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Zorluk: ZorThermal Expansion of Liquids and Anomalous Expansion of Water

A rigid solid object with negligible thermal expansivity is completely submerged in a container of water initially at 10∘C10^\circ\text{C}. The water is then uniformly cooled down to 0∘C0^\circ\text{C}. How does the upthrust (buoyant force) exerted by the water on the submerged object vary during this cooling process?

  1. It increases to a maximum value at 4∘C4^\circ\text{C} and then decreases as the temperature falls to 0∘C0^\circ\text{C}.Cevap
  2. B
    It decreases continuously from 10∘C10^\circ\text{C} down to 0∘C0^\circ\text{C} as the liquid cools.
  3. C
    It remains constant throughout the cooling process because the volume of the submerged object does not change.
  4. D
    It decreases to a minimum value at 4∘C4^\circ\text{C} and then increases as the temperature reaches 0∘C0^\circ\text{C}.

Cevap

The upthrust increases to a maximum value at 4∘C4^\circ\text{C} and then decreases as cooling continues to 0∘C0^\circ\text{C}.
According to Archimedes' principle, upthrust is given by U=ρfluidVgU = \rho_{\text{fluid}} V g. For a submerged object of constant volume, upthrust is directly proportional to the density of water. As water cools from 10∘C10^\circ\text{C} to 4∘C4^\circ\text{C}, it contracts normally, increasing its density to a maximum at 4∘C4^\circ\text{C} (1000 kg m−31000\text{ kg m}^{-3}). Upon further cooling from 4∘C4^\circ\text{C} to 0∘C0^\circ\text{C}, water undergoes anomalous expansion, increasing in volume and decreasing in density. Consequently, the upthrust reaches a maximum at 4∘C4^\circ\text{C} and decreases down to 0∘C0^\circ\text{C}.

Adım Adım Çözüm

1
Identify the expression for upthrust (buoyant force)
U=ρwater⋅Vobject⋅gU = \rho_{\text{water}} \cdot V_{\text{object}} \cdot g
By Archimedes' principle, upthrust depends directly on the density of the displaced liquid ρwater\rho_{\text{water}} when the volume VobjectV_{\text{object}} and gravitational acceleration gg are constant.
2
Analyze the density behavior of water from 10∘C10^\circ\text{C} down to 4∘C4^\circ\text{C}
Density increases, reaching its maximum value ρmax=1000 kg m−3\rho_{\text{max}} = 1000\text{ kg m}^{-3} at 4∘C4^\circ\text{C}.
Between 10∘C10^\circ\text{C} and 4∘C4^\circ\text{C}, water contracts normally upon cooling.
3
Analyze the density behavior of water from 4∘C4^\circ\text{C} down to 0∘C0^\circ\text{C}
Density decreases as temperature drops from 4∘C4^\circ\text{C} to 0∘C0^\circ\text{C}.
Water exhibits anomalous expansion between 4∘C4^\circ\text{C} and 0∘C0^\circ\text{C}, expanding in volume and consequently decreasing in density.
4
Relate density variation directly to upthrust variation
Upthrust increases from 10∘C10^\circ\text{C} up to a peak at 4∘C4^\circ\text{C}, then decreases from 4∘C4^\circ\text{C} to 0∘C0^\circ\text{C}.
Since upthrust is directly proportional to density, its value mirrors the density profile of water.

Anahtar Kavram

Anomalous expansion of water and its effect on density and upthrust
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Konular

Thermal Expansion of Liquids and Anomalous Expansion of Water

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