A straight rod consists of a 1.2 -cm-long piece of aluminum...

A straight rod consists of a 1.2 -cm-long piece of aluminum attached to a $2.0-\mathrm{cm}$ -long piece of steel. By how much will the length of this rod change if its temperature is increased from $20^{\circ} \mathrm{C}$ to $40^{\circ} \mathrm{C} ?$

Key Concepts

Composite Material Analysis in Thermal Expansion

In systems where multiple materials with different thermal expansion properties are used together, each component’s expansion is calculated independently. The overall change in the system is determined by summing the individual contributions, which is essential for accurately predicting dimensional changes in composite objects.

Temperature Change Calculation

Calculating the temperature difference (?T) between the initial and final states is vital, as it directly influences the extent of thermal expansion. The magnitude of ?T is used along with the coefficient of thermal expansion to assess the resulting change in dimensions.

Linear Thermal Expansion

This concept describes how a material's length changes with temperature according to the formula ?L = ? L ?T, where ?L is the change in length, ? is the material’s linear coefficient of thermal expansion, L is the original length, and ?T is the temperature change. It is fundamental for predicting dimensional changes in solids subject to temperature variations.

Coefficient of Thermal Expansion

The coefficient of thermal expansion is a material-specific constant that measures how much a material expands or contracts per degree of temperature change. It is crucial because different materials, like metals, can have significantly different expansion properties, which must be taken into account, especially in composite structures.

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