1. Ma'anar ƙa'idar Baƙar fata
Idan muka haɗa ruwan zafi da sanyi a cikin akwati a buɗe (misali bokiti), zafi yana canjawa daga ruwan zafi zuwa ruwan sanyi. Saboda akwatin a buɗe yake, to wani zafi yana motsawa zuwa iska. Akwatin kuma yana ɗumi. Zafin da ruwan zafi ke fitarwa ba wai kawai ruwan sanyi yake sha ba, har ma yana sha ta yanayi da kwantena. A wannan yanayin, bokiti tsarin da ba a keɓe shi ba ne. Idan muka haɗa ruwan zafi da sanyi a cikin thermos ɗin da aka rufe, zafi yana canjawa daga ruwan zafi zuwa ruwan sanyi. Thermos tsarin da aka keɓe ne, don haka babu zafi da ke motsawa cikin iska ko thermos. Ruwan sanyi yana sha kawai zafin da ruwan zafi ke fitarwa har sai cakuda ruwan zafi da ruwan sanyi ya kai daidaiton zafi.
Dokar Baƙi ta bayyana cewa a cikin tsarin rufewa da aka keɓe, zafi da wani abu mai zafi mai yawa ke fitarwa = zafi da wani abu mai ƙarancin zafin jiki ke sha.
2. Tsarin ƙa'idar baƙar fata
Sakin Q = Sha Q
Sakin Q = zafi da abubuwa masu zafi sosai ke fitarwa, sha Q = zafi da abubuwa masu ƙarancin zafi ke sha.
3. Misalan tambayoyi da tattaunawa
Misalin matsala ta 1.
Ana saka ƙarfe mai zafi mai nauyin kilogiram 1 da zafin jiki na 100 oC a cikin akwati mai ɗauke da kilogiram 2 na ruwa da zafin jiki na 20 oC . Menene zafin haɗin ƙarshe? Takamaiman zafin ƙarfe = 450 J/kg C o , takamaiman zafin ruwa = 4200 J/kg C o.
An sani:
Nauyin ƙarfe (m) = 1 kg
Zafin ƙarfe (T) = 100 oC
Nauyin ruwa (m) = 2 kg
Zafin ruwa (T) = 20 oC
Takamaiman zafi ga ƙarfe (c) = 450 J/kg C o
Takamaiman zafi ga ruwa (c) = 4200 J/kg C o
Ana so: T?
Magani:
Iron yana da zafi fiye da ruwa, don haka ƙarfe yana fitar da zafi, ruwa yana shan zafi.
Sakin Q = Sha 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 o C
Zafin ƙarshe na cakuda ƙarfe mai zafi da ruwan sanyi idan duka biyun suna cikin ma'aunin zafi shine 24 oC.
Misalin matsala ta 2.
Nauyin kankara 0.2 kg a gauraya da shayi mai dumi tare da nauyin kilogiram 0.2. Zafin ice = -10 oC , zafin shayi mai dumi = 40 oC . Takamammen zafin ice = 2100 J/kg C o , takamaiman zafin ruwa = 4200 J/kg C o , zafin haɗuwa don ruwa = 334000 J/kg. Ana haɗa kankara da shayi a cikin tsarin da aka keɓe, a rufe.
An sani:
Nauyin kankara (m) = 0.2 kg
Nauyin shayi (m) = 0.2 kg
Takamaiman zafin ruwa (c) = 4180 J/kg C o
Takamaiman zafin kankara (c) = 2100 J/kg C o
Zafin haɗa ruwa (L F ) = 334 x 10 3 J/kg
Zafin kankara (T kankara ) = -10 oC
Zafin shayi (T shayin ) = 40 oC
Ana so: Cakuda T
Magani:
Mataki na farko, kimanta yanayin ƙarshe
Zafin da dole ne a saki ta ruwa don rage zafin 0.2 kg na shayi mai dumi, daga 40 oC zuwa 0 oC
Sakin Q = mc ∆T
Sakin Q = (0.2 kg) (4180 J/Kg C o ) (40 o C – 0 o C)
Sakin Q = (0.2 kg) (4180 J/Kg C o ) (40 o C)
Sakin Q = Joule 33,440
Sakin Q = 33.44 kJ
Ana sha zafi ta hanyar 0.2 kg na kankara don ƙara zafin jiki daga -10 oC zuwa 0 oC
Q da aka sha = mc ∆T
Q da aka sha = (0.2 kg) (2100 J/Kg C o ) (0 o C – (-10 o C))
Q da aka sha = (0.2 kg) (2100 J/Kg C o ) (10 o C)
Q da aka sha = Joule 4,200
Q da aka sha = 4.2 kJ
Zafin da ake sha don narke 0.2 kg na kankara (zafin da ake buƙata don narke dukkan kankara zuwa ruwa)
Haɗin Q = m L F
Haɗin Q = (0.2 kg) (334 x 10 3 J/kg)
Haɗin Q = 66.8 x 10 Joule 3
Haɗin Q = 66.8 kJ
Dangane da lissafin da ke sama, sakamakon:
Sakin Q = 33.44 kJ
Shafar Q = 4.2 kJ
Haɗin Q = 66.8 kJ
Idan shayin ya fitar da zafi har zuwa 33.44 kJ, zafin shayin yana canzawa daga 40 oC zuwa 0 oC . Ana amfani da wani zafi da aka saki (kimanin 4.2 kJ) don ɗaga zafin kankara daga -10 oC zuwa 0 oC . 33.44 kJ – 4.2 kJ = 29.24 kJ. Sauran zafi = 29.24 kJ. Don narke dukkan kankara zuwa ruwa yana buƙatar zafi na 66.8 kJ. Sauran zafi shine 29.24 kJ kawai.
A ƙarshe, ana amfani da zafin da shayin ɗumi ke fitarwa ne kawai don ɗaga zafin kankara daga -10 oC zuwa 0 oC sannan a narkar da wasu kankara. Wasu kankara sun narke zuwa ruwa; wasu kuma ba su narke ba. A lokacin canza wani abu mai tauri zuwa ruwa, zafin ba ya canzawa. Saboda haka, zafin cakuda na ƙarshe = 0 oC.
Misalin matsala ta 3.
nauyin shayi mai zafi (m) = 0.4 kg,
nauyin kankara (m) = 0.2 kg,
zafin kankara = -10 oC
zafin shayi mai zafi = 90 oC.
Idan duka biyun sun haɗu, menene zafin cakuda na ƙarshe?
Takamaiman zafin ruwa (c) = 4180 J/kg C o ,
Takamaiman zafin kankara (c) = 2100 J/kg C o ,
Zafin haɗa ruwa (L F ) = 334 x 103 J/kg
Magani:
Mataki na farko: Kimanta yanayin ƙarshe
Zafin da dole ne a saki ta ruwa don rage zafin 0.4 kg na shayi mai zafi, daga 90 o C zuwa 0 o C
Sakin Q = mc ∆T
Sakin Q = (0.4 kg) (4180 J/Kg C o ) (90 o C – 0 o C)
Sakin Q = (0.4 kg) (4180 J/Kg C o ) (90 o C)
Sakin Q = Joule 150,480
Sakin Q = 150.48 kJ
Zafin da kilogiram 0.2 na kankara ke sha don ƙara zafinsa daga -10 oC zuwa 0 oC
Q da aka sha = mc ∆T
Q da aka sha = (0.2 kg) (2100 J/Kg C o ) (0 o C – (-10 o C))
Q da aka sha = (0.2 kg) (2100 J/Kg C o ) (10 o C)
Q da aka sha = Joule 4,200
Q da aka sha = 4.2 kJ
Zafin da ake buƙata don narke 0.2 kg na kankara (zafin da ake buƙata don mayar da dukkan kankara zuwa ruwa)
Haɗin Q = m L F
Haɗin Q = (0.2 kg) (334 x 10 3 J/Kg)
Haɗin Q = 66.8 x 10 Joule 3
Haɗin Q = 66.8 kJ
Dangane da lissafin da ke sama, sakamakon:
Sakin Q = 150.48 kJ
Q da aka sha = 4.2 kJ
Haɗin Q = 66.8 kJ
Lokacin da shayin zafi ya fitar da zafi 150.48 kJ, zafin shayin mai zafi ya canza daga 90 oC zuwa 0 oC . An yi amfani da wani zafi da aka saki (kimanin 4.2 kJ) don ɗaga zafin kankara daga -10 oC zuwa 0 oC.
150.48 kJ – 4.2 kJ = 146.28 kJ. Sauran zafi = 146.28 kJ.
Zafin da ake buƙata don narke dukkan kankara zuwa ruwa shine 66.8 kJ kawai. 146.28 kJ – 66.8 kJ = 79.48 kJ. Ya bayyana cewa abin da ya wuce shi ne 79.48 kJ. Shayin zafi ba ya fitar da dukkan zafi har sai an rage zafin zuwa 0 oC . Kammalawa: zafin cakuda na ƙarshe dole ne ya fi 0 oC.
Mataki na Biyu: Ƙayyade zafin jiki na ƙarshe (T)
Zafin da ake buƙata don ƙara zafin kankara daga -10 o C zuwa 0 o C = Joules 4200
Zafin dole ne ya narke dukkan kankara zuwa ruwa wanda aka fi sani da zafi mai ɓoye = Joules 66,800
Zafin ya ƙara zafin ruwan (ruwan da ke fitowa daga dukkan haɗakar ƙanƙara) daga 0 o C zuwa T = (ƙanshin ƙanƙara) (zafin ruwa) (T – 0 o C) = (0.2 kg) (4180 J/kg C o )(T) = (836 T) J/C o
Zafin da shayin ɗumi ke fitarwa don rage zafin jiki daga 90 oC zuwa T = (tarin ruwan zafi) (nau'in ruwan zafi) (90 oC – T) = (0.4 kg) (4180 J/kg C o ) (90 oC – T) = 1672 J/C o (90 oC – 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 o C
Zafin ƙarshe = 31.7 oC
