ke kālaikūlohea

1. ʻO ka lōʻihi o ke kikowaena o kahi aniani convex he 10 kenimika a me ka mea mamao he 20 kenimika. E hoʻoholo (a) ka mamao o ke kiʻi (b) ka hoʻonui ʻana o ke kiʻi

ʻIke ʻia:

Ka lōʻihi o ke kikowaena (f) = -10 kenimika

Hōʻike ka hōʻailona minus he virtual ke kiko kikowaena o ke aniani convex

Ka mamao o ka mea (d_o) = 20 kenimika

Lōlā:

Ka hoʻokumu ʻia ʻana o ke kiʻi e ke aniani concave:

ʻO ka mamao o ke kiʻi (d_i):

1/d_i = 1/f – 1/d_o = -1/10 – 1/20 = -2/20 – 1/20 = -3/20

d_i = -20/3 = -6.7 kenimika

Hōʻike ka hōʻailona hoʻēmi he virtual ke kiʻi.

Ka hoʻonui ʻana o ke kiʻi:

m = - d_i / d_o = -(-6.7)/20 = 6.7/20 = 0.3

m = 0,3 manawa liʻiliʻi ma mua o ka mea.

Hōʻike ka hōʻailona hoʻohui ua piʻi ke kiʻi i luna.

2. Ua kau ʻia kahi mea he 10 kenimika ke kiʻekiʻe i mua o ke aniani convex me ka lōʻihi o ke kikowaena he 20 kenimika. E hoʻoholo i ke kiʻekiʻe o ke kiʻi inā ʻo ka mamao o ka mea he (a) 10 kenimika (b) 30 kenimika (c) 40 kenimika (d) 50 kenimika

ʻIke ʻia:

ʻO ka lōʻihi o ke kikowaena o ke aniani convex (f) = -20 kenimika

Hōʻike ka hōʻailona minus he virtual ke kiko kikowaena

ʻO ke radius o ke kūlou (r) = 2 f = 2(20) = 40 kenimika

Ke kiʻekiʻe o ka mea (h) = 10 kenimika

Lōlā:

a) ka lōʻihi o ke kikowaena (f) = -20 kenimika a me ka mamao o ka mea (d_o) = 10 kenimika

ʻO ka mamao o ke kiʻi (d_i) :

1/d_i = 1/f – 1/d_o = -1/20 – 1/10 = -1/20 – 2/20 = -3/20

d_i = -20/3 = -6.7

Hōʻike ka hōʻailona hoʻēmi he virtual ke kiʻi a i ʻole aia ke kiʻi ma hope o ke aniani.

Ka hoʻonui ʻana i ke kiʻi (m):

m = -d_i / d_o = -(-6.7)/10 = 6.7/10 = 0.67

Hōʻike ka hōʻailona hoʻohui ua kū pololei ke kiʻi.

ʻOi aku ka liʻiliʻi o ke kiʻi ma mua o ka mea he 0.67.

Ke kiʻekiʻe o ke kiʻi (h_i):

m = h_i / h_o

h_i = h_o m = (10 kenimika)(0.67) = 6.7 kenimika

b) ka lōʻihi o ke kikowaena (f) = -20 kenimika a me ka mamao o ka mea (d_o) = 30 kenimika

Ka mamao o ke kiʻi (d_i):

1/d_i = 1/f – 1/d_o = -1/20 – 1/30 = -3/60 – 2/60 = -5/60

d_i = -60/5 = -12

Hōʻike ka hōʻailona hoʻēmi he virtual ke kiʻi a i ʻole aia ke kiʻi ma hope o ke aniani.

Ka hoʻonui ʻana i ke kiʻi (m):

m = -d_i / d_o = -(-12)/30 = 12/30 = 0.4

Hōʻike ka hōʻailona hoʻohui ua kū pololei ke kiʻi.

ʻOi aku ka liʻiliʻi o ke kiʻi ma mua o ka mea he 0,4 manawa.

Ke kiʻekiʻe o ke kiʻi (h_i):

m = h_i / h_o

h_i = h_o m = (10 kenimika)(0.4) = 4 kenimika

c) Ka lōʻihi o ke kikowaena (f) = -20 kenimika a me ka mamao o ka mea (d_o) = 40 kenimika

Ka mamao o ke kiʻi (d_i):

1/d_i = 1/f – 1/d_o = -1/20 – 1/40 = -2/40 – 1/40 = -3/40

d_i = -40/3 = -13.3

Hōʻike ka hōʻailona hoʻēmi he virtual ke kiʻi a i ʻole aia ke kiʻi ma hope o ke aniani convex.

Ka hoʻonui ʻana i ke kiʻi (m):

m = - d_i / d_o = -(-13.3)/40 = 13.3/40 = 0.3

Hōʻike ka hōʻailona hoʻohui ua kū pololei ke kiʻi.

ʻOi aku ka liʻiliʻi o ke kiʻi ma mua o ka mea he 0.3.

Ke kiʻekiʻe o ke kiʻi (h_i) :

m = h_i / h_o

h_i = h_o m = (10 kenimika)(0.3) = 3 kenimika

d) Ka lōʻihi o ke kikowaena (f) = -20 kenimika a me ka mamao o ka mea (d_o) = 50 kenimika

Ka mamao o ke kiʻi (d_i):

1/d_i = 1/f – 1/d_o = -1/20 – 1/50 = -5/100 – 2/100 = -7/100

d_i = -100/7 = -14.3

Hōʻike ka hōʻailona hoʻēmi he virtual ke kiʻi a i ʻole aia ke kiʻi ma hope o ke aniani convex.

Ka hoʻonui ʻana i ke kiʻi (m):

m = - d_i / d_o = -(-14.3)/50 = 14.3/50 = 0.3

Hōʻike ka hōʻailona hoʻohui ua kū pololei ke kiʻi.

ʻOi aku ka liʻiliʻi o ke kiʻi ma mua o ka mea he 0.3.

Ke kiʻekiʻe o ke kiʻi (h_i) :

m = h_i / h_o

h_i = h_o m = (10 kenimika)(0.3) = 3 kenimika

3. Aia ka mea ma kahi he 20 kenimika i mua o ke aniani convex. Inā he 1/5 manawa ke kiʻekiʻe o ke kiʻi i ke kiʻekiʻe o ka mea, e hoʻoholo i (a) ka lōʻihi o ke kiʻi b) ka lōʻihi o ke kikowaena c) nā waiwai o ke kiʻi

ʻIke ʻia:

Ka mamao o ka mea (d_o) = 20 kenimika

Ke kiʻekiʻe o ke kiʻi (h_i) = 1/5 hola = 0.2 hola

Ke kiʻekiʻe o ka mea (h) = h

Lōlā:

a) ka mamao o ke kiʻi (d_i)

Ke ʻano o ka hoʻonui ʻana o ke kiʻi :

m = h_i / h_o = 0.2h / h = 0.2

Hōʻike ka hōʻailona hoʻohui ua kū pololei ke kiʻi.

ʻOi aku ka liʻiliʻi o ke kiʻi ma mua o ka mea he 0.2.

Ka mamao o ke kiʻi (d_i):

-d_i = md_o

d_i = - m d_o = -(0.2)(20 kenimika) = -4 kenimika

Hōʻike ka hōʻailona hoʻēmi he virtual ke kiʻi a i ʻole aia ke kiʻi ma hope o ke aniani convex.

b) ʻO ka lōʻihi o ke kikowaena (f)

Ka lōʻihi o ke kikowaena (f):

1/f = 1/d_o + 1/ d_i = 1/20 – 1/4 = 1/20 – 5/20 = -4/20

f = -20/4 = -5 kenimika

Hōʻike ka hōʻailona huaʻole he virtual ke kiko kikowaena.

c) Nā ʻano o ke kiʻi:

- Ua pololei

- Kaʻuʻuku

- ʻike kamepiula

4. Pā ka mālamalama i ke aniani convex e kūlike ana i ke axis e hōʻike ʻia….

A. i ke kiko kikowaena o ke aniani

B. mai ke kiko kikowaena o ke aniani

C. ma o ke kikowaena o ke kūlou ʻana o ke aniani

D. kū pololei i ka mokulele aniani

pāʻoihana

Ua kaha ʻia ka pilikia ma ke kiʻi ma lalo nei.

ʻO ka pane pololei ʻo B.

5. ʻIke kekahi mea holo paikikala i ke kiʻi o kahi mokokaikala ma hope ona he 1/6 manawa o kona nui mua i ka wā he 30 mika ka mamao ma waena o ka mea holo paikikala a me ka mokokaikala. E hoʻoholo i ka radius o ke kūlou o ke aniani hope…

A. 7.14 m

B. 8.57 m

C. 12.00 m

D. 24.00 m

ʻIke ʻia:

Hoʻonui ʻia o ke kiʻi (M) = 1/6 manawa

Ka mamao o ka mea (d) = 30 mika

Makemake: ʻO ke radius o ke kūlou ʻana o ke aniani hope (R)

Lōlā:

E helu i ka mamao o ke kiʻi (d')

Ma muli o ka ʻike ʻia ʻana o ka hoʻonui ʻana o ke kiʻi (M) a me ka mamao o ka mea (s), hiki ke ʻike ʻia ka mamao o ke kiʻi ma o ka hoʻohana ʻana i ke ʻano hoʻonui kiʻi:

ʻO ka hōʻailona maikaʻi ʻole, ʻo ia hoʻi he kiʻi virtual. Aia ke kiʻi ma hope o ke aniani convex.

E helu i ka lōʻihi o ke kikowaena (f)

ʻOiai ka mamao o ka mea (d) a me ka mamao o ke kiʻi (d'), a laila hiki ke helu ʻia ka lōʻihi o ke kikowaena me ka hoʻohana ʻana i ke ʻano o ke aniani:

ʻO ke radius o ke kūlou (R)

ʻO ke anawaena o ke piʻo ʻana o ke aniani convex he pālua ia o ka lōʻihi o ke kikowaena o ke aniani convex.
R = 2 f = 2 (6 mika) = 12 mika
ʻO ke radius o ke kūlou ʻana o ke aniani convex he 12 mika.
ʻO ka pane pololei ʻo C.

6. Ua koho ʻia ke aniani convex ma ke ʻano he aniani hope o kahi mokokaikala no ka mea ʻo nā ʻano o ke kiʻi i hana ʻia e ke aniani…

A. maoli, pololei, hoʻemi ʻia

B. maoli, kū pololei, hoʻonui ʻia

C. virtual, pololei, hoʻemi ʻia

D. ʻoiaʻiʻo, kū pololei, hoʻonui ʻia

Lōlā:

Ma muli o nā kiʻi ʻelua ma luna, hiki ke hoʻoholo ʻia he virtual, pololei, nā waiwai o ke kiʻi hoʻohaʻahaʻa ʻia.

ʻO ka pane pololei ʻo C.

7. He Aia ka mea he 12 kenimika i mua o ke aniani convex me ka radius o 6 kenimika. ʻO nā ʻano o ke kiʻi…

A. maoli, i hoʻohuli ʻia ma kahi mamao o 12 kenimika

B. maoli, kū pololei ma kahi mamao o 4 kenimika

C. virtual, kū pololei ma kahi mamao o 2.4 kenimika

D. virtual, i hoʻohuli ʻia ma kahi mamao o 6 kenimika

ʻIke ʻia:

Ka mamao o ka mea (d) = 12 kenimika

Radius o ke aniani convex (r) = 6 kenimika.

ʻO ka lōʻihi o ke kikowaena o ka aniani convex (f) = 6 kenimika / 2 = -3 kenimika

ʻO ka lōʻihi o ke kikowaena o ke aniani convex ua hōʻailona ʻia he maikaʻi ʻole no ka mea he virtual. Virtual no ka mea ʻaʻole ia i hala ʻia e ka mālamalama.

Makemake ʻia: Nā waiwai kiʻi

Lōlā:

Ka mamao o ke kiʻi (d'):

1/d' = 1/f – 1/d = -1/3 – 1/12 = -4/12 – 1/12 = -5/12

d' = -12/5 = -2.4 kenimika

ʻO ka mamao o ke kiʻi i hōʻailona ʻia me ka maikaʻi ʻole, ʻo ia hoʻi he virtual ke kiʻi.

Hoʻonui ʻia o ke kiʻi (m):

m = -d' / d = -(-2.4) / 12 = 2.4 / 12 = 0.2 manawa

ʻO ka hoʻonui ʻia ʻana o ke kiʻi i hōʻailona ʻia he maikaʻi ʻo ia hoʻi ua kū pololei ke kiʻi a ʻo ka hoʻonui ʻia ʻana o ke kiʻi he 0.2 ʻo ia hoʻi ua liʻiliʻi ka nui o ke kiʻi ma mua o ka nui o ka mea (ua hoʻemi ʻia).

ʻO ka pane pololei ʻo C.

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1. Nā pilikia a me nā hoʻonā o ke aniani concave
2. Nā pilikia a me nā hoʻonā o ke aniani convex
3. Nā pilikia a me nā hoʻonā o ka diverging lens
4. Nā pilikia a me nā hoʻonā o ka lens converging
5. Nā mea hana optical nā pilikia a me nā hoʻonā o ka maka kanaka
6. Nā pilikia a me nā hoʻonā no nā mea hana optical
7. Nā aniani maka mea hana maka
8. Nā pilikia a me nā hoʻonā o nā mea hana optical hoʻonui aniani
9. ʻO ka microscope mea hana optical - nā pilikia a me nā hoʻonā
10. Nā pilikia a me nā hoʻonā o nā teleskope mea hana optical

heluhelu hou

1. Ua kau ʻia kekahi mea ma kahi mamao o 10 kenimika mai kahi aniani ʻūpā. ʻO ka lōʻihi o ke kikowaena he 5 kenimika. E hoʻoholo (a) i ke kiʻi mamao (b) ka hoʻonui ʻana o ke kiʻi

ʻIke ʻia:

Ka lōʻihi o ke kikowaena (f) = 5 kenimika

Ka mamao o ka mea (d_o) = 10 kenimika

pāʻoihana :

Ka hoʻokumu ʻia ʻana o ke kiʻi e ke aniani concave:

Ka mamao o ke kiʻi:

1/d_i = 1/f – 1/d_o = 1/5 – 1/10 = 2/10 – 1/10 = 1/10

d_i = 10/1 = 10 kenimika

ʻO ka mamao o ke kiʻi 10 wm.

Ka hoʻonui ʻana:

m = –d_i / d_o = -10/10 = -1

ʻO ke ʻano o 1, ua like ke kiʻi me ka mea.

ʻO ka hōʻailona minus hōʻike ua hoʻohuli ʻia ke kiʻi. Inā maikaʻi ka hōʻailona a laila kū pololei ke kiʻi.

2. Ua kau ʻia kahi mea he 5 kenimika ke kiʻekiʻe i mua o ke aniani concave me ka radius o ke kūlou ʻana o 20 kenimika. E hoʻoholo i ke kiʻekiʻe o ke kiʻi inā ʻo ka mamao o ka mea 5 kenimika, 15 kenimika, 20 kenimika, 30 kenimika.

ʻIke ʻia:

ʻO ke radius o ke kūlou (r) = 20 kenimika

Ka lōʻihi o ke kikowaena (f) = R/2 = 20/2 = 10 kenimika

Ke kiʻekiʻe o ka mea (h_o) = 5 kenimika

Lōlā:

a) ka lōʻihi o ke kikowaena (f) = 10 kenimika a me ka mamao o ka mea (d_o) = 5 kenimika

Ka hoʻokumu ʻia ʻana o ke kiʻi e ke aniani concave:

Ka mamao o ke kiʻi (d_i):

1/d_i = 1/f – 1/d_o = 1/10 – 1/5 = 1/10 – 2/10 = -1/10

d_i = -10/1 = -10 kenimika

Hōʻike ka hōʻailona minus kēlā kiʻi he virtual a i ʻole aia ke kiʻi ma hope o ke aniani.

Ka hoʻonui ʻana i ke kiʻi (m):

m = -d_i / d_o = -(-10)/5 = 10/5 = 2

Hōʻike ka hōʻailona hoʻohui ua kū pololei ke kiʻi.

Ke kiʻekiʻe o ke kiʻi (h_i):

m = h_i / h_o

h_i = h_o m = (5 kenimika)(2) = 10 kenimika

ʻO 10 ke kiʻekiʻe o ke kiʻi knm

b) Ka lōʻihi o ke kikowaena (f) = 10 kenimika a me ka mamao o ka mea (d_o) = 15 kenimika

Ka hoʻokumu ʻia ʻana o ke kiʻi e ke aniani concave:

Ka mamao o ke kiʻi (d_i):

1/d_i = 1/f – 1/d_o = 1/10 – 1/15 = 3/30 – 2/30 = 1/30

d_i = 30/1 = 30 kenimika

Hōʻike ka hōʻailona hoʻohui he ʻoiaʻiʻo ke kiʻi a i ʻole ke kiʻi he 30 kenimika i mua o ke aniani, ma ka ʻaoʻao like me ka mea.

Ka hoʻonui ʻana i ke kiʻi (m):

m = -d_i / d_o = -30/15 = -2

Hōʻike ka hōʻailona hoʻēmi ua hoʻohuli ʻia ke kiʻi.

ʻElua manawa ka nui o ke kiʻi ma mua o ka mea.

Ke kiʻekiʻe o ke kiʻi (h_i):

m = h_i / h_o

h_i = h_o m = (5 kenimika)(2) = 10 kenimika

He 10 kenimika ke kiʻekiʻe o ke kiʻi.

c) ʻO ka lōʻihi o ke kikowaena (f) = 10 kenimika a me ka mamao o ka mea (d_o) = 20 kenimika

Ka hoʻokumu ʻia ʻana o ke kiʻi e ke aniani concave:

ʻO ka mamao o ke kiʻi (d_i):

1/d_i = 1/f – 1/d_o = 1/10 – 1/20 = 2/20 – 1/20 = 1/20

d_i = 20/1 = 20 kenimika

Hōʻike ka hōʻailona maikaʻi he ʻoiaʻiʻo ke kiʻi a i ʻole ke kiʻi he 20 kenimika i mua o ke aniani, ma ka ʻaoʻao like me ka mea.

Ka hoʻonui ʻana i ke kiʻi (m):

m = -d_i / d_o = -20/20 = -1

ʻO ke ʻano o ka hōʻailona maikaʻi ʻole, ua hoʻohuli ʻia ke kiʻi.

Ke kiʻekiʻe o ke kiʻi (hi):

m = h_i / h_o

h_i = h m = (5 kenimika)(1) = 5 kenimika

d) Ka lōʻihi o ke kikowaena (f) = 10 kenimika a me ka mamao o ka mea (d_o) = 30 kenimika

Ka mamao o ke kiʻi (d_i):

1/d_i = 1/f – 1/d_o = 1/10 – 1/30 = 3/30 – 1/30 = 2/30

d_i = 30/2 = 15 kenimika

Hōʻike ka hōʻailona hoʻohui he ʻoiaʻiʻo ke kiʻi a i ʻole aia ke kiʻi he 15 kenimika i mua o ke aniani, ma ka ʻaoʻao like me ka mea.

Ka hoʻonui ʻana i ke kiʻi (m) :

m = -d_i / d_o = -15/30 = -0.5

Hōʻike ka hōʻailona hoʻēmi ua hoʻohuli ʻia ke kiʻi.

ʻOi aku ka liʻiliʻi o ke kiʻi ma mua o ka mea he 0.5.

Ke kiʻekiʻe o ke kiʻi (h_i):

m = h_i / h_o

h_i = h_o m = (5 kenimika)(0.5) = 2.5 kenimika

3. ʻOi aku ka nui o ke kiʻi i hana ʻia e ke aniani concave i ʻehā manawa ma mua o ka mea. Inā he 20 kenimika ke radius o ke kūlou ʻana, e hoʻoholo i ka mamao o ka mea i mua o ke aniani!

ʻIke ʻia:

Ka hoʻonui ʻana i ke kiʻi (m) = 4

ʻO ke radius o ke kūlou (r) = 20 kenimika

Ka lōʻihi o ke kikowaena (f) = r/2 = 20/2 = 10 kenimika

makemake : Ka mamao o ka mea (d_o)

Lōlā:

m = - d_i / d_o

4 = – d_{i /} d_o

- d_i = 4 d_o

d_i = – 4 d_o

1/f = 1/d_o + 1/d_i

1/10 = 1/d_o + 1/4d_o

4 / 40 = 4 / 4d_o + 1/4d_o

4 / 40 = 5 / 4d_o

(4)(4s) = (5)(40)

16 d_o = 200

d_o = 12.5 knm

Ka mamao o ka mea = 12.5 wm.

4. Ua kau ʻia kahi mea 1-cm ke kiʻekiʻe he 10 cm mai ke aniani concave me ka lōʻihi o ke kikowaena, f = 15 cm. E hoʻoholo:

A. Ka mamao o ke kiʻi?

B. Ke kiʻekiʻe o ke kiʻi?

C. Nā ʻano o ke kiʻi i hoʻokumu ʻia e ke aniani concave?

ʻIke ʻia:

ʻO ke kiʻekiʻe o ka mea (h) = 1 kenimika

ʻO ka mamao o ka mea (d_o) = 10 kenimika

ʻO ka lōʻihi o ke kikowaena o ke aniani concave (f) = 15 kenimika

Lōlā:

A. Ka mamao o ke kiʻi (d_i)

1/f = 1/d_o + 1/lā_i

1/d_i = 1/f – 1/d_o = 1/15 – 1/10 = 2/30 – 3/30 = -1/30

d_i = -30/1 = -30 kenimika

Hōʻike ka hōʻailona maikaʻi ʻole he virtual ke kiʻi a i ʻole aia ke kiʻi ma hope o ke aniani.

B. Ke kiʻekiʻe o ke kiʻi (h_i)

Ka hoʻonui ʻana o ke kiʻi (M):

M = -d_i/d_o = h_i/h_o

M = -(-30)/10 = 30/10 = 3 mau manawa

Ke kiʻekiʻe o ke kiʻi (h_i):

M = h_i / h_o

3 = h_i / 1 knm

h_i = 3 (1 kenimika)

h_i = 3 knm

ʻO ke kiʻekiʻe o ke kiʻi he 3 kenimika. Hōʻike ka hōʻailona hoʻohui ua piʻi ke kiʻi i luna.

C. Nā ʻano o ke kiʻi:

ʻIkepili, i luna, ʻoi aku ka nui ma mua o ka mea

5. ʻO ka hoʻonui ʻana o ke kiʻi, e like me ke kiʻi ma lalo nei.

ʻIke ʻia:

ʻO ka mamao o ka mea (d_o) = 60 kenimika

ʻO ka lōʻihi o ke kikowaena (f) = 20 kenimika

Makemake ʻia: Ka hoʻonui ʻana i ke kiʻi (M)

Lōlā:

Ka mamao o ke kiʻi:

1/f = 1/d_o + 1/lā_i

1/d_i = 1/f – 1/d_o = 1/20 kenimika – 1/60 kenimika = 3/60 kenimika – 1/60 kenimika = 2/60 kenimika

d_i = 60/2 kenimika = 30 kenimika

Ka hoʻonui ʻana o ke kiʻi (M):

M = d_i/d_o = 30 kenimika / 60 kenimika = 1/2 manawa

6. Inā Ke waiho ʻia ka mea ma kahi o 6 kenimika mai ke aniani concave, ʻo ka mamao o ke kiʻi he 12 kenimika e like me ka mea i hōʻike ʻia ma ke kiʻi ma lalo. He aha ka mamao o ke kiʻi inā e hoʻoneʻe ʻia ka mea mai ke kūlana mua he 1 kenimika ka mamao mai ke aniani aku.

ʻIke ʻia:

ʻO ka mamao o ka mea (d_o) = 6 kenimika

ʻO ka mamao o ke kiʻi (d_i) = 12 kenimika

Makemake ʻia: inā ka mamao o ka mea (d_o) = 7 kenimika a laila ʻo ka mamao o ke kiʻi he …

Lōlā:

1/f = 1/do + 1/di = 1/6 + 1/12 = 2/12 + 1/12 = 3/12

f = 12/3 = 4 kenimika

He maikaʻi ka lōʻihi o ke kikowaena, ʻo ia hoʻi he ʻoiaʻiʻo ke kiko kikowaena a i ʻole hele nā ​​kukuna ma waena o ke kiko.

Ka mamao o ke kiʻi:

1/d_i = 1/f – 1/d_o = 1/4 – 1/7 = 7/28 – 4/28 = 3/28

d_i = 28/3 = 9.3 kenimika

7. Nānā a nānā kekahi kauka niho i nā niho o ka mea maʻi me ka hoʻohana ʻana i ke aniani me ka radius 8 kenimika. I mea e ʻike maopopo ʻia ai ka lua e ke kauka, he aha ka mamao ma waena o nā niho o ka mea maʻi a me ke aniani?

A. emi ma mua o 4 kenimika i mua o ke aniani ʻūpā

B. emi ma mua o 4 kenimika i mua o ke aniani convex

C. ʻoi aku ma mua o 4 kenimika ma mua o ke aniani concave

D. ʻoi aku ma mua o 4 kenimika ma mua o ke aniani convex

ʻIke ʻia:

Ka laulā o ke aniani (r) = 8 kenimika

ʻO ka lōʻihi o ke kikowaena o ke aniani (f) = r / 2 = 8 / 2 = 4 kenimika

Makemake ʻia: ʻO ka mamao ma waena o nā niho o ka mea maʻi a me ke aniani

Lōlā:

ʻO ke aniani i hoʻohana ʻia he aniani concave a he aniani convex paha? I mea e ʻike maopopo ʻia ai ka lua o ka niho e ke kauka, pono e hiki i ke aniani i hoʻohana ʻia ke hoʻonui i ke kiʻi o ka niho a pono e kū pololei ke kiʻi. Hoʻopuka mau nā aniani convex i nā kiʻi i hoʻohuli ʻia a ʻoi aku ka liʻiliʻi o ka nui o ke kiʻi ma mua o ka nui o ka mea. I ka ʻaoʻao ʻē aʻe, hiki i ke aniani concave ke hana i kahi kiʻi kū pololei inā ʻoi aku ka liʻiliʻi o ka mamao o ka mea (d) ma mua o ka lōʻihi focal (f). Inā ʻoi aku ka nui o ka mamao o ka mea ma mua o ka lōʻihi focal (f) a laila hana ke aniani concave i kahi kiʻi i hoʻohuli ʻia.

ʻO ka lōʻihi o ke kikowaena (f) o ke aniani concave he 4 kenimika, no laila e emi nā niho o ka mea maʻi ma mua o 4 kenimika ma mua o ke aniani concave.

ʻO ka pane pololei ʻo A.

8. He 24 kenimika ka radius o ke kūlou ʻana o ke aniani concave. Inā kau ʻia ka mea he 20 kenimika i mua o ke aniani a laila e hoʻoholo i nā ʻano o ke kiʻi.

A. Maoli, kū pololei a hoʻonui ʻia

B. Maoli, hoʻohuli ʻia a hoʻonui ʻia

C. ʻAno like, kū pololei a hoʻonui ʻia

D. Virtual, inverted a liʻiliʻi

ʻIke ʻia:

Radius o curvature (r) = 24 kenimika

Ka lōʻihi o ke kikowaena (f) = R/2 = 24/2 = +12 kenimika

He maikaʻi a he maoli paha ka lōʻihi o ke kikowaena o ke aniani concave no ka mea, hele ka mālamalama ma ke kiko kikowaena o ke aniani.

Ka mamao o ka mea (d) = 20 kenimika

Makemake ʻia: Nā waiwai kiʻi

Lōlā:

He kiʻi maoli a he kiʻi maoli paha? E helu i ka mamao o ke kiʻi (s'):

1/d + 1/d' = 1/f

1/d' = 1/f – 1/d

1/d' = 1/12 – 1/20

1/d' = 5/60 – 3/60

1/d' = 2/60

d' = 60/2

d' = 30 kenimika

ʻO ka mamao o ke kiʻi i hōʻailona ʻia he maikaʻi ʻo ia hoʻi he ʻoiaʻiʻo ke kiʻi no ka mea ua hala ʻia e ka mālamalama.

Ua hoʻonui ʻia ke kiʻi? Kū pololei a hoʻohuli ʻia paha? E helu mua i ka hoʻonui ʻana o ke kiʻi (M):

M = -d' / d = -30/20 = -1.5

ʻO M > 1 ke ʻano ua hoʻonui ʻia ke kiʻi, ʻo M kahi hōʻailona maikaʻi ʻole ke ʻano he kiʻi i hoʻohuli ʻia. No laila, he ʻoiaʻiʻo, hoʻohuli ʻia, hoʻonui ʻia nā ʻano o ke kiʻi.

ʻO ka pane pololei ʻo B.

9. Hoʻopuka kahi aniani poepoe i kahi kiʻi he 5 manawa ka nui ma mua o ka mea ma ka pale, 5 mika ka mamao mai ka mea. ʻO ke aniani…..

A. concave me ka lōʻihi o ke kikowaena o 25/24 m

B. convex me ka lōʻihi o ke kikowaena o 25/24 m

C. concave me ka lōʻihi o ke kikowaena o 24/25 m

D. convex me ka lōʻihi o ke kikowaena o 24/25 m

ʻIke ʻia:

Hoʻonui ʻia o ke kiʻi (M) = 5 mau manawa

Ka mamao ma waena o ka mea a me ke kiʻi = 5 mika

Lōlā:

ʻOi aku ka liʻiliʻi o ka nui o ke kiʻi i hana ʻia e ke aniani convex ma mua o ka nui o ka mea, no laila, he aniani concave ke aniani.

Ka mamao o ka mea (d) = x

Ka mamao o ke kiʻi (d') = x + 5

Hoʻonui kiʻi (M) = 5 mau manawa

ʻO ke ʻano o ka hoʻonui ʻana i ke kiʻi:

ʻO ke ʻano o ka lōʻihi o ke kikowaena (f):

ʻO ka pane pololei ʻo A.

[wpdm_package id='858′]

1. Nā pilikia a me nā hoʻonā o ke aniani concave
2. Nā pilikia a me nā hoʻonā o ke aniani convex
3. Nā pilikia a me nā hoʻonā o ka diverging lens
4. Nā pilikia a me nā hoʻonā o ka lens converging
5. Nā mea hana optical nā pilikia a me nā hoʻonā o ka maka kanaka
6. Nā pilikia a me nā hoʻonā no nā mea hana optical
7. Nā aniani maka mea hana maka
8. Nā pilikia a me nā hoʻonā o nā mea hana optical hoʻonui aniani
9. ʻO ka microscope mea hana optical - nā pilikia a me nā hoʻonā
10. Nā pilikia a me nā hoʻonā o nā teleskope mea hana optical

heluhelu hou

1. 1 kg o ka wai ma 100^oC i hui pū ʻia me 1 kg o ka wai ma 10^oC i loko o kahi ʻōnaehana kaʻawale. ʻO ka wela kikoʻī o ka wai 4200 J/kg ^oC. E hoʻoholo i ka hopena wela o ka hui ʻana!

ʻIke ʻia:

Ka Mass o ka wai wela (m₁) = 1 kg

Mahana o ka wai wela (T₁) = 100^oC

Ka nui o ka wai anuanu (m₂) = 1 kg

Mahana o ka wai anuanu (T₂) = 10^oC

Makemake ʻia: Ka mahana hope loa (T)

Lōlā:

Wela i nalowale = Wela i loaʻa (ʻōnaehana kaʻawale)

m c ΔT = m c ΔT

m ΔT = m ΔT

m₁ (T₁ – T) = m₂ (T – T₂)

(1)(100 – T) = (1)(T – 10)

100 – T = T – 10

100 + 10 = T + T

110 = 2T

T = 110 / 2

T = 55

ʻO ka mahana hope loa 55^oC.

2. He poloka kēpau 3 kg ma 80^o i kau ʻia i loko o 10 kg o ka wai. ʻO ka wela kikoʻī o ke kēpau he 1400 J.kg^-1C^-1 a ʻo ka wela kikoʻī o ka wai he 4200 J.kg^-1C^-1ʻO ka mahana hope loa ma ke kaulike wela 20^oC. E hoʻoholo i ka mahana mua o ka wai!

ʻIke ʻia:

Ka Mass (m₁) = 3 kg

ʻO ka wela kikoʻī o ke kēpau (c₁) = 1400 J.kg^-1C^-1

Ka mahana o ke kēpau (T₁) = 80 ^oC

Ka nui o ka wai (m₂) = 10 kg

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

Ka mahana o ke kaulike wela (T) = 20 ^oC

Makemake ʻia: Ka mahana mua o ka wai (T₂)

Lōlā:

Wela i nalowale = Wela i loaʻa

Q alakai =Q ka wai

m₁ c₁ ΔT = m₂ c₂ ΔT

(3)(1400)(80-20) = (10)(4200)(20-T)

(4200)(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 14^oC.

3. He poloka keleawe ma 100^oC i hoʻokomo ʻia i loko o 128 grams o ka wai ma 30 ^oC. ʻO ka wela kikoʻī o ka wai 1 cal.g^-1oC^-1 a ʻo ka wela kikoʻī o ke keleawe 0.1 cal.g^-1oC^-1. Inā ʻo ka mahana o ke kaulike wela 36 ^oC, e hoʻoholo i ka nui o ke keleawe!

ʻIke ʻia:

Ka mahana o ke keleawe (T₁) = 100 ^oC

ʻO ka wela kikoʻī o ke keleawe (c₁) = 0.1 cal.g^-1oC^-1

Ka nui o ka wai (m₂) = 128 grams

Mahana wai (T₂) = 30 ^oC

ʻO ka wela kikoʻī o ka wai (c₂) = 1 cal.g^-1oC^-1

Ka mahana o ke kaulike wela (T) = 36 ^oC

Makemake ʻia: Ka nui o ke keleawe (m₁)

Lōlā:

Wela i nalowale = Wela i loaʻa

Q keleawe =Q ka 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 120 gram.

4. He poloka hau M-kg ma 0^oC i hoʻokomo ʻia i loko o 340 grams o ka wai ma 20^oC i loko o kahi pahu wai. Inā ʻo ka wela o ka hoʻoheheʻe ʻana no ka wai = 80 kal g^-1, ʻo ka wela kikoʻī o ka wai 1 kal g^{-1 o}C^-1. Hoʻoheheʻe ʻia nā hau a pau a me ka mahana o ke kaulike wela is 5^oC, e hoʻoholo i ka nui o ka hau!

ʻIke ʻia:

Ka nui o ka wai (m) = 340 grams

Ka mahana o ka hau (T _{Ka hau}) = 0^oC

Ka mahana o ka wai (T _{ka wai}) = 20^oC

Ka mahana o ke kaulike wela (T) = 5^oC

Ka wela o ka fusion no ka wai (L) = 80 cal g^-1

ʻO ka wela kikoʻī o ka wai (c _{ka wai}) = 1 cal g^{-1 o}C^-1

Makemake ʻia: Ka Mass o ka hau (M)

Lōlā:

Wela i nalowale = Wela i loaʻa

Wai Q = hau Q

m c (ΔT) = m_es L_es +m c (ΔT)

(340)(1)(20-5) = M (80) + M (1)(5-0)

(340)(15) = 80M + 5M

5100 = 85M

M = 5100/85

M = 60 grams

[wpdm_package id='714′]

1. Ke hoʻololi nei i nā unahi mahana
2. Hoʻonui laina
3. Hoʻonui ʻāina
4. Hoʻonui leo
5. wela
6. ʻO ke kūlike mechanical o ka wela
7. Ka wela kikoʻī a me ka mana wela
8. Wela huna, wela o ka hoʻoheheʻe ʻana, wela o ka mahu
9. Ka mālama ʻana i ka ikehu no ka hoʻoili wela

heluhelu hou

4 Ka wela huna Ka wela o ka fusion Ka wela o ka vaporization - Nā pilikia a me nā hoʻonā

1. E helu i ka nui o wela i hoʻohui ʻia i 1 gram gula e hoʻololi i ke ʻano mai ka paʻa a i ka wai. ʻO ka wela o ka hoʻoheheʻe ʻana no ke gula he 64.5 x 10³ J/kg.

ʻIke ʻia:

Ka Mass (m) = 1 gram = 1 x 10^-3 kg

Ka wela o ka hoʻoheheʻe ʻana (L_F) = 64.5 x 10³ J / kg

Makemake ʻia: Wela (Q)

Lōlā:

Q = m L_F

Q = (1 x 10^-3 kg)(64.5 x 10³ (J/kg)

Q = 64.5 Joule

2. E helu i ka nui o ka wela i hoʻokuʻu ʻia e 1 gram o ka mercury e hoʻololi i ke ʻano mai ka wai a i ka paʻa. ʻO ka wela o ka fusion no ka mercury he 11.8 x 10³ J/kg.

ʻIke ʻia:

Nuipaʻa (m) = 1 gram = 1 x 10^-3 kg

Ka wela o ka hoʻoheheʻe ʻana (L_F) = 11.8 x 10³ J / kg

Makemake ʻia: Wela (Q)

Lōlā:

Q = m L_F

Q = (1 x 10^-3 kg)(11.8 x 10³ (J/kg)

Q = 11.8 Joule

3. E hoʻoholo i ka nui o ka wela i omo ʻia e 1 kg wai e hoʻololi i ke ʻano mai ka wai a i ka mahu (mahana). Ka wela o ka mahu no ka wai = 2256 x 10³ J / kg

ʻIke ʻia:

Nuipaʻa (m) = 1 kg

Ka wela o ka mahu (L_V) = 2256 m 10³ J / kg

Makemake ʻia: Wela (Q)

Lōlā:

Q = m L_V

Q = (1 kg)(2256 m 10³ (J/kg)

Q = 2256 x 10³ Joule

4. E hoʻoholo i ka nui o ka wela i hoʻokuʻu ʻia e ka naikokene e hoʻololi i ke ʻano mai ka mahu a i ka wai. Ka wela o ka vaporization no ka naikokene = 200 m 10³ J / kg

ʻIke ʻia:

Nuipaʻa (m) = 1 gram = 1 x 10^-3 kg

Ka wela o ka mahu (L_V) = 200 m 10³ J / kg

ʻIke ʻia: Wela (Q)

Lōlā:

Q = m L_V

Q = (1 x 10^-3 kg)(200 m 10³ (J/kg)

Q = 200 Joule

1. Ke hoʻololi nei i nā unahi mahana
2. Hoʻonui laina
3. Hoʻonui ʻāina
4. Hoʻonui leo
5. wela
6. ʻO ke kūlike mechanical o ka wela
7. Ka wela kikoʻī a me ka mana wela
8. Wela huna, wela o ka hoʻoheheʻe ʻana, wela o ka mahu
9. Ka mālama ʻana i ka ikehu no ka hoʻoili wela

heluhelu hou

1. He kino me nuipa 2 kg hoʻopili i ka wela 100 nā calorie i ka wā wela hoʻāla mai 20^oC i ka 70^oC. He aha ka wela kikoʻī o ke kino?

ʻIke ʻia:

Nuipaʻa (m) = 2 kg = 2000 gr

wela (Q) = 100 cal

Ka loli o ka mahana (ΔT) = 70^oC - 20^oC = 50^oC

Makemake ʻia: ʻO ka wela kikoʻī (c)

Lōlā:

c = Q / m ΔT

c = 100 kal / (2000 gr)(50^oC)

c = 100 kal / 100,000 gr ^oC

c = 10² kal / 10⁵ gr ^oC

c = (10² kal)(10^-5 gr^{-1 o}C^-1)

c = 10^-3 kāhea gr^{-1 o}C^-1

c = 10^-3 kal/gr ^oC

ʻO ka wela kikoʻī o ke kino 10^-3 kal/gr ^oC

2. ʻO ka wela kikoʻī o ka wai 4180 J/kg C^o. ʻEhia ka nui o ka hiki ke hoʻomehana i 2 kg o ka wai…

ʻIke ʻia:

ʻO ka wela kikoʻī (c) = 4180 J/kg C^o

Ka Mass (m) = 2 kg

Makemake ʻia: Makahiki wela (C)

Lōlā:

C = mc

C = (2 kg)(4180 J/kg C^o)

C = (2)(4180 J/C^o)

C = 8360 J/C^o

3. ʻO ka wela kikoʻī o ka alumini 900 J/kg C^o. ʻEhia ka nui o ka mana wela o 2 grams o ka alumini… ..

ʻIke ʻia:

ʻO ka wela kikoʻī o ka alumini (c) = 900 J/kg C^o = 9x10² J/kg C^o

Nuipaʻa (m) = 2 grams = 2/1000 kg = 2/10³ kg = 2 x 10^-3 kg

Makemake ʻia: Makahiki wela (C)

Lōlā:

C = mc

C = (2 x 10^-3 kg)(9 m 10² J/kg C^o)

C = 18 x 10^-3 x 10² J/C^o

C = 18 x 10^-1 J/C^o

C= 1.8 J/C^o

[wpdm_package id='710′]

1. Ke hoʻololi nei i nā unahi mahana
2. Hoʻonui laina
3. Hoʻonui ʻāina
4. Hoʻonui leo
5. wela
6. ʻO ke kūlike mechanical o ka wela
7. Ka wela kikoʻī a me ka mana wela
8. Wela huna, wela o ka hoʻoheheʻe ʻana, wela o ka mahu
9. Ka mālama ʻana i ka ikehu no ka hoʻoili wela

heluhelu hou

1. 2 tausanicʻal (kilo)calorie) = ….. calorie ?

pāʻoihana

1 kcal = 1000 calorie

2 kcal = 2 (1000 calorie) = 2000 calorie

2. 4 Calorie = ….. calorie ?

pāʻoihana

1 Calorie (he Kapikala C) = 1 kcal = 1000 calorie

4 Calorie = 4 (1000 calorie) = 4000 calorie

3. 10 calorie = ….. Joule

pāʻoihana

1 calorie = 4.186 Joule

10 calorie = 10 (4.186 Joules) = 41.86 Joules

4. 5 tausanical = ….. Joule ?

pāʻoihana

1 kcal = 1000 cʻalorie = 4186 Joule

5 kcal = 5 (4186 Joule) = 20930 Joule

5. 2000 Joules = ….. kcʻal?

pāʻoihana

4186 Joules = 1 kJcal

8372 Joules = 8372 / 4186 = 2 kcal

2000 Joules = 2000 / 4186 = 0.4777 kcal

[wpdm_package id='706′]

1. Ke hoʻololi nei i nā unahi mahana
2. Hoʻonui laina
3. Hoʻonui ʻāina
4. Hoʻonui leo
5. wela
6. ʻO ke kūlike mechanical o ka wela
7. Ka wela kikoʻī a me ka mana wela
8. Ka wela huna, ka wela o ka fusion, ka wela o ka vaporization
9. Ka mālama ʻana i ka ikehu no ka hoʻoili wela

heluhelu hou

9 Ka nuipa wela Ka wela kikoʻī Ka loli o ka mahana - Nā pilikia a me nā hoʻonā

1. Ua hoʻomehana ʻia kahi kēpau 2 kg mai 50^oC i ka 100^oC. ʻO ka wela kikoʻī o ke kēpau 130 J.kg^{-1 o}C^-1. ʻehia wela ua omo ʻia e ke kēpau?

ʻIke ʻia:

Ka Mass (m) = 2 kg

ʻO ka wela kikoʻī (c) = 130 J.kg^-1C^-1

Ka loli o ka mahana (ΔT) = 100^oC - 50^oC = 50^oC

Makemake ʻia: wela (Q)

Lōlā:

Q = mc ΔT

Q = wela, m = ka nuipaʻa, c = ka wela kikoʻī, ΔT= ka loli o ka mahana

ʻO ka wela i omo ʻia e ke kēpau:

Q = (2 kg)(130 J.kg^-1C^-1)(50^oC)

Q = (100)(130)

Q = 13,000 ʻO Joule

Q = 1.3 x 10⁴ Joule

2. ʻO ka wela kikoʻī o ke keleawe he 390 J/kg ^oC, ʻo ka loli o ka mahana 40^oC. Inā omo ke keleawe i 40 Joules o ka wela, he aha ke kaumaha o ke keleawe!

ʻIke ʻia:

ʻO ka wela kikoʻī o ke keleawe (c) = 390 J/kg^oC

Ka loli o ka mahana (ΔT) = 40^oC

Wela (Q) = 40 J

Makemake ʻia: Nui (m) o ke keleawe

Lōlā:

Q = mc ΔT

40 J = (m)(390 J/kg ^oC)(40^oC)

40 = (m)(390 /kg)(40)

40 = (m)(390/kg)(4)

40 = (m)(1560/kg)

m = 40 / 1560

m = 0.026 kg

m = 26 grams

3. ʻO ka mahana mua o 20 grams o ka wai he 30^oC. ʻO ka wela kikoʻī o ka wai he 1 cal g^{-1 o}C^-1Inā omo ka wai i 300 mau kaloli o ka wela, e hoʻoholo i ka mahana hope loa!

ʻIke ʻia:

Nuipaʻa (m) = 20 gr

Ka mahana mua (T₁) = 30^oC

ʻO ka wela kikoʻī o ka wai (c) = 1 kal gr^{-1 o}C^-1

wela (Q) = 300 kal

Makemake ʻia: Ka mahana hope loa o ka wai

Lōlā:

Q = mc ΔT

300 kal = (20 gr)(1 kal g^{-1 o}C^-1)(T₂-30)

300 = (20)(1)(T₂-30)

300 = 20 (T₂-30)

300 = 20T₂ - 600

300 + 600 = 20T₂

900 = 20T₂

T₂ = 900/20

T₂ = 45

ʻO ka loli o ka mahana he 45^oC - 30^oC = 15^oC.

4. Tka loli o ka mahana o ka wai kai is 1^oC ke omo ka wai i 3900 Joules o ka wela. ʻO ka wela kikoʻī o ka wai kai 3.9 × 10³ J/kg°C, he aha ke kaumaha o ka wai kai.

ʻIke ʻia:

Ka loli o ka mahana (ΔT) = 1^oC

wela (Q) = 3900 Joule

ʻO ka wela kikoʻī o ka wai kai (c) = 3.9 x 10³ J/kg°C = 3900 J/Kg°C

Makemake ʻia: Ka Mass (M)

Lōlā:

Q = mc ΔT

Q = wela, m = ka nuipaʻa, c = wela kikoʻī, ΔT= ka loli o ka mahana

m = Q / c ΔT = 3900 / (3900)(1) = 3900 / 3900 = 1 kg

5. He keleawe 2-kg hoʻopili i 39,000 J o ka wela ma 30°C. Inā ʻo ka wela kikoʻī o ke keleawe he 390 J/kg °C, he aha ka mahana hope loa o ke keleawe…

ʻIke ʻia:

Nuipaʻa (m) = 2 kg

Mahana mua (T₁) = 30^oC

wela (Q) = 39,000 Joule

Wela wela (c) o ke keleawe = 390 J/kg ^oC

makemake : Ka mahana hope loa (T₂)

Lōlā:

Q = mc ΔT

Q = wela, m = ka nuipaʻa, c = wela kikoʻī, ΔT = ka loli o ka mahana

Q = mc ΔT = mc (T₂ - T₁)

39,000 = (2)(390)(T₂ - 30)

100 = (2)(1)(T₂ - 30)

100 = (2)(T₂ - 30)

50 = T₂ - 30

T₂ = 50 + 30

T₂ = 80^oC

6. Ua hoʻomehana ʻia kahi wai 5-kg mai 15°C a i 40°C. He aha ka wela i omo ʻia e ka wai. ʻO ka wela kikoʻī o ka wai 4.2 × 10³ J/Kg° C.

ʻIke ʻia:

Nuipaʻa (m) = 5 kg

Mahana mua (T₁) = 15°C

Mahana hope loa (T₂) = 40°C

Ka wela kikoʻī o ka wai (c) = 4.2 × 10³ J/kg°C

Makemake ʻia: wela (Q)

Lōlā:

Q = mc ΔT

Q = (5 kg)(4.2 × 10³ J/kg°C)(40°C – 15°C)

Q = (5)(4.2 × 10³ J)(25)

Q = 525 x 10³ J

Q = 525,000 Joule

7. Ua hoʻomehana ʻia kahi wai 2-kg mai 24°C a i 90°C. He aha ka wela i omo ʻia e ka wai. ʻO ka wela kikoʻī o ka wai 4.2 × 10³ J/Kg° C.

ʻIke ʻia:

Nuipaʻa (m) = 2 kg

Mahana mua (T₁) = 24°C

Mahana hope loa (T₂) = 90°C

Ka wela kikoʻī o ka wai (c) = 4,200 Joules/kg°C

Makemake ʻia :: wela (Q)

Lōlā:

Q = m c ΔT

Q = (2 kg)(4,200 Joules/kg°C)(90°C – 24°C)

Q = (2 kg)(4,200 Joules/kg°C)(66°C)

Q = (132)((4,200 Joules)

Q = 554,400 Joule

8. Ua hoʻomehana ʻia kahi wai 5-gram mai 10°C a i 40°C. He aha ka wela i omo ʻia e ka wai. ʻO ka wela kikoʻī o ka wai he 1 ×10³ kāhea/gr°C.

ʻIke ʻia:

Nuipaʻa (m) = 5 grams

Mahana mua (T₁) = 10^oC

Mahana hope loa (T₂) = 40^oC

Ka wela kikoʻī o ka wai (c) = 1 cal/ gr°C

makemake : Wela

Lōlā:

Q = mc ΔT

Q = (5 grams)(1 kal/gr°C)(40^oC - 10^oC)

Q = (5)(1 cal)(30)

Q = 150 calories

9. Hoʻopili ka wai 0.2-kg i 42,000 Joules o ka wela ma 25^oC. ʻO ka wela kikoʻī o ka wai he 4200 J/kg ^oC, he aha ka mahana hope loa o ka wai.

ʻIke ʻia:

Ka Mass o ka wai (m) = 0.2 kg

wela (Q) = 42,000 Joule

Ka wela kikoʻī o ka wai (c) = 4200 J/kg ^oC

Mahana mua (T₁) = 25^oC

Makemake ʻia: Mahana hope loa (T₂)

Lōlā:

Q = mc ΔT = mc (T₂ - T₁)

Q = wela, m = ka nuipaʻa, c = wela kikoʻī, ΔT = ka loli o ka mahana, T₁ = ka mahana mua, T₂ = ka mahana hope loa

Q = mc (T₂ - T₁)

42,000 = (0.2)(4200)(T₂ - 25)

42,000 = 840 (T₂ - 25)

42,000 = 840 T₂ - 21,000

42,000 + 21,000 = 840 T₂

63,000 = 840 T₂

T₂ = 63,000/840

T₂ = 75^oC

1. Ke hoʻololi nei i nā unahi mahana
2. Hoʻonui laina
3. Hoʻonui ʻāina
4. Hoʻonui leo
5. wela
6. ʻO ke kūlike mechanical o ka wela
7. Ka wela kikoʻī a me ka mana wela
8. Wela huna, wela o ka hoʻoheheʻe ʻana, wela o ka mahu
9. Ka mālama ʻana i ka ikehu no ka hoʻoili wela

heluhelu hou

ʻIke wale ʻia ka hoʻonui laina e nā mea paʻa; ʻike ʻia ka hoʻonui nui e nā mea a pau, ʻo ka mea paʻa, ka wai, a me ke kinoea. Ua like ke kaulike o ka hoʻonui nui me ka kaulike o ka hoʻonui laina.

Wehewehe: V_o = Ka nui mua, V = Ka nui hope loa, ΔV = V – V_o = Ka loli o ka leo, T_o = Mahana mua, T = Mahana hope loa, ΔT = T – T_o = Ka loli o ka mahana, β = ke koina o ka hoʻonui ʻana o ka leo. Anakahi o β = (C^o) ^-1

Pili wale nō ka hoʻohālikelike hoʻonui leo i luna i ka wā e liʻiliʻi ai nā loli i ka leo o nā mea (ʻo ka mea paʻa, ka wai, a me ke kinoea) ma mua o ka leo mua o ka mea. Inā ʻoi aku ka nui o ka loli o ka leo o kahi mea ma mua o ka leo mua o ka mea, ʻaʻole hāʻawi ka hoʻohālikelike o ka hoʻonui leo i nā hopena kūpono. ʻO ka maʻamau, ʻaʻole nui loa nā loli i ka leo i ʻike ʻia e nā mea paʻa. Ma ka ʻaoʻao ʻē aʻe, nui ka coefficient o ka hoʻonui leo o ka wai a me ke kinoea. Maʻalahi hoʻi ke hoʻololi i ka coefficient o ka hoʻonui leo no nā mea kinoea inā loli ka mahana. No laila, hoʻohana wale ʻia ke ʻano ma luna no ka hoʻonui ʻana o nā mea paʻa.

1. Ma ka 30 ^oʻO ka nui o ka poepoe alumini he 30 kenimika³ʻO ke koina o hoʻonui laina he 24 x 10^{-6 o}C^-1Inā he 30.5 kenimika ka nui hope loa³, he aha ka mahana hope loa o ka poepoe alumini?

ʻIke ʻia:

ʻO ke koina o ka hoʻonui linear (α) = 24 x 10^{-6 o}C^-1

ʻO ke koena o hoʻonui leo (β) = 3 α = 3 m 24 m 10^{-6 o}C^-1 = 72x10^{-6 o}C^-1

ka loiloi mua wela (T₁) = 30^oC

Ka nui mua (V₁) = 30 kenimika³

ʻO ka leo hope loa (V₂) = 30.5 kenimika³

Ka loli o ka leo (ΔV) = 30.5 kenimika³ - 30 knm³ = 0.5 knm³

Makemake ʻia: Ka mahana hope loa (T₂)

Lōlā:

ΔV= β (V₁)(ΔT)

ΔV= β (V₁)(T₂ - T₁)

0.5 cm³ = (72 m 10^{-6 o}C^-1)(30 knm³)(T₂ - 30^oC)

0.5 = (2160 x 10^-6)(T₂ - 30)

0.5 = (2.160 x 10^-3)(T2 - 30)

0.5 = (2.160 x 10^-3)(T₂ - 30)

0.5 / (2.160 x 10^-3) = T₂ - 30

0.23 m 10³ =T₂ - 30

0.23 x 1000 = T₂ - 30

230 = T₂ - 30

230 + 30 = T₂

T₂ = 260^oC

2. ʻO ke koina o ka hoʻonui linear o kahi poepoe metala he 9 x 10^{-6 o}C^-1ʻO ke anawaena o loko o ka poepoe metala ma 20 ^oʻO C he 2.2 kenimika. Inā he 2.8 kenimika ke anawaena hope loa, he aha ka mahana hope loa!

ʻIke ʻia:

ʻO ke koina o ka hoʻonui linear (α) = 9 x 10^{-6 o}C^-1

ʻO ke koina o ka hoʻonui ʻana o ka leo (β) = 3 α = 3 m 9 m 10^{-6 o}C^-1 = 27x10^{-6 o}C^-1

Ka mahana mua (T₁) = 20^oC

ʻO ke anawaena mua (D₁) = 2.2 kenimika

ʻO ke anawaena hope loa (D₂) = 2.8 kenimika

ʻO ka radius mua (r₁) = D₁ / 2 = 2.2 kenimika³ / 2 = 1.1 kenimika³

ʻO ka radius hope loa (r₂) = D₂ / 2 = 2.8 kenimika³ / 2 = 1.4 kenimika³

Ka nui mua (V₁) = 4/3 pi r₁³ = (4/3)(3.14)(1.1 kenimika)³ = (4/3)(3.14)(1.331 kenimika³) = 5.57 kenimika³

ʻO ka leo hope loa (V₂) = 4/3 π r₂³ = (4/3)(3.14)(1.4 kenimika)³ = (4/3)(3.14)(2.744 kenimika³) = 11.48 kenimika³

Ka loli o ka leo (ΔV) = 11.48 kenimika³ - 5.57 knm³ = 5.91 knm³

Makemake ʻia: Ka mahana hope loa (T₂)

Lōlā:

ΔV= β (V₁)(ΔT)

5.91 cm³ = (27 m 10^{-6 o}C^-1)(5.57 cm³)(T₂ - 20^oC)

5.91 = (150.39 x 10^-6)(T₂ - 20)

5.91/150.39 x 10^-6 =T₂ - 20

0.039 m 10⁶ =T₂ - 20

39 m 10³ =T₂ - 20

39,000 = T₂ - 20

39,000 + 20 = T₂

T₂ = 39,020 ^oC

3. He 2000-kenimika³ pahu alumini, piha i ka wai ma 0^oC. A laila hoʻomehana ʻia i 90^oC. Inā ʻo ke koina o ka hoʻonui linear no ka alumini he 24 x 10^-6 (^oC)^-1 a ʻo ke koina o ka hoʻonui ʻana o ka nui no ka wai he 6.3 x 10^-4 (^oC)^-1, e hoʻoholo i ka nui o ka wai i ninini ʻia.

ʻIke ʻia:

ʻO ka nui mua o ka pahu alumini a me ka wai (V_o) = 2000 kenimika³ = 2x10³ cm³

ʻO ka mahana mua o ka pahu alumini a me ka wai (T₁) = 0^oC

ʻO ka mahana hope loa o ka pahu alumini a me ka wai (T₂) = 90^oC

ʻO ke koina o ka hoʻonui linear no ka alumini (α) = 24 x 10^-6 (^oC)^-1

ʻO ke koina hoʻonui leo no ka alumini (γ) = 3α = 3 (24 x 10^-6 (^oC)^-1 ) = 72 x 10^{-6 o}C^-1

ʻO ke koina o ka hoʻonui ʻana o ka nui no ka wai (γ) = 6.3 x 10^-4 (^oC)^-1

Makemake ʻia: Ka nui o ka wai i ninini ʻia

Lōlā:

ʻO ke kaulike o ka hoʻonui ʻana o ka leo:

V = V_o + γ V_o ΔT

V–V_o = γ V_o ΔT

ΔV = γ V_o ΔT

V = ka nui hope loa, V_o = ka nui mua, ΔV = ka loli o ka leo, γ = ke koina o ka hoʻonui ʻana o ka leo, ΔT = ka loli o ka mahana

E helu i ka loli o ka nui o ka ipu alumini:

ΔV = γ V_o ΔT = (72 x 10^-6)(2 x 10³)(90) = 12960 x 10^-3 = 12.960 knm³

E helu i ka loli o ka nui o ka wai:

ΔV = γ V_o ΔT = (6.3 m 10^-4)(2 x 10³)(90) = 1134 x 10^-1 = 113.4 knm³

ʻOi aku ka nui o ka loli o ka nui o ka wai ma mua o ka ipu alumini a no laila ua ninini ʻia kekahi wai.

E helu i ka nui o ka wai i ninini ʻia:

113.4 cm³ - 12.960 knm³ = 100.44 knm³

[wpdm_package id='702′]

1. Ke hoʻololi nei i nā unahi mahana
2. Hoʻonui laina
3. Hoʻonui ʻāina
4. Hoʻonui leo
5. wela
6. ʻO ke kūlike mechanical o ka wela
7. Ka wela kikoʻī a me ka mana wela
8. Ka wela huna, ka wela o ka fusion, ka wela o ka vaporization
9. Ka mālama ʻana i ka ikehu no ka hoʻoili wela

heluhelu hou

1. I ka 20 ^oC, ʻo ka lōʻihi o kahi ʻāpana kila he 50 cm a ʻo ka laulā he 30 cm. Inā ʻo ke koina o hoʻonui laina no ke kila he 10^{-5 o}C^-1, e hoʻoholo i ka loli o ka ʻāpana a me ka ʻāpana hope loa ma 60 ^oC.

ʻIke ʻia:

ka loiloi mua wela (T₁) = 20^oC

ʻO ka mahana hope loa (T₂) = 60^oC

Ka loli ʻana o ka mahana (ΔT) = 60^oC - 20^oC = 40^oC

ʻO ka ʻāpana mua (A₁) = ka lōʻihi x ka laulā = 50 kenimika x 30 kenimika = 1500 kenimika²

ʻO ke koina o ka hoʻonui linear no ke kila (α) = 10^{-5 o}C^-1

ʻO ke koena o hoʻonui ʻāina no ke kila (β) = 2α = 2 m 10^{-5 o}C^-1

Makemake ʻia: ʻO ka loli ʻana o ka wahi (ʻΔA)

Lōlā:

ʻO ka loli ʻana o ka wahi (ʻΔA):

ΔA = β A₁ ΔT

ΔA = (2 m 10^{-5 o}C^-1)(1500 kenimika²)(40^oC)

ʻΔA = (80 x 10^-5)(1500 kenimika²)

ΔA = 120,000 m 10^-5 cm²

ΔA = 1.2 m 10⁵ x 10^-5 cm²

ΔA = 1.2 cm²

ʻO ka ʻāpana hope loa (A₂):

A₂ =A₁ + ʻΔA

A₂ = 1500 knm² + 1.2 cm²

A₂ = 1501.2 cm²

2. I ka 30 ^oC, ʻo ka ʻāpana o kahi pepa alumini he 40 cm² a ʻo ke koina o ka hoʻonui linear he 24 x 10^-6 /^oC. E hoʻoholo i ka mahana hope loa inā he 40.2 kenimika ka ʻāpana hope loa².

ʻIke ʻia:

ʻO ka mahana mua (T₁) = 30^oC

ʻO ke koina o ka hoʻonui linear (α) = 24 m 10^{-6 o}C^-1

ʻO ke koina o ka hoʻonui ʻana o ka ʻāpana (β) = 2a = 2 m 24 m 10^{-6 o}C^-1 = 48 x 10^{-6 o}C^-1

ʻO ka ʻāpana mua (A₁) = 40 kenimika²

ʻO ka ʻāpana hope loa (A₂) = 40.2 kenimika²

ʻO ka loli ʻana o ka wahi (ΔA) = 40.2 cm² - 40 knm² = 0.2 knm²

Makemake ʻia: E hoʻoholo i ka mahana hope loa (T₂)

Lōlā:

ʻO ke ʻano o ka loli o ka wahi (ΔA) :

ΔA = β A₁ ΔT

ʻO ka mahana hope loa (T₂):

ʻΔA = β A₁ (T₂ - T₁)

0.2 cm² = (48 x 10^{-6 o}C^-1)(40 kenimika²)(T₂ - 30^oC)

0.2 = (1920 x 10^-6)(T₂ - 30)

0.2 = (1.920 x 10^-3)(T₂ - 30)

0.2 = (2 x 10^-3)(T₂ - 30)

0.2 / (2 x 10^-3) = T₂ - 30

0.1 x 10³ = T₂ - 30

1 m 10² =T₂ - 30

100 = T₂ - 30

100 + 30 = T₂

T₂ = 130

ʻO ka mahana hope loa = 130^oC

3. ʻO ke anawaena o ke apo ma 20 ^oHe 20 kenimika ʻo C. Inā ʻo ka radius hope loa ma 100 ^oʻO C he 20.5 kenimika, e hoʻoholo i ke koina o ka hoʻonui ʻana o ka ʻāpana a me ke koina o ka hoʻonui linear…

ʻIke ʻia:

ʻO ka mahana mua (T₁) = 30^oC

ʻO ka mahana hope loa (T₂) = 100^oC

Ka loli ʻana o ka mahana (ΔT) = 100^oC - 30^oC = 70^oC

ʻO ke anawaena mua (r₁) = 20 kenimika

ʻO ka radius hope loa (r₂) = 20.5 kenimika

Makemake ʻia: ʻO ke koina o ka hoʻonui ʻana o ka ʻāpana (β)

Lōlā:

ʻO ka ʻāpana mua (A₁) = π r₁² = (3.14)(20 kenimika)² = (3.14)(400 kenimika²) = 1256 kenimika²

ʻO ka ʻāpana hope loa (A₂) = π r₂² = (3.14)(20.5 kenimika)² = (3.14)(420.25 kenimika²) = 1319.585 kenimika²

ʻO ka loli ʻana o ka wahi (ΔA) = 1319.585 cm² - 1256 cm² = 63.585 knm²

ʻO ke ʻano o ka loli o ka wahi (ΔA) :

ΔA = β A₁ ΔT

ʻO ke koina o ka hoʻonui ʻana o ka ʻāpana:

ΔA = β A₁ ΔT

63.585 cm² = b (1256 cm²)(70 ^oC)

63.585 = b (87,920 ^oC)

= 63.585 / 87,920 ^oC

β = 0.00072 /^oC

β = 7.2 x 10^-4 /^oC

β = 7.2 x 10^{-4 o}C^-1

ʻO ke koina o ka hoʻonui linear (α):

β = 2 α

α = β / 2

α = (7.2 x 10^-4) / 2

α = 3.6 x 10^{-4 o}C^-1

[wpdm_package id='698′]

1. Ke hoʻololi nei i nā unahi mahana
2. Hoʻonui laina
3. Hoʻonui ʻāina
4. Hoʻonui leo
5. wela
6. ʻO ke kūlike mechanical o ka wela
7. Ka wela kikoʻī a me ka mana wela
8. Wela huna, wela o ka hoʻoheheʻe ʻana, wela o ka mahu
9. Ka mālama ʻana i ka ikehu no ka hoʻoili wela

heluhelu hou