Kuwedzera huwandu hwehuwandu - matambudziko nemhinduro

Kukura kwemutsetse kunongowanikwa nezvinhu zvakasimba chete; kuwedzera kwevhoriyamu kunowanikwa nezvinhu zvese, zvese zvakasimba, zvemvura, uye zvegasi. Kukura kwevhoriyamu kwakafanana nekukura kwemutsetse.

Tsananguro: V_o = Vhoriyamu yekutanga, V = Vhoriyamu yekupedzisira, ΔV = V – V_o = Kuchinja kwevhoriyamu, T_o = Tembiricha yekutanga, T = Tembiricha yekupedzisira, ΔT = T – T_o = Kuchinja kwetembiricha, β = chiyero chekuwedzera kwevhoriyamu. Chikamu che β = (C^o) ^-1

Equation yekuwedzera vhoriyamu iri pamusoro apa inoshanda chete kana shanduko muhuwandu hwezvinhu (zvese zvakasimba, zvemvura, uye zvegasi) dziri diki pane vhoriyamu yekutanga yechinhu. Kana shanduko muhuwandu hwechinhu yakakura kupfuura vhoriyamu yekutanga yechinhu, equation yekuwedzera vhoriyamu haipe mhedzisiro chaiyo. Kazhinji, shanduko muhuwandu hunowanikwa nezvinhu zvakasimba hadzisi dzakanyanya kukura. Kune rumwe rutivi, coefficient yekuwedzera vhoriyamu yemvura negasi yakakura. Coefficient yekuwedzera vhoriyamu yezvinhu zvine gasi iri nyorewo kuchinja kana tembiricha ikachinja. Saka fomura iri pamusoro inoshandiswa chete pakuwedzera kwezvinhu zvakasimba.

1. Pa 30 ^oC vhoriyamu yesimbi yearuminiyamu i30 cm³. Chiyero che kuwedzera kwakatwasuka i24 x 10^{-6 o}C^-1Kana vhoriyamu yekupedzisira iri 30.5 cm³, tembiricha yekupedzisira yesimbi yearuminiyamu ndeyei?

Zvinozivikanwa:

Kuwanda kwekuwedzera kwakabatana (α) = 24 x 10^{-6 o}C^-1

Coefficient ye kuwedzera kwevhoriyamu (β= = 3 α = 3 X 24 X 10^{-6 o}C^-1 = 72 x gumi^{-6 o}C^-1

The kwokutanga tembiricha (T₁= = 30^oC

Vhoriyamu yekutanga (V₁) = 30 cm³

Vhoriyamu yekupedzisira (V₂) = 30.5 cm³

Kuchinja kwehuwandu (ΔV) = 30.5 cm³ - 30 cm³ = 0.5 masendimita³

Zvaidiwa: Tembiricha yekupedzisira (T₂)

Solution:

ΔV= β (V)₁)(ΔT)

ΔV= β (V₁)(T)₂ - T₁)

0.5 masendimita³ = (72 X 10^{-6 o}C^-1)(30 cm³)(T)₂ - 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 X 10³ =T₂ - 30

0.23 x 1000 = T₂ - 30

230=T₂ - 30

230 + 30 = T₂

T₂ = 260^oC

2. Kuwanda kwekuwedzera kwesimbi kwakaenzana i9 x 10^{-6 o}C^-1Dhayamita yemukati mesimbi iri pa20 ^oC i2.2 cm. Kana dhayamita yekupedzisira iri 2.8 cm, tembiricha yekupedzisira ndeyei!

Zvinozivikanwa:

Kuwanda kwekuwedzera kwakabatana (α) = 9 x 10^{-6 o}C^-1

Kuwanda kwekuwedzera kwevhoriyamu (β) = 3 α = 3 X 9 X 10^{-6 o}C^-1 = 27 x gumi^{-6 o}C^-1

Tembiricha yekutanga (T₁= = 20^oC

Dhayamita yekutanga (D₁) = 2.2 cm

Dhayamita yekupedzisira (D₂) = 2.8 cm

Nharaunda yekutanga (r₁) = D₁ / 2 = 2.2 cm³ / 2 = 1.1 cm³

Nharaunda yekupedzisira (r₂) = D₂ / 2 = 2.8 cm³ / 2 = 1.4 cm³

Vhoriyamu yekutanga (V₁) = 4/3 π r₁³ = (4/3)(3.14)(1.1 cm)³ = (4/3)(3.14)(1.331 cm³) = 5.57 cm³

Vhoriyamu yekupedzisira (V₂) = 4/3 π r₂³ = (4/3)(3.14)(1.4 cm)³ = (4/3)(3.14)(2.744 cm³) = 11.48 cm³

Kuchinja kwehuwandu (ΔV) = 11.48 cm³ - 5.57 cm³ = 5.91 masendimita³

Zvaidiwa: Tembiricha yekupedzisira (T₂)

Solution:

ΔV= β (V)₁)(ΔT)

5.91 masendimita³ = (27 X 10^{-6 o}C^-1)(5.57 masendimita³)(T)₂ - 20^oC)

5.91 = (150.39 x 10^-6)(T₂ - 20)

5.91/150.39 x 10^-6 =T₂ - 20

0.039 X 10⁶ =T₂ - 20

39 X 10³ =T₂ - 20

39,000=T₂ - 20

39,000 + 20 = T₂

T₂ = 39,020 ^oC

3. A 2000-cm³ aluminium mudziyo, yakazadzwa nemvura pa 0^oC. Uye wobva wadziisa kusvika pa90^oC. Kana chiyero chekuwedzera kwearuminiyamu chiri 24 x 10^-6 (^oC)^-1 uye chiyero chekuwedzera kwehuwandu hwemvura i6.3 x 10^-4 (^oC)^-1, tarisa huwandu hwemvura yadeuka.

Zvinozivikanwa:

Vhoriyamu yekutanga yemudziyo wearuminiyamu nemvura (V)_o) = 2000 cm³ = 2 x gumi³ cm³

Kupisa kwekutanga kwemudziyo wearuminiyamu nemvura (T)₁) = 0^oC

Kupisa kwekupedzisira kwemudziyo wearuminiyamu nemvura (T)₂= = 90^oC

Kuwanda kwekuwedzera kwearuminiyamu (α) = 24 x 10^-6 (^oC)^-1

Kuwedzerwa kwehuwandu hwearuminiyamu (γ) = 3α = 3 (24 x 10)^-6 (^oC)^-1 ) = 72 x 10^{-6 o}C^-1

Kuwanda kwehuwandu hwemvura (γ) = 6.3 x 10^-4 (^oC)^-1

Zvaidiwa: Huwandu hwemvura yakadururwa

Solution:

Kuenzanisa kwekuwedzera kwevhoriyamu:

V = V_o + γ V_o ΔT

V - V_o = γ V_o ΔT

ΔV = γ V_o ΔT

V = vhoriyamu yekupedzisira, V_o = vhoriyamu yekutanga, ΔV = kuchinja kwehuwandu, γ = chiyero chekuwedzera kwevhoriyamu, ΔT = kuchinja kwekupisa

Verenga shanduko yehuwandu hwechirongo chearuminiyamu:

ΔV = γ V_o ΔT = (72) x 10^-6)(2 x 10³)(90) = 12960 x 10^-3 = 12.960 masendimita³

Verenga shanduko muhuwandu hwemvura:

ΔV = γ V_o ΔT = (6.3 X 10^-4)(2 x 10³)(90) = 1134 x 10^-1 = 113.4 masendimita³

Kuchinja kwehuwandu hwemvura kwakakura kupfuura mudziyo wearuminiyamu zvekuti mvura inodururwa.

Verenga huwandu hwemvura yakadururwa:

113.4 masendimita³ - 12.960 cm³ = 100.44 masendimita³

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1. Kuchinja zviyero zvekupisa
2. Linear kuwedzera
3. Kuwedzera kwenzvimbo
4. Kuwedzera inzwi
5. Heat
6. Kuenzana kwekupisa kwemuchina
7. Kupisa kwakananga uye kugona kupisa
8. Kupisa kwakahwanda, kupisa kwekusanganiswa, kupisa kwekupfuta
9. Kuchengetedza simba rekutamisa kupisa