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The volume coefficient of expansion holds great importance when considering how materials like mercury expand when subjected to temperature changes. It is represented by the symbol \( \beta \) and is a measure indicating how much a substance's volume increases per degree Celsius rise in temperature. In the context of mercury in the original exercise, \( \beta \) is given as \(0.00018 \, {}^{\circ} \mathrm{C}^{-1}\). This coefficient effectively quantifies the fractional change in volume for every one-degree increase in temperature.
The concept of the volume coefficient might seem abstract, but it facilitates the prediction of volume changes in materials, ranging from everyday objects to industrial applications.

• High volume coefficients imply a significant expansion with temperature increase.
• Conversely, low volume coefficients suggest minimal change.

Understanding this coefficient is crucial for calculations involving thermal expansion, ensuring that predictions of volume change are accurate.

Understanding temperature change is key to solving problems involving thermal expansion. In the exercise, the temperature change is calculated as the difference between the final and initial temperatures. The given temperatures are \(10^{\circ} \mathrm{C}\) and \(35^{\circ} \mathrm{C}\), resulting in a temperature change, \( \Delta T \), of \(25^{\circ} \mathrm{C}\).
The formula used is: \[\Delta T = T_2 - T_1\]Where:

• \(T_1\) is the initial temperature.
• \(T_2\) is the final temperature.
• \(\Delta T\) represents the change in temperature.

Temperature change is a straightforward concept but serves as a critical factor when calculating changes in other properties, such as volume, in materials subjected to thermal expansion. It helps transition from what physical conditions initially were to what they become after heating or cooling.

The volume expansion formula is used to calculate how much a given substance expands in volume when subjected to a temperature change. The formula applied in the given exercise is:\[\Delta V = V_0 \times \beta \times \Delta T\]Where:

• \(\Delta V\) is the change in volume.
• \(V_0\) is the initial volume.
• \(\beta\) is the volume coefficient of expansion.
• \(\Delta T\) is the change in temperature.

This formula highlights the direct relationship between volume change and temperature change, as well as the role of the volume coefficient. In the example, substituting the known values gives:\[ \Delta V = 100 \, \mathrm{cm}^3 \times 0.00018 \, {}^{\circ} \mathrm{C}^{-1} \times 25^{\circ} \mathrm{C} = 0.45 \, \mathrm{cm}^3\]The result indicates that the mercury's volume increases by \(0.45 \, \mathrm{cm}^3\) with the specified temperature change. Understanding this formula helps in predicting thermal behavior in various practical applications by accounting for changes in material volume with temperature fluctuations.