Nā nīnau hoʻohālike o ke Kumumanaʻo ʻEleʻele

15 mau laʻana o nā nīnau kumu o Black

1. Ua hui ʻia ka hau he 0,2 kg ke kaumaha me ke kī mehana he 0,2 kg ke kaumaha. ʻO ka mahana o ka hau = – 10^oC, mahana kī mehana = 40^oC. Ka wela kikoʻī o ka hau = 2100 J/kg C^o, ka wela kikoʻī o ka wai = 4200 J/kg C^o, ka wela o ka hoʻohuihui ʻana o ka wai = 334.000 J/kg. Inā hui ʻia ka hau a me ke kī wela i loko o kahi ʻōnaehana pani kaʻawale, e hoʻoholo i ka mahana hope loa o ka hui ʻana.

Pahana
Ua ʻike ʻia :
Ka nui o ka hau (m es) = 0,2 kg
Ka nuipa o ka wai tī mehana (m tī) = 0,2 kg
Ka wela kikoʻī o ka wai (c wai) = 4180 J/kg C^o
Ka wela kikoʻī o ka hau (c es) = 2100 J/kg C^o
Ka wela o ka hoʻohuihui ʻana o ka wai (L)_f wai) = 334.000 J/kg
Mahana hau (T es) = -10^oC
Mahana wai kī mehana (T kī) = 40^oC
Ua nīnau ʻia : ka mahana hope loa o ka hui ʻana (hui ʻana o T) ?
Pane :
ʻO ka hana mua, e kuhi i ke kūlana hope loa.
ʻO ka wela e pono e hoʻokuʻu ʻia e ka wai e hoʻohaʻahaʻa i ka mahana o 0,2 kg o ke kī mehana mai 40^oC a i 0^oC:
ʻO ka wela i omo ʻia e 0,2 kg o ka hau e hoʻokiʻekiʻe i kona mahana mai -10^oC a i 0^oC:
Ka wela i omo ʻia e hoʻoheheʻe i ka 0,2 kg o ka hau (ka wela e pono ai e hoʻololi i ka hau a pau i ka wai):
Ma muli o nā helu ʻana ma luna, ua loaʻa nā hopena penei:
Ua hoʻokuʻu ʻia ʻo Q = 33,444 kJ
Q i loaʻa = 4,2 kJ
Q heheʻe = 66,8 kJ

Ke hoʻokuʻu ke kī wela i 33,44 kJ o ka wela, loli ka mahana o ke kī wela mai 40oC a i 0oC. Hoʻohana ʻia kekahi o ka wela i hoʻokuʻu ʻia (ma kahi o 4,2 kJ) e hoʻokiʻekiʻe i ka mahana o ka hau mai -10°C a i 0°C. ^oC a i 0^oC. 33,44 kJ – 4,2 kJ = 29,24 kJ. No ka hoʻoheheʻe ʻana i ka hau a pau i loko o ka wai, pono 66,8 kJ o ka wela. ʻO ke koena o ka wela he 29,24 kJ.

Hiki ke hoʻoholo ʻia ʻo ka wela i hoʻokuʻu ʻia e ke kī mehana e hoʻohana wale ʻia e hoʻokiʻekiʻe i ka mahana o ka hau mai -10 ^oC a i 0^oC a hoʻoheheʻe i kekahi o ka hau. Ua lilo kekahi o ka hau i wai, ʻaʻole kekahi. I ke kaʻina hana o ka hoʻololi ʻana mai ka paʻa a i ka wai, ʻaʻole loli ka mahana. No laila, ʻo ka mahana hope loa o ka hui ʻana he 0^oC.

2. Nui o ke kī wela = 0,4 kg, nui o ka hau = 0,2 kg, mahana o nā pahu hau = -10^oC, ka mahana o ke kī wela = 90^oC. Inā hui ʻia nā mea ʻelua, he aha ka mahana hope loa o ka hui ʻana?
Pahana
Ka hana mua: e kuhi i ke kūlana hope loa
ʻO ka wela e pono e hoʻokuʻu ʻia e ka wai e hoʻohaʻahaʻa i ka mahana o 0,4 kg o ka wai tī wela mai 90^oC a i 0^oC:
ʻO ka wela i loaʻa e 0,2 kg o ka hau e hoʻokiʻekiʻe i kona mahana mai -10^oC a i 0^oC:
ʻO ka wela e pono ai e hoʻoheheʻe i ka 0,2 kg o ka hau (ka wela e pono ai e hoʻololi i ka hau a pau i ka wai):
Ma muli o nā helu ʻana ma luna, ua loaʻa nā hopena penei:
Ua hoʻokuʻu ʻia ʻo Q = 150,48 kJ
Q i loaʻa = 4,2 kJ
Q heheʻe = 66,8 kJ
Ke hoʻokuʻu ke kī wela i 150,48 kJ o ka wela, loli ka mahana o ke kī wela mai 90oC a i 0oC. Hoʻohana ʻia kekahi o ka wela i hoʻokuʻu ʻia (4,2 J) e hoʻokiʻekiʻe i ka mahana o ka hau mai -10 oC a i 0oC. 150,48 kJ – 4,8 kJ = 146,28 kJ. ʻO ke koena o ka wela = 146,28 kJ.
ʻO ka wela e pono ai e hoʻoheheʻe i ka hau a pau i loko o ka wai he 66,8 kJ wale nō. 146,28 kJ - 66,8 kJ = 79,48 kJ. ʻAʻole pono ke kī wela e hoʻokuʻu i kona wela a pau a hiki i ka hāʻule ʻana o kona mahana i ka 0.^oC. I ka hopena, pono e ʻoi aku ka mahana hope loa o ka hui ʻana ma mua o 0^oC.

ʻO ka lua o ka hana: e hoʻoholo i ka mahana hope loa (T)
ʻO ka wela e pono ai e hoʻokiʻekiʻe i ka mahana o ka hau mai -10^oC a i 0^oʻO C he 4200 J.
ʻO ka wela e pono ai e hoʻoheheʻe i ka hau a pau i loko o ka wai (wela latent) = 66.800 J
ʻO ka wela e pono ai e hoʻokiʻekiʻe i ka mahana o ka wai (ka wai i loaʻa mai ka hoʻoheheʻe ʻana o ka hau a pau) mai ka 0^oC a i T^oC = (ka nuipa o ka hau) (ka wela kikoʻī o ka wai)(T – 0) = (0,2)(4180)(T) = 836 T
ʻO ka wela i hoʻokuʻu ʻia e ke kī mehana e hoʻohaʻahaʻa i kona mahana mai 90oC a i T = (ka nui o ka wai)(90-T) = (0,4)(4180)(90 – T) = 1672 (90-T) = 150.480 – 1672 T

 

3. 60 grams o ka wai ma ka mahana o 90^oC (ka wela kikoʻī o ka wai = 1 cal.g^-1.^oC^-1) i hui pū ʻia me 40 grams o ka wai like ma ka mahana o 25^oC. Inā ʻaʻohe mea ʻē aʻe e hoʻopilikia i kēia kaʻina hana, a laila ʻo ka mahana hope loa o ka hui ʻana…

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

Pahana
Ua ʻike ʻia :
Ka nui o ka wai 1 (m₁) = 60 grams
Mahana wai 1 (T₁) = 90^oC
Ka nui o ka wai 2 (m₂) = 40 grams
Mahana wai 2 (T₂) = 25^oC
Wela kikoʻī wai (c) = 1 cal.g^-1.^oC^-1
Ua nīnau ʻia : ka wela hui hope loa
Pane :
Ka wela i hoʻokuʻu ʻia e ka wai wela kiʻekiʻe (Q i hoʻokuʻu ʻia) = ka wela i omo ʻia e ka wai wela haʻahaʻa (Q i omo ʻia)
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
ʻO D ka pane pololei.

4. He 500 grams ke kaumaha o kahi ʻāpana alumini a he 30 kona mahana ^oHoʻokomo ʻia ʻo C i loko o kahi ipu i loaʻa ka wai me ke kaumaha o 200 grams a me ka mahana o 90 ^oC. Inā ʻike ʻia ka wela kikoʻī o ka alumini he 0,22 cal/g C^o a ʻo ka wela kikoʻī o ka wai he 1 cal/g C^o, a laila ʻo ka mahana hope loa o ka wai a me ka alumini he...
H. 20,3 ^oC
B. 42,2 ^oC
C. 68,7 ^oC
D. 80,5 ^oC
E. 100 ^oC
Kūkākūkā:
ʻAʻole pono e hoʻololi ʻia ke anakahi o ka nuipa, grams (g) i kilokani (kg) no ka mea ua hōʻike ʻia ka wela kikoʻī o ka alumini a me ka wela kikoʻī o ka wai ma cal/g C^o.
Ua ʻike ʻia :
m alumini = 500 grams
c alumini = 0,22 cal/gC^o
T alumini = 30 ^oC
m wai = 200 grams
wai = 1 cal/gC^o
T wai = 90 ^oC
Ua nīnau ʻia :
Mahana hope loa (T) o ka wai a me ka alumini?
Pane :

ʻAno wela Q = (m)(c)(delta T)

Q wai = = (200 grams)(1 cal/gC^o)(90 ^oC – T)
Q alumini = (500 grams)(0,22 cal/gC^o)(T– 30 ^oC)

ʻO ke ʻano hana maʻamau o Black : N _pio =Q _omo

ʻOi aku ka mahana mua o ka wai (90 ^oC) i mea e hoʻokuʻu ai ka wai i ka wela, ʻoi aku ka haʻahaʻa o ka mahana mua o ka alumini (30 ^oC) i mea e omo ai ka alumini i ka wela. Pono ka mahana hope loa o ka hui ʻana o ka wai a me ka alumini e haʻahaʻa ma mua o ka mahana mua o ka wai a ʻoi aku ke kiʻekiʻe ma mua o ka mahana mua o ka alumini.
(200 grams)(1 cal/gC^o)(90 ^oC – T) = (500 grams)(0,22 cal/g 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
ʻO ka mahana hope loa o ka hui pū ʻana o ka wai a me ka alumini he 68,7 ^oC.
ʻO C ka pane pololei.

5. He ʻāpana metala me ke kaumaha o 300 grams ma ka mahana o 80 ^oC i hoʻoluʻu ʻia i loko o 200 grams o ka wai ma 40 ^oC. Ka wela kikoʻī o ka wai = 1 cal/g C^oInā he 50 ka mahana hope loa o ka hui ʻana o ka metala a me ka wai^o C a ʻaʻole omo ka ipu i ka wela, a laila ʻo ka wela kikoʻī o ka metala…
A. 0,15 kal/g C^o
B. 0,22 kal/g C^o
C. 1,50 kal/g C^o
D. 4,8 kal/g C^o
E. 7,2 kal/g C^o
Kūkākūkā:
Ua ʻike ʻia :
metala m = 300 grams
T metala = 80 ^oC
m wai = 200 grams
T wai = 40 ^oC
wai = 1 cal/g C^o
ʻO ka hui hope loa o ka metala a me ka wai = 50 ^oC
Ua nīnau ʻia :
metala c?
Pane :
Q metala = (m)(c)(delta T) = (300 grams)(c metala)(80^oC - 50^oC) = (300 grams)(c metala)(30 C^o)
Q wai = (m)(c)(delta T) = (200 grams)(1 cal/g C^o)(60^oC - 50^oC) = (200 grams)(1 cal/g C^o)(10 C^o)

ʻO ke ʻano hana maʻamau o Black : N _pio =Q _omo

ʻOi aku ka mahana mua o ka metala (80 ^oC) i mea e hoʻokuʻu ai ka metala i ka wela, ua emi ka mahana mua o ka wai (40 ^oC) i mea e omo ai ka wai i ka wela.
(300 grams)(c metala)(30 C^o) = (200 grams)(1 cal/g C^o)(10 C^o)
(300)(c)(30) = (200)(1)(10)
9000 c = 2000
c = 2000 / 9000
c = 0,22 kal/g C^o
ʻO ka wela kikoʻī o ka metala he 0,22 cal/g C^o.
ʻO ka pane pololei ʻo B.

6. ʻElua mau pōpō like i like ka mahana o 40 ^oC, he 10 gram a he 40 gram ke kaumaha o nā pōpō ʻelua. Hoʻokomo ʻia nā pōpō ʻelua i loko o kahi wai, i piʻi ai ka mahana o nā pōpō ʻelua i 60^oC. Inā he 2 cal/gr C ka wela kikoʻī o ka pōpō^o a ʻo 1 calorie = 4,2 Joules, a laila ʻo ka ʻokoʻa o ka wela i omo ʻia e kēlā me kēia pōpō he...
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
Kūkākūkā:
Ua ʻike ʻia :
m₁ = 10 grama
m₂ = 40 grama
T₁ =T₂ = 40 ^oC
T _hopena = 60 ^oC
c pōpō = 2 cal/gr C^o
Ua nīnau ʻia :
He aha ka ʻokoʻa o ka wela i omo ʻia e kēlā me kēia pōpō?
Pane :
Piʻi ka mahana o nā pōpō ʻelua no ka mea pono nā pōpō ʻelua e omo i ka wela.
Q₁ = (10 gr)(2 cal/gr C^o)(60^oC–40^oC) = (10 gr)(2 cal/gr C^o)(20 C^o) = 400 kaila = (400)(4,2 J) = 1680 Joule
Q₂ = (40 gr)(2 cal/gr C^o)(60^oC–40^oC) = (40 gr)(2 cal/gr C^o)(20 C^o) = 1600 kaila = (1600)(4,2 J) = 6720 Joule
ʻO ka ʻokoʻa o ka wela i omo ʻia e kēlā me kēia pōpō:
6720 J – 1680 J = 5040 J = 5,04 x 10³ J
ʻO A ka pane pololei.

7. Ua hui ʻia ka wai me ke kaumaha o 200 grams ma ka mahana o 30°C me ka wai e paila ana me ke kaumaha o 100 grams a me ka mahana o 90°C. (Ka wela kikoʻī o ka wai = 1 cal.gram^-1° C^-1). ʻO ka mahana o ka wai i hui ʻia i ka manawa o ke kaulike wela….

A. 10°C

B. 30°C

C. 50°C

D. 75°C

E. 150°C

Pahana

Ua ʻike ʻia :

Ka nui o ka wai 1 (m₁) = 200 grams

Mahana wai 1 (T₁) = 30^oC

Ka nui o ka wai 2 (m₂) = 100 grams

Mahana wai 2 (T₂) = 90^oC

Ka wela kikoʻī o ka wai (c) = 1 cal.gram^-1° C^-1

Ua nīnau ʻia : ka mahana hope loa o ka hui ʻana

Pane :

Ka wela i hoʻokuʻu ʻia e ka wai wela kiʻekiʻe (Q i hoʻokuʻu ʻia) = ka wela i omo ʻia e ka wai wela haʻahaʻa (Q i omo ʻia)

ʻO C ka pane pololei.

8. Aa hiki i ka 60 grams ma ka mahana o 90^oC (ka wela kikoʻī o ka wai = 1 cal.g^-1.^oC^-1) i hui pū ʻia me 40 grams o ka wai like ma ka mahana o 25^oC. Inā ʻaʻohe mea ʻē aʻe e hoʻopilikia i kēia kaʻina hana, a laila ʻo ka mahana hope loa o ka hui ʻana…

H. 15,4 ^oC

B. 23,0 ^oC

C. 46,0 ^oC

D. 64,0 ^oC

E. 77,0 ^oC

Pahana

Ua ʻike ʻia :

Ka nui o ka wai 1 (m₁) = 60 grams

Mahana wai 1 (T₁) = 90^oC

Ka nui o ka wai 2 (m₂) = 40 grams

Mahana wai 2 (T₂) = 25^oC

Ka wela kikoʻī o ka wai (c) = 1 cal.g^-1.^oC^-1

Ua nīnau ʻia : ka mahana hope loa o ka hui ʻana

Pane :

Ka wela i hoʻokuʻu ʻia e ka wai wela kiʻekiʻe (Q i hoʻokuʻu ʻia) = ka wela i omo ʻia e ka wai wela haʻahaʻa (Q i omo ʻia)

ʻO D ka pane pololei.

9. He hau me ka nui o M grams ma ka mahana o 0^oC, e hoʻokomo i loko o ka wai he 340 grams ke kaupaona ʻana ma ka mahana o 20^oC i hoʻokomo ʻia i loko o kahi ipu kūikawā. Manaʻo ʻaʻole e omo/hoʻokuʻu ka ipu i ka wela. Inā ʻo L_es = 80 kal g^-1, l_ea = 1 kal g^{-1 o}C^-1, heheʻe nā hau a pau a hiki i ke kaulike wela ma ka mahana o 5^oC, a laila ʻo ke kaumaha o ka hau (M) he…

A. 60 grams

B. 68 grams

C. 75 grams

D. 80 grams

E. 170 grams

Pahana

Ua ʻike ʻia :

Ka nuipa o ka wai (m) = 340 grams

Mahana hau (T_es) = 0^oC

Mahana wai (T_ea) = 20^oC

Mahana kaulike wela (T) = 5^oC

Ka wela o ka hoʻohuihui ʻana o ka hau (L_es) = 80 kal g^-1

Ka wela kikoʻī o ka wai (c_ea) = 1 kal g^{-1 o}C^-1

Ua nīnau ʻia : Ka nui o ka hau (M)

Pane :

Kumumanaʻo ʻEleʻele ʻōlelo ʻia i loko o kahi ʻōnaehana pani kaʻawale, ʻo ka wela i hoʻokuʻu ʻia e kahi mea wela kiʻekiʻe ua like ia me ka wela i omo ʻia e kahi mea wela haʻahaʻa.

Ka wela i hoʻokuʻu ʻia e ka wai (Q i hoʻokuʻu ʻia) = ka wela i omo ʻia e ka hau (Q i omo ʻia)

ʻO A ka pane pololei.

Catatan:

Inā ua ʻōlelo ʻia he 0 ka mahana o ka hau^o a laila aia nō ka wai i loko o ke ʻano paʻa. Inā ʻōlelo ʻia he 0 ka mahana o ka wai^oC a laila aia ka wai ma ke ʻano wai. E hoʻokaʻawale i ka hoʻohana ʻana o nā huaʻōlelo hau a me ka wai. No ka mea aia nō ka wai ma ke ʻano paʻa a hau paha, hoʻohana mua ʻia ka wela i omo ʻia e hoʻoheheʻe i ka hau āpau i loko o ka wai, no laila ma ka ʻaoʻao ʻākau o ka hoohalike ma luna, ua hoʻohui ʻia kahi haʻilula e helu i ka nui o ka wela e hoʻoheheʻe ai i ka hau (m_es L_esMa hope o ka heheʻe ʻana o ka hau a pau i loko o ka wai, hoʻohana ʻia ka wela hou e hoʻokiʻekiʻe i ka mahana o ka hau mai 0.^oLilo ʻo C i 5^oC.

10. He metala keleawe ma ka mahana o 100^oHoʻokomo ʻia ʻo C i loko o ka wai me ke kaumaha o 128 grams a me ka mahana o 30 ^oC. Ka wela kikoʻī o ka wai 1 cal.g^-1oC^-1 a ʻo ka wela kikoʻī o ke keleawe he 0,1 cal.g^-1oC^-1Inā kū ke kaulike wela ma ka mahana o 36 ^oC, a laila ʻo ke kaumaha o ka metala he….

A. 140 grams

B. 120 grams

C. 100 grams

D. 80 grams

E. 75 grams

Pahana

Ua ʻike ʻia:

Mahana keleawe (T₁) = 100 ^oC

Ka wela kikoʻī o ke keleawe (c)₁) = 0,1 kal.g^-1oC^-1

Nui wai (m₂) = 128 grams

Mahana wai (T₂) = 30 ^oC

Ka wela kikoʻī o ka wai (c₂) = 1 kal.g^-1oC^-1

Mahana kaulike wela (T) = 36 ^oC

Ua nīnau ʻia: Ka nuipa o ke keleawe (m₁)

Pane:

ʻŌlelo ke kumumanaʻo o Black ʻo ka wela i hoʻokuʻu ʻia e kahi mea wela kiʻekiʻe = ka wela i loaʻa e kahi mea wela haʻahaʻa.

ʻO ka pane pololei ʻo B.

11. ʻEkolu kilokani o ke koʻokoʻo kēpau ʻeleʻele me ka wela kikoʻī o 1400 J.kg^-1C^-1 mahana 80^oUa hoʻokomo ʻia ʻo C i loko o 10 kg o ka wai me ka wela kikoʻī o 4200 J.kg^-1C^-1Ma hope o ke kaulike wela, ʻo ka mahana hope loa o ka hui ʻana he 20^oC. ʻO ka mahana mua o ka wai….

H. 20 ^oC

B. 18 ^oC

C. 14 ^oC

D. 12 ^oC

E. 10 ^oC

Pahana

Ua ʻike ʻia:

Ka nui o ke kēpau (m₁) = 3 kg

Ka wela kikoʻī o ka tin (c₁) = 1400 J.kg^-1C^-1

Mahana o ka tin (T₁) = 80 ^oC

Nui wai (m₂) = 10 kg

Ka wela kikoʻī o ka wai (c₂) = 4200 J.kg^-1C^-1

Mahana kaulike wela (T) = 20 ^oC

Ua nīnau ʻia: Mahana wai mua (T₂)

Pane:

ʻO C ka pane pololei.

12. Ua hoʻomehana ʻia kahi ʻāpana kālā he 50 gram i ka mahana o 85^oC, a laila hoʻoluʻu ʻia i loko o kahi ipu me 50 grams o ka wai ma ka mahana o 29,8^oC (ka wela kikoʻī o ka wai = 1 cal.g^-1.^oC^-1). Inā he 37 ka mahana hope loa o ka ʻōnaehana^oC a manaʻo ʻaʻohe loli o ka wela ma o ka ipu, a laila ʻo ka wela kikoʻī o ka metala…

A. 0,12 kal.g^-1.^oC^-1

B. 0,30 kal.g^-1.^oC^-1

C. 1,50 kal.g^-1.^oC^-1

D. 4,8 kal.g^-1.^oC^-1

E. 7,2 kal.g^-1.^oC^-1

Pahana

Ua ʻike ʻia:

Ka nuipa o ke kālā (m) = 50 grams

Ka mahana mua o ke kālā (T₁) = 85^oC

Ka nuipa o ka wai (m) = 50 grams

Mahana wai mua (T₂) = 29,8^oC

Ka wela kikoʻī o ka wai = 1 cal.g^-1.^oC^-1

Ka mahana hope loa o ka ʻōnaehana (T) = 37^oC

Ua nīnau ʻia: Ka wela kikoʻī o ka metala (c)

Pane:

ʻŌlelo ke kumumanaʻo o Black ʻo ka wela i hoʻokuʻu ʻia = ka wela i omo ʻia. Hoʻokuʻu ʻia ka wela e ke kālā a omo ʻia ka wela e ka wai, a hiki i ka loaʻa ʻana o ke kaulike wela.

Ua hōʻike ʻia nā ʻāpana āpau ma nā grama no laila ʻaʻohe pono e hoʻololi i nā ʻāpana.

Q _pio =Q _omo

m_metala c ΔT = m_ea 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 kal.g^-1.^oC^-1

13. Metala keleawe ma ka mahana o 100^oHoʻokomo ʻia ʻo C i loko o ka wai me ke kaumaha o 128 grams a me ka mahana o 30 ^oC. Ka wela kikoʻī o ka wai 1 cal.g^{-1 o}C^-1 a ʻo ka wela kikoʻī o ke keleawe he 0,1 cal.g^{-1 o}C^-1Inā kū ke kaulike wela ma ka mahana o 36 ^oC, a laila ʻo ke kaumaha o ka metala he….

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

Pahana
Ua ʻike ʻia:
Mahana keleawe (T₁) = 100 ^oC
Ka wela kikoʻī o ke keleawe (c)₁) = 0,1 kal.g^{-1 o}C^-1

Nui wai (m₂) = 128 grams
Mahana wai (T₂) = 30 ^oC
Ka wela kikoʻī o ka wai (c₂) = 1 kal.g^{-1 o}C^-1

Mahana kaulike wela (T) = 36 ^oC
Nīnau: Nui o ke keleawe (m₁)
Pane:

ʻŌlelo ke kumumanaʻo o Black ʻo ka wela i hoʻokuʻu ʻia e kahi mea wela kiʻekiʻe = ka wela i loaʻa e kahi mea wela haʻahaʻa.
Q keleawe = 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
ʻO ke kaumaha o ke keleawe he 120 grams.
ʻO ka pane pololei ʻo B.

14. ʻEkolu kilokani o ke koʻokoʻo kēpau ʻeleʻele me ka wela kikoʻī o 1400 J.kg^-1 C^-1 mahana 80^oUa hoʻokomo ʻia ʻo C i loko o 10 kg o ka wai me ka wela kikoʻī o 4200 J.kg^-1 C^-1Ma hope o ke kaulike wela, ʻo ka mahana hope loa o ka hui ʻana he 20^oC. ʻO ka mahana mua o ka wai….

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

Pahana
Ua ʻike ʻia:
Ka nui o ke kēpau (m₁) = 3 kg
Ka wela kikoʻī o ka tin (c₁) = 1400 J.kg^-1 C^-1
Mahana o ka tin (T₁) = 80 ^oC

Nui wai (m₂) = 10 kg
Ka wela kikoʻī o ka wai (c₂) = 4200 J.kg^-1 C^-1

Mahana kaulike wela (T) = 20 ^oC
Makemake ʻia: Mahana wai mua (T₂)
Pane:
Q i hoʻokuʻu ʻia = Q i loaʻa
Q tin = 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
ʻO ka mahana mua o ka wai he 14^oC.
ʻO C ka pane pololei.

15. Hau me ka nui o M grams ma ka mahana o 0^oC, e hoʻokomo i loko o ka wai he 340 grams ke kaupaona ʻana ma ka mahana o 20^oC i hoʻokomo ʻia i loko o kahi ipu kūikawā. Manaʻo ʻaʻole e omo/hoʻokuʻu ka ipu i ka wela. Inā ʻo L_es = 80 kal g^-1, l_ea = 1 kal g^{-1 o}C^-1, ua heheʻe nā hau a pau a ke kaulike wela i loaʻa ma ka mahana o 5^oC, a laila ʻo ke kaumaha o ka hau (M) he…

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

Pahana
Ua ʻike ʻia :
Ka nuipa o ka wai (m) = 340 grams
Mahana hau (T_es) = 0^oC
Suhu wai (T_ea) = 20^oC
Mahana kaulike wela (T) = 5^oC
Ka wela o ka hoʻohuihui ʻana o ka hau (L_es) = 80 kal g^-1
Ka wela kikoʻī o ka wai (c_ea) = 1 kal g^{-1 o}C^-1
Ua nīnau ʻia : Ka nui o ka hau (M)
Pane :

Kumumanaʻo ʻEleʻele ʻōlelo ʻia i loko o kahi ʻōnaehana pani kaʻawale, ʻo ka wela i hoʻokuʻu ʻia e kahi mea wela kiʻekiʻe ua like ia me ka wela i omo ʻia e kahi mea wela haʻahaʻa.
Ka wela i hoʻokuʻu ʻia e ka wai (Q i hoʻokuʻu ʻia) = ka wela i omo ʻia e ka hau (Q i omo ʻia)
m_ea c_ea (T) = m_es L_es +m_es c_ea (T)
(340)(1)(20-5) = M (80) + M (1)(5-0)
(340)(15) = 80M + 5M
5100 = 85M
M = 5100/85
M = 60 grams
ʻO A ka pane pololei.

Catatan:
Inā ua ʻōlelo ʻia he 0 ka mahana o ka hau^o a laila aia nō ka wai i loko o ke ʻano paʻa. Inā ʻōlelo ʻia he 0 ka mahana o ka wai^oC a laila aia ka wai ma ke ʻano wai. E hoʻokaʻawale i ka hoʻohana ʻana o nā huaʻōlelo hau a me ka wai. No ka mea aia nō ka wai ma ke ʻano paʻa a hau paha, hoʻohana mua ʻia ka wela i omo ʻia e hoʻoheheʻe i ka hau āpau i loko o ka wai, no laila ma ka ʻaoʻao ʻākau o ka hoohalike ma luna, ua hoʻohui ʻia kahi haʻilula e helu i ka nui o ka wela e hoʻoheheʻe ai i ka hau (m_es L_esMa hope o ka heheʻe ʻana o ka hau a pau i loko o ka wai, hoʻohana ʻia ka wela hou e hoʻokiʻekiʻe i ka mahana o ka hau mai 0.^oLilo ʻo C i 5^oC.

Puna nīnau:

Nā Nīnau Hoʻokolohua Lahui no ke Kino no ke Kula Kiʻekiʻe/Kula Kiʻekiʻe ʻOihana