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Zorluk: OrtaThermal Expansion of Liquids and Anomalous Expansion of Water

A metal container with a volume of 200 cm3200\text{ cm}^3 at 30∘C30^\circ\text{C} is completely filled with an oil. The linear expansivity of the metal container is 2.0×10−5 K−12.0 \times 10^{-5}\text{ K}^{-1} and the real cubic expansivity of the oil is 6.0×10−4 K−16.0 \times 10^{-4}\text{ K}^{-1}. If the temperature of the system is raised to 80∘C80^\circ\text{C}, what volume of oil (in cm3\text{cm}^3) will overflow?

Cevap: 5.4 cm^3

Cevap

The volume of oil that overflows is 5.4 cm35.4\text{ cm}^3.
When a container filled to the brim with liquid is heated, both the liquid and container expand. The apparent cubic expansivity of the liquid is the difference between its real cubic expansivity and the volumetric expansivity of the vessel (3 * alpha). Subtracting 0.6 * 10^-4 K^-1 from 6.0 * 10^-4 K^-1 gives an apparent cubic expansivity of 5.4 * 10^-4 K^-1. Multiplying this by the initial volume of 200 cm^3 and the temperature rise of 50 K gives an overflow volume of 5.4 cm^3.

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1
Determine the temperature increase (\Delta T)
\Delta T = 80^\circ\text{C} - 30^\circ\text{C} = 50\text{ K}
Thermal expansion depends directly on the change in temperature.
2
Calculate the cubic expansivity of the container (\gamma_v)
\gamma_v = 3\alpha = 3 \times (2.0 \times 10^{-5}\text{ K}^{-1}) = 6.0 \times 10^{-5}\text{ K}^{-1} = 0.6 \times 10^{-4}\text{ K}^{-1}
The volumetric expansivity of an isotropic solid container is three times its linear expansivity.
3
Calculate the apparent cubic expansivity of the liquid (\gamma_a)
\gamma_a = \gamma_r - \gamma_v = 6.0 \times 10^{-4}\text{ K}^{-1} - 0.6 \times 10^{-4}\text{ K}^{-1} = 5.4 \times 10^{-4}\text{ K}^{-1}
Apparent expansivity accounts for the simultaneous expansion of the vessel containing the liquid.
4
Calculate the volume of liquid that overflows (\Delta V)
\Delta V = V_0 \times \gamma_a \times \Delta T = 200\text{ cm}^3 \times 5.4 \times 10^{-4}\text{ K}^{-1} \times 50\text{ K} = 5.4\text{ cm}^3
The overflow volume equals the apparent expansion of the liquid volume.

Anahtar Kavram

Real and Apparent Expansion of Liquids
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Konular

Thermal Expansion of Liquids and Anomalous Expansion of Water

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