A Pyrex container is completely filled with 275 cm^3 of mercury at 10.0^∘ C . How much mercury

step 1 In this example, we're told that we have a container completely filled with 275 cubic centimeter

A Pyrex container is completely filled with 275 cm^3 of...

Key Concepts

Temperature Change and Its Effects on Volume

Temperature change plays a fundamental role in thermal expansion. The volume change in a substance is directly proportional to the temperature difference, the initial volume, and the material's coefficient of thermal expansion. Recognizing and calculating the effects of temperature change is critical in determining how much a substance, such as a liquid in a container, will expand or contract under thermal conditions.

Differential Expansion between Container and Contents

Differential expansion refers to the situation where different materials expand at different rates due to distinct thermal expansion coefficients. In systems where a liquid is contained in a solid container, the mismatched expansion rates can lead to phenomena like overflow or spillage. This concept is especially important when the liquid has a much larger volumetric expansion coefficient compared to the container material, as even small temperature changes can cause significant volume mismatches.

Thermal Expansion

Thermal expansion is the tendency of matter to change its shape, area, volume, and density with a change in temperature. This concept applies to both solids and liquids, with the general result being that most substances expand when heated and contract when cooled. Understanding thermal expansion is crucial in many practical applications, including how containers and their contents behave under temperature variations.

Coefficient of Thermal Expansion

The coefficient of thermal expansion quantifies the extent to which a material expands per degree change in temperature. It differs for liquids (usually given as a volumetric coefficient) and solids (often given as a linear coefficient). These coefficients allow us to calculate the change in dimensions or volume when the temperature is varied, making them essential for predicting behaviors such as spillage when a liquid expands more than its container.

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