Okpomọkụ na okpomọkụ - nsogbu na ngwọta
1. Na temometa X, ebe mmiri na-ajụ oyi na -30 o na ebe mmiri na-esi na 90 o . 60 o X = ….. o C.
A maara:
Ebe oyi mmiri na-atụ = -30 o
Ebe mmiri na-esi mmiri = 90 o
Achọrọ: 60 o X = ….. o C
Ngwọta:
N'ọkwa Fahrenheit, ebe mmiri na-ajụ oyi bụ 32 o F ebe mmiri na-esi esi bụ 212 o F. N'etiti ebe oyi na-ajụ oyi na ebe mmiri na-esi esi, 212 o – 32 o = 180 o.
N'ọkwa Celsius, ebe mmiri na-ajụ oyi bụ 0 o C ebe ebe mmiri na-esi esi bụ 100 o C. N'etiti ebe oyi na-ajụ oyi na ebe mmiri na-esi esi, 100 o – 0 o = 100 o.
Na nha X , ebe oyi mmiri na - ajụ oyi bụ -30 o
Gbanwee nha X ka ọ bụrụ nha Celsius:
2. Mkpanaka ígwè a na-ekpo ọkụ site na 30oC na 80oC. Ogologo ikpeazụ nke mkpanaka ahụ bụ 115 cm. Ọnụ ọgụgụ nke Mgbasawanye ahịrị is 3.10-3 oC-1. Kedu ogologo mbụ nke mkpanaka ígwè ahụ?
A maara:
Okpomọkụ mbụ ( T 1 ) = 30 oC
Okpomọkụ ikpeazụ (T2 ) = 80 oC
Mgbanwe na okpomọkụ (ΔT) = 80 o C – 30 o C = 50 o C
Ọnụọgụ nke mgbasawanye ahịrị (α) = 3.10 -3 o C -1
Ogologo ikpeazụ nke ígwè ahụ (L) = 115 cm
Achọtara: Ogologo mbụ nke mkpanaka ígwè (L o )
Ngwọta:
Usoro nke mgbasawanye ahịrị:
L = L o + ΔL
L = L o + α L o ΔT
L = L o (1 + α ΔT)
115 = L o (1 + 3.10 -3 .50)
115 = L o (1 + 150.10 -3 )
115 = L o (1 + 0.15)
115 = L o (1.15)
L o = 115 / 1.15
L o = 100 cm
3. Ogologo mbụ nke mkpanaka ọla bụ 40 cm. Mgbe a kpochara ya ọkụ, ogologo ikpeazụ nke ọla ahụ bụ 40.04 cm, okpomọkụ ikpeazụ bụkwa 40.04 cm. 80oC. Ọ bụrụ na ọnụọgụgụ nke mgbasawanye linear nke ọla ahụ bụ 2.0 x 10-5 oC-1, kedu ka okpomọkụ mbụ nke mkpanaka ọla ahụ dị?
A maara:
Okpomọkụ ikpeazụ (T2 ) = 80 oC
Ogologo mbụ (L o ) = 40 cm
Ogologo ikpeazụ (L) = 40.04 cm
Mmụba n'ogologo (ΔL) = 40.04 cm – 40 cm = 0.04 cm
Ọnụọgụ nke mgbasawanye ahịrị (α) = 2.0 x 10 -5 o C -1
Ngwọta: Okpomọkụ mbụ (T 1 )
Ngwọta;
Usoro nke mgbasawanye ahịrị:
L = L o + α L o ΔT
L – L o = α L o ΔT
ΔL = α L o ΔT
ΔL = α L o (T 2 – T 1 )
0.04 = (2.0 x 10 -5 )(40)(80 – T 1 )
0..04 = (80 x 10 -5 )(80 – T 1 )
0.04 = 0.0008 (80 – T 1 )
0.04 = 0.064 – 0.0008 T 1
0..0008 T 1 = 0.064 – 0.040
0.0008 T 1 = 0.024
T 1 = 30 o C
4. Ogwe ígwè abụọ nwere otu nha mana ụdị dị iche iche, dịka egosiri na eserese dị n'okpuru. Nhazi okpomọkụ nke ígwè I = okpukpu anọ nke nhazi okpomọkụ nke ígwè II. Kedu okpomọkụ dị n'etiti ígwè abụọ ahụ.
A maara:
Nha nke mkpanaka abụọ ahụ bụ otu.
Ọkwa okpomọkụ nke ígwè I = 4k
Ọkwa okpomọkụ nke metal II = k
Okpomọkụ nke otu nsọtụ ígwè I = 50 0 C
Okpomọkụ nke otu nsọtụ ígwè II = 0 0 C
Achọrọ: Okpomọkụ dị n'etiti mkpanaka ígwè abụọ ahụ
Ngwọta:
Usoro nke nnyefe okpomọkụ:
Q/t = ọnụego nke nnyefe okpomọkụ , k = nnyefe okpomọkụ , A = mpaghara obe , T 1 -T 2 = mgbanwe na okpomọkụ , l = ogologo mkpanaka ahụ.
Okpomọkụ dị n'etiti mkpanaka abụọ ahụ:
Okpomọkụ dị n'etiti mkpanaka ígwè abụọ ahụ bụ 40 o C.
5.
(1) Nhazi nke ígwè
(2) Ọdịiche nke okpomọkụ
(3) Ogologo ígwè
(4) Oke ígwè
Ihe ndị na-ekpebi ọnụego nke ikuku ọkụ na ọla bụ....
Ngwọta:
Dabere na nha anya nke nnyefe okpomọkụ, ihe ndị na-ekpebi ọnụego nnyefe okpomọkụ na ọla bụ njikwa nke ígwè (k), ọdịiche nke okpomọkụ (T) na ogologo nke ígwè (l).
6. Mkpara abụọ nke nha ha dị otu mana ụdị ha dị iche iche, dịka egosiri na eserese dị n'okpuru. Nduzi okpomọkụ nke mkpara P dị okpukpu abụọ nke nduzi okpomọkụ nke mkpara Q. Kedu okpomọkụ dị n'etiti mkpara abụọ ahụ?
A maara:
Mkpara abụọ ahụ nwere otu nha.
Ọkwa okpomọkụ nke mkpanaka P (k P ) = 2k
Ọkwa okpomọkụ nke mkpanaka Q (k Q ) = k
Achọrọ: Okpomọkụ dị n'etiti mkpanaka abụọ ahụ
Ngwọta:
Usoro nke nnyefe okpomọkụ:
Q/t = ọnụego nke nnyefe okpomọkụ , k = nnyefe okpomọkụ , A = mpaghara obe , T 1 -T 2 = mgbanwe na okpomọkụ , l = ogologo mkpanaka ahụ.
Okpomọkụ dị n'etiti mkpanaka abụọ ahụ:
8. A na-etinye mmanụ gram 100 na 20 oC na ígwè gram 50 na 75 oC n'ime akpa ígwè gram 200. Mmụba okpomọkụ nke akpa ahụ bụ 5 oC na okpomọkụ mmanụ kpọmkwem bụ 0.43 cal/g oC . Kedu okpomọkụ kpọmkwem nke ígwè ahụ?
A maara:
Ibu nke akpa ígwè (m) = 200 gr
Okpomọkụ mbụ nke akpa ígwè (T 1 ) = okpomọkụ mmanụ = 20 oC
Okpomọkụ ikpeazụ nke akpa ígwè ahụ (T2 ) = 20 oC + 5 oC = 25 oC
Ọnụọgụ mmanụ (m) = gram 100
Okpomọkụ kpọmkwem nke mmanụ (c mmanụ ) = 0.43 cal/g o C
Okpomọkụ mbụ nke mmanụ (T 1 ) = 20 oC
Okpomọkụ ikpeazụ nke mmanụ (T2 ) = 20 oC + 5 oC = 25 oC
Ibu ígwè (m) = gram 50
Okpomọkụ mbụ nke mmanụ (T 1 ) = 75 oC
Okpomọkụ ikpeazụ nke mmanụ (T2 ) = 25 oC
Achọtara: Okpomọkụ kpọmkwem nke ígwè (c iron)
Ngwọta:
Okpomọkụ nke ígwè na-ewepụta:
Q = mc ΔT = (50)(c)(75-25) = (50)(c)(50) = 2500c kalori
Okpomọkụ nke akpa ígwè ahụ na-amịkọrọ:
Q = mc ΔT = (200)(c)(25-20) = (200)(c)(5) = 1000c kalori
Okpomọkụ mmanụ na-amịkọrọ:
Q = mc ΔT = (100)(0.43)(25-20) = (43)(5) = kalori 215
Ụkpụrụ ojii na-ekwu na n'ime sistemụ dịpụrụ adịpụ, okpomọkụ nke ihe na-ekpo ọkụ na-ewepụta, nke ihe na-ajụ oyi na-amịkọrọ.
Mwepụta Q = Ntinye Q
2500c = 1000c + 215
2500c – 1000c = 215
1500c = 215
c = 215/1500
c = 0.143 kalori/g o C
9. Mmiri gram 200 na 20°C nke e tinyere n'ime ice gram 50 na -2°C. Ọ bụrụ na mgbanwe nke okpomọkụ dị naanị n'etiti mmiri na ice, kedu okpomọkụ ikpeazụ nke ngwakọta ahụ? Okpomọkụ kpọmkwem nke mmiri bụ 1 cal/gr°C, okpomọkụ kpọmkwem nke ice bụ 0.5 cal/gr°C, okpomọkụ nke ngwakọta maka ice bụ 80 cal/gr.
A maara:
Mmiri dị arọ (m ) = gram 200
Okpomọkụ mmiri (T mmiri ) = 20 oC
Okpomọkụ kpọmkwem nke mmiri (c mmiri ) = 1 kalori/gr°C
Ibu ice (mita ice ) = gram 50
Okpomọkụ nke ice (T ice ) = -2 oC
Okpomọkụ kpọmkwem nke ice (c ice ) = 0.5 cal/gr°C
Okpomọkụ nke njikọta maka ice (L) = 80 cal/gr
Ngwọta:
Okpomọkụ iji mee ka ice dịkwuo elu site na -2 oC ruo 0 oC :
Q = mc ΔT
Q = (gram 50)(0.5 kalori/gr°C)(0 o C – (-2 o C))
Q = (50)(0.5 cal)(2)
Q = kalori 50
Okpomọkụ maka ịgbaze ice niile:
Q = m L = (gram 50)(cal 80/gram) = kalori 4000
Okpomọkụ maka ibelata okpomọkụ mmiri niile site na 20 oC ruo 0 oC :
Q = mc ΔT
Q = (gram 200)(1 kalori/gr°C)(0 o C – (20 o C))
Q = (200)(1 cal)(-20)
Kalori Q = -4000
Akara mgbakwunye ahụ na-egosi na a na-agbakwunye okpomọkụ ahụ, akara mwepu ahụ na-egosi na a na-ahapụ okpomọkụ ahụ.
A chọrọ kalori iri ise (50-calorie) nke okpomọkụ iji mee ka okpomọkụ ice dịkwuo elu ruo 0 oC na kalori iri anọ (4000-calorie) dị mkpa iji gbazee ice niile. Okpomọkụ zuru oke = kalori iri anọ na ise (4050). Okpomọkụ mmiri na-ewepụta bụ kalori iri anọ (4000).
Ụfọdụ ice anaghị agbaze, yabụ okpomọkụ ikpeazụ nke ice na mmiri bụ 0 oC.
10. Aluminom gram 200 na 20 oC nke e tinyere n'ime mmiri gram 100 na 80 oC n'ime akpa. Okpomọkụ kpọmkwem nke aluminom bụ 0.22 cal/g oC na okpomọkụ kpọmkwem nke mmiri bụ 1 cal/g o C. Kedu okpomọkụ ikpeazụ nke aluminom?
A maara:
Ibu nke aluminom = gram 200
Okpomọkụ nke aluminom = 20 oC
Mmiri dị arọ = gram 100
Okpomọkụ mmiri = 80 oC
Okpomọkụ kpọmkwem nke aluminom = 0.22 cal/ g oC
Okpomọkụ kpọmkwem nke mmiri = 1 kalori/g o C
Chọrọ: Okpomọkụ ikpeazụ nke aluminom
Ngwọta:
Aluminom na mmiri dị n'ọkwa okpomọkụ nke mere na okpomọkụ ikpeazụ nke aluminom = okpomọkụ ikpeazụ nke mmiri.
Okpomọkụ nke mmiri ọkụ na-ewepụta (Q release) = okpomọkụ nke aluminom na-amịkọrọ (Q receptor)
mmiri m c ( Δ T) = m aluminom c ( Δ T)
(100)(1)(80 – T) = (200)(0.22)(T – 20)
(100)(80 – T) = (44)(T – 20)
8000 – 100T = 44T – 880
8000 + 880 = 44T + 100T
8880 = 144T
T = 62 o C
11. E tinyere ígwè gram 50 na 85 Celsius n'ime mmiri gram 50 na 29.8 Celsius. Okpomọkụ mmiri kpọmkwem = 1 cal.g —1 .°C —1 . Okpomọkụ ikpeazụ bụ 37 Celsius. Kedu ihe bụ okpomọkụ kpọmkwem nke ígwè?
A maara:
Ibu ígwè (m ) = gram 50
Okpomọkụ nke ígwè = 85 o C
Mmiri dị arọ (m ) = gram 50
Okpomọkụ mmiri = 29,8 oC
Okpomọkụ kpọmkwem nke mmiri (c mmiri ) = 1 cal.g -1 .°C -1
Okpomọkụ ikpeazụ nke mmiri = 37 o C
Achọrọ: Okpomọkụ kpọmkwem nke ígwè (c metal)
Ngwọta:
Okpomọkụ nke ígwè ọkụ na-ewepụta (Q release) = okpomọkụ nke mmiri na-amịkọrọ (Q resept)
m ígwè c ( Δ T) = m mmiri c ( Δ T)
(50)(c)(85 – 37) = (50)(1)(37 – 29.8)
(c)(85 – 37) = (1)(37 – 29.8)
48 c = 7.2
c = 0.15 kalori.g -1 .°C -1
12. Otu mkpọ ice nke nwere ibu gram 50 na 0°C na mmiri gram 200 na 30°C, nke a na-etinye n'ime akpa. . Ọ bụrụ na okpomọkụ mmiri kpọmkwem bụ 1 cal.g – 1 °C –1 na okpomọkụ nke ngwakọta maka ice bụ 80 cal.g – 1. Gịnị bụ okpomọkụ ikpeazụ nke ngwakọta ahụ.
A maara:
Ibu ice (mita ice ) = gram 50
Okpomọkụ nke ice = 0°C
Mmiri dị arọ (m ) = gram 200
Okpomọkụ mmiri = 30 oC
Okpomọkụ kpọmkwem nke mmiri (c mmiri ) = 1 cal.g – 1 °C –1
Okpomọkụ nke njikọta maka ice (L ice ) = 80 cal.g –1
Achọrọ: Okpomọkụ ikpeazụ
Ngwọta:
Mee atụmatụ maka ọnọdụ ikpeazụ:
Okpomọkụ mmiri na-ewepụta iji belata okpomọkụ ya site na 30 oC ruo 0 oC :
Mwepụta Q = m mmiri c mmiri ( Δ T) = (200)(1)(30-0) = (200)(30) = 6000
Okpomọkụ dị mkpa iji gbazee ice niile:
Q = m ice L ice = (50)(80) = 4000
Okpomọkụ e ji agbaze ice niile bụ 4000, ebe okpomọkụ mmiri na-ewepụta bụ 6000. A pụrụ ikwubi na okpomọkụ ikpeazụ nke ngwakọta ahụ karịrị 0 oC.
Ụkpụrụ ojii:
Okpomọkụ nke mmiri na-ewepụta = okpomọkụ maka ịgbaze ice niile + okpomọkụ iji mee ka okpomọkụ ice dịkwuo elu.
(m mmiri )(c mmiri )( Δ T) = (m ice )(L ice ) + (m ice )(c mmiri )( Δ T)
(200)(1)(30-T) = (50)(80) + (50)(1)(T-0)
(200)(30-T) = (50)(80) + (50)(T-0)
6000 – 200T = 4000 + 50T – 0
6000 – 4000 = 50T + 200T
2000 = 250T
T = 2000/250
T = 8 o C
