao anake, engari ka mimitia hoki e te hau me ngā ipu. I tēnei wā, he pūnaha kore-motuhake te peere. Ina whakaranua e tātou te wai wera me te wai matao ki roto i tētahi termos kua kati, ka whakawhitia te wera mai i te wai wera ki te wai matao. He pūnaha motuhake ngā termos, nō reira kāore he wera e neke ki te hau, ki te termos rānei. Ka mimitia noa e te wai matao te wera e tukuna ana e te wai wera kia tae rā anō te ranunga o te wai wera me te wai matao ki te taurite wera.
E ai ki te Mātāpono Pango, i roto i tētahi pūnaha kati motuhake, ko te wera e tukuna ana e tētahi mea pāmahana-tiketike he wera e mimitihia ana e tētahi mea pāmahana-iti.
2. Tātai mātāpono pango
Tukunga Q = mimitinga Q
Tukunga Q = te wera e tukuna ana e ngā mea pāmahana teitei, mimitinga Q = te wera e mimitia ana e ngā mea pāmahana iti.
3. Ngā tauira o ngā pātai me ngā kōrero
Tauira o te raruraru 1.
Ka whakanohoia he rino wera, he 1 kg te taumaha, ā, he 100 ° C te pāmahana, ki roto i tētahi ipu kei roto ko te 2 kg o te wai, ā, he 20 ° C te pāmahana. He aha te pāmahana o te ranunga whakamutunga? Ko te wera motuhake o te rino = 450 J/kg C o , ko te wera motuhake o te wai = 4200 J/kg C o.
Mōhiotia:
Taumaha o te rino (m) = 1 kg
Te pāmahana o te rino (T) = 100 ° C
Taumaha o te wai (m) = 2 kg
Te pāmahana o te wai (T) = 20 ° C
Te wera motuhake mō te rino (c) = 450 J/kg C o
Te wera motuhake mō te wai (c) = 4200 J/kg C o
E hiahiatia ana: T?
Rongoā:
He teitei ake te pāmahana o te rino i te wai, nō reira ka tukuna te wera e te rino, ka mimiti te wera e te wai.
Tukunga Q = mimitinga Q
mc ΔT = mc ΔT
(1)(450)(100-T) = (2)(4200)(T-20)
(450)(100-T) = (8400)(T-20)
45000 – 450T = 8400 T – 168000
45000 + 168000 = 8400 T + 450 T
213000 = 8850 T
T = 213000 : 8850
T = 24 ° C
Ko te pāmahana whakamutunga o te ranunga o te rino wera me te wai matao ina noho tahi rāua i te taurite wera ko 24 ° C.
Tauira o te putanga 2.
0.2 kg te papatipu hukapapa i konatunatua ki te tī mahana he 0.2 kg te papatipu. Te pāmahana o te hukapapa = -10 ° C, 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 mō te wai = 334000 J/kg. Ka konatunatua te hukapapa me te tī ki roto i tētahi pūnaha motuhake, kati.
Mōhiotia:
Taumaha o te huka (m) = 0.2 kg
Taumaha o te tī (m) = 0.2 kg
Te wera motuhake o te wai (c) = 4180 J/kg C o
Te wera motuhake o te hukapapa (c) = 2100 J/kg C o
Te wera o te hanumitanga mō te wai (L F ) = 334 x 103 J /kg
Te pāmahana o te huka (T huka ) = -10 ° C
Te pāmahana o te tī (T tī ) = 40 ° C
E hiahiatia ana: Ranunga T
Rongoā:
Te taahiraa tuatahi, whakatau tata i te āhua whakamutunga
Ko te wera me tuku e te wai hei whakaiti i te pāmahana o te 0.2 kg o te tī mahana, mai i te 40°C ki te 0°C.
Tukunga Q = mc ∆T
Tukunga Q = (0.2 kg) (4180 J/Kg C o ) (40 o C – 0 o C)
Tukunga Q = (0.2 kg) (4180 J/Kg C o ) (40 C )
Tukunga Q = 33,440 Joule
Tukunga Q = 33.44 kJ
Ka mimitia te wera e te 0.2 kg o te hukapapa hei whakanui ake i te pāmahana mai i te -10 ° C ki te 0 ° C.
Q mimiti = mc ∆T
Q i mimitia = (0.2 kg) (2100 J/Kg C o ) (0 o C – (-10 o C))
Q i mimitia = (0.2 kg) (2100 J/Kg C o ) (10 o C)
Q mimiti = 4,200 Joule
Q i mimitia = 4.2 kJ
Te wera e mimitia ana hei whakarewa i te 0.2 kg o te hukapapa (te wera e hiahiatia ana hei whakarewa i ngā hukapapa katoa ki roto i te wai)
Q fusion = m L F
Te hanumitanga Q = (0.2 kg) (334 x 103 J /kg)
Te hanumitanga Q = 66.8 x 103 Joule
Te hanumitanga Q = 66.8 kJ
I runga i ngā tātaitanga o runga ake nei, ko ngā hua:
Tukunga Q = 33.44 kJ
Q mimiti = 4.2 kJ
Te hanumitanga Q = 66.8 kJ
Ina tukuna te wera e te tī ki te 33.44 kJ, ka huri te pāmahana o te tī mai i te 40 ° C ki te 0 ° C. Ko tētahi wera e tukuna ana (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. Ko te wera e toe ana = 29.24 kJ. Hei whakarewa i te hukapapa katoa ki te wai, me whakamahi he wera 66.8 kJ. Ko te wera e toe ana he 29.24 kJ anake.
Hei whakamutunga, ko te wera e tukuna ana e te tī mahana ka whakamahia hei whakaara ake i te pāmahana hukapapa mai i te -10 ° C ki te 0 ° C, hei whakarewa hoki i ētahi hukapapa. Kua rewa ētahi hukapapa hei wai; ko ētahi kāore. I te tukanga hurihanga o te totoka hei wai, kāore te pāmahana e rerekē. Nō reira, ko te pāmahana o te ranunga whakamutunga = 0 ° C.
Tauira o te raruraru 3.
te taumaha o te tī wera (m) = 0.4 kg,
te papatipu o te huka (m) = 0.2 kg,
te pāmahana o te hukapapa = -10 ° C
te pāmahana o te tī wera = 90 ° C.
Mena ka konatunatua ngā mea e rua, he aha te pāmahana o te ranunga whakamutunga?
Ko te wera motuhake mō te wai (c) = 4180 J/kg C o ,
Ko te wera motuhake mō te hukapapa (c) = 2100 J/kg C o ,
Te wera o te hanumitanga mō te wai (L F ) = 334 x 103 J/kg
Rongoā:
Hipanga tuatahi: Whakatau tata i te āhua whakamutunga
Ko te wera me tuku e te wai hei whakaiti i te pāmahana o te 0.4 kg o te tī wera, mai i te 90 ° C ki te 0 ° C.
Tukunga Q = mc ∆T
Tukunga Q = (0.4 kg) (4180 J/Kg C o ) (90 o C – 0 o C)
Tukunga Q = (0.4 kg) (4180 J/Kg C o ) (90 C )
Tukunga Q = 150,480 Joule
Tukunga Q = 150.48 kJ
Ko te wera e mimitihia ana e te 0.2 kg o te hukapapa hei whakanui ake i tōna pāmahana mai i te -10 ° C ki te 0 ° C
Q mimiti = mc ∆T
Q i mimitia = (0.2 kg) (2100 J/Kg C o ) (0 o C – (-10 o C))
Q i mimitia = (0.2 kg) (2100 J/Kg C o ) (10 o C)
Q mimiti = 4,200 Joule
Q i mimitia = 4.2 kJ
Te wera e hiahiatia ana hei whakarewa i te 0.2 kg o te hukapapa (te wera e hiahiatia ana hei huri i ngā hukapapa katoa hei wai)
Q fusion = m L F
Te hanumitanga Q = (0.2 kg) (334 x 103 J /Kg)
Te hanumitanga Q = 66.8 x 103 Joule
Te hanumitanga Q = 66.8 kJ
I runga i ngā tātaitanga o runga ake nei, ko ngā hua:
Tukunga Q = 150.48 kJ
Q i mimitia = 4.2 kJ
Te hanumitanga Q = 66.8 kJ
I te tukunga o te wera o te tī wera i te 150.48 kJ, ka huri te pāmahana o te tī wera mai i te 90 ° C ki te 0 ° C. Ko ētahi wera i tukuna (tata ki te 4.2 kJ) i whakamahia hei whakaara ake i te pāmahana hukapapa mai i te -10 ° C ki te 0 ° C.
150.48 kJ – 4.2 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. I kitea ko te nui rawa he 79.48 kJ. Kāore te tī wera e tuku i te wera katoa kia heke rā anō te pāmahana ki te 0 ° C. Whakatau: me nui ake te pāmahana o te ranunga whakamutunga i te 0 ° C.
Hipanga Tuarua: Whakatauhia te pāmahana whakamutunga (T)
Ko te wera e hiahiatia ana hei whakanui ake i te pāmahana hukapapa mai i te -10 ° C ki te 0 ° C = 4200 Joules
Nā te wera i whakarewa ngā huka katoa ki roto i te wai, arā, te wera huna = 66,800 Joules
Nā te wera i whakapiki ake te pāmahana o te wai (te wai mai i te hanumitanga hukapapa katoa) mai i te 0 ° C ki te T = (papatipu hukapapa) (wera o te wai) (T – 0 ° C) = (0.2 kg) (4180 J/kg C o )(T) = (836 T) J/C o
Ko te wera i tukuna e te tī mahana hei whakaiti i te pāmahana mai i te 90 ° C ki te T = (papatipu o te wai wera) (momo wera o te wai) (90 ° C – T) = (0.4 kg) (4180 J/kg C o ) (90 ° C – T) = 1672 J/C o (90 ° C – T) = 150,480 J – (1672 T) J/C o
4200 J + 66,800 J + (836 T) J/C o = 150,480 J – (1672 T) J/C o
71,000 J + (836 T) J/C o = 150,480 J – (1672 T) J/C o
(836 T) J/C o + (1672 T) J/C o = 150,480 J – 71,000 J
(2508 T) J/C o = 79,480 J
T = 31.7 ° C
Te pāmahana whakamutunga = 31.7 o C
