Tauira o ngā Pātai Kōrero mō te Calorimetry
I roto i te ahupūngao, ko te ine wera he peka pūtaiao e ako ana i te ine i te wera i roto i ngā tauhohenga matū, i ngā huringa ā-tinana rānei. Ko te taputapu e whakamahia ana hei ine i te nui o te wera ka kiia he ine wera. He mahi nui tā te ine wera, inā koa i roto i te thermodynamics me te matū ā-tinana, te wāhi e tirohia ai, e inehia ai ngā huringa o te pūngao wera.
Ngā Mātāpono Taketake o te Calorimetry
Ko te kaupapa matua o te ine ine taumaha e ahu mai ana i te ture tiaki pūngao, arā, kāore e taea te hanga, te whakangaro rānei i te pūngao, engari ka taea anake te whakarerekē mai i tētahi momo pūngao ki tētahi atu. I roto i te horopaki o te ine taumaha, me ōrite te pūngao wera e ngaro ana i te pūnaha ki te pūngao wera e mimitihia ana e te taiao. Ko te taputapu matua i roto i ngā whakamātautau ine taumaha he ine taumaha, ka taea te ine taumaha ngāwari, arā, he ine taumaha wai, he ine taumaha uaua ake rānei, pērā i te ine taumaha poma.
Ngā Tātai Calorimetry Taketake
Ko te tauira taketake o te ine ine karori ko:
\[ Q = m \cdot c \cdot \Delta T \]
kāore i te mana:
– Ko te \( Q \) te nui o te wera (i roto i ngā joule, i ngā kaora rānei)
– Ko te \( m \) te papatipu o te matū (i roto i te karamu, i te kirokaramu rānei)
– Ko te wera motuhake o te matū ko te \( c \) (i roto i te J/(g°C) cal/(g°C) rānei)
– Ko te huringa o te pāmahana (i roto i te °C) \( \Delta T \)
Me titiro tātou ki ētahi tauira pātai me ngā kōrerorero kia pai ake ai te mārama ki te ariā me te whakamahinga o te ine karori.
Ngā Pātai Tauira me te Kōrero 1
Pātai:
Ka whakamahanahia he konganuku 200 karamu te taumaha ki te 100°C, kātahi ka tōia ki roto i te 100 karamu wai i te 20°C. Ko te pāmahana whakamutunga o te ranunga he 27°C. Tātaihia te wera motuhake o te konganuku! (te wera motuhake o te wai = 4,18 J/(g°C))
Kōrero:
Ko te taahiraa tuatahi ko te tatau i te wera e mimitihia ana e te wai. Mā te whakamahi i te tātai taketake:
\[ Q_{\text{air}} = m_{\text{air}} \cdot c_{\text{air}} \cdot \Delta T_{\text{air}} \]
Me te \( m_{\text{air}} = 100 \) karamu, \( c_{\text{air}} = 4.18 \) J/(g°C), me te \( \Delta T_{\text{air}} = 27°C – 20°C = 7°C \),
\[ Q_{\text{air}} = 100 \times 4.18 \times 7 = 2926 \text{ J} \]
He rite tonu te wera e tukuna ana e te konganuku ki te wera e mimitia ana e te wai, nō reira:
\[ Q_{\text{konganuku}} = 2926 \text{ J} \]
Mā te whakamahi i te tātai wera:
\[ m_{\text{whakarewa}} \cdot c_{\text{whakarewa}} \cdot \Delta T_{\text{whakarewa}} = Q_{\text{whakarewa}} \]
me te \( m_{\text{metal}} = 200 \) karamu, \(\Delta T_{\text{metal}} = 100°C – 27°C = 73°C \),
\[ 200 \cdot c_{\text{metal}} \cdot 73 = 2926 \text{ J} \]
\[ c_{\text{konganuku}} = \frac{2926}{200 \times 73} \]
\[ c_{\text{konganuku}} = 0.2 \text{ J/(g°C)} \]
Nō reira, ko te wera motuhake o te konganuku he 0.2 J/(g°C).
Ngā Pātai Tauira me te Kōrero 2
Pātai:
Ka whakanohoia he poraka hukapapa he 50 karamu te taumaha i te pāmahana o te 0°C ki roto i te 200 karamu o te wai i te pāmahana o te 30°C i roto i te ine wera. Tātaihia te pāmahana whakamutunga o te ranunga i muri i te taenga ki te taurite wera! (te wera o te hanumitanga o te hukapapa = 334 J/g, te wera motuhake o te wai = 4,18 J/g°C)
Kōrero:
Ko te taahiraa tuatahi ko te tatau i te wera e hiahiatia ana hei whakarewa i te huka:
\[ Q_{\text{melt}} = m_{\text{es}} \cdot L \]
me te \( m_{\text{es}} = 50 \) karamu me te \( L = 334 \) J/g,
\[ Q_{\text{rewa}} = 50 \times 334 = 16700 \text{ J} \]
Muri iho, kimihia te wera e mimitihia ana e te hukapapa i muri i te rewa kia tae atu ki te pāmahana whakamutunga \( T \) (mehemea ko T te pāmahana whakamutunga o te ranunga):
\[ Q_{\text{wai hukapapa}} = m_{\text{es}} \cdot c_{\text{hau}} \cdot (T – 0°C) \]
me \( c_{\text{air}} = 4.18 \text{ J/g°C} \),
\[ Q_{\text{wai hukapapa}} = 50 \times 4.18 \times T \]
Te wera i tukuna e te wai matao (mai i te 30°C ki te T):
\[ Q_{\text{air}} = m_{\text{air}} \cdot c_{\text{air}} \cdot (30°C – T) \]
me te \( m_{\text{air}} = 200 \) karamu,
\[ Q_{\text{air}} = 200 \times 4.18 \times (30 – T) \]
I te taurite wera, ko te nui o te wera e mimitihia ana e te hukapapa (ka rewa, ka wera ki te T) ka rite ki te nui o te wera e tukuna ana e te wai:
\[ Q_{\text{rewa}} + Q_{\text{wai hukapapa}} = Q_{\text{wai}} \]
\[ 16700 + 50 \times 4.18 \times T = 200 \times 4.18 \times (30 – T) \]
\[ 16700 + 209T = 8360 \times (30 – T) \]
\[ 16700 + 209T = 250800 – 8360T \]
\[ 8569T = 234100 \]
\[ T = \frac{234100}{8569} \tata ki te 27.3°C \]
Nō reira, ko te pāmahana whakamutunga o te ranunga i muri i te taenga ki te taurite wera he tata ki te 27.3°C.
Whakamutunga
He tikanga nui te ine wera i roto i te ahupūngao me te matū e whakamahia ana hei whakatau i te nui o te pūngao wera i roto i tētahi tukanga ā-tinana, ā-matū rānei. Mā te whakamahi i ngā mātāpono me ngā tauira taketake o te ine wera, ka taea e tātou te tatau i ngā tawhā rerekē pērā i te wera motuhake o tētahi matū, te huringa o te pāmahana, te pūngao rānei e mimitihia/e tukuna ana i roto i tētahi tukanga. I roto i tēnei tuhinga, kua tirohia e tātou ngā tauira rapanga me ā rātou otinga i roto i te horopaki o te mārama ki te ine wera. He mea nui te mārama pai ki ēnei ariā hei whakaoti rapanga i ngā momo rapanga thermodynamic me ētahi atu tono mahi.
