What is the change in length of a 3.00-cm -long column of mercury if its temperature changes fro

step 1 So we have a 3 centimeter column of mercury and the temperature has changed. Let's we know that

What is the change in length of a 3.00-cm -long column of...

What is the change in length of a $3.00-\mathrm{cm}$ -long column of mercury if its temperature changes from $37.0^{\circ} \mathrm{C}$ to $40.0^{\circ} \mathrm{C}$ , assuming the mercury is unconstrained?

Key Concepts

Thermal Expansion

Thermal expansion is the phenomenon where a material experiences a change in its dimensions—whether length, area, or volume—when its temperature changes. This process is fundamental in many areas of physics and engineering as it explains how materials respond to temperature variations, and it is crucial in designing systems that encounter fluctuating thermal environments.

Coefficient of Thermal Expansion

The coefficient of thermal expansion quantifies the rate at which a material expands per unit change in temperature. For solids, this is typically given as the linear coefficient, while for liquids and isotropic materials, the volume coefficient is more appropriate. In many cases, especially for isotropic materials, the linear expansion can be related to the volumetric expansion by a factor (often one-third), reflecting uniform expansion in all directions.

Temperature Change

Temperature change, often represented as ?T, is the difference between the final and initial temperatures of a material. It is a key parameter in calculations involving thermal expansion because the amount a material expands is directly proportional to the magnitude of its temperature change.

Unconstrained Expansion

Unconstrained expansion refers to a situation where the material is free to expand without any external constraints or forces hindering its movement. This means that the expansion is solely dictated by the material’s properties and the temperature change, allowing for straightforward calculations using thermal expansion coefficients without the need to consider additional mechanical stresses or resistances.

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