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In physics, the coefficient of volume expansion is a measure of how much a substance expands when its temperature increases. Materials change size when heated because their molecules move faster and tend to move apart. - The coefficient, denoted as \( \beta \), quantifies this expansion. - It is expressed in units of per degree Celsius (掳C鈦宦�). - For liquids like water or coffee, this coefficient is relatively small, reflecting that they do expand but not excessively.In the context of our exercise, the coefficient of volume expansion for coffee (or water) is \( \beta = 207 \times 10^{-6} \) 掳C鈦宦�. This means that for every degree Celsius rise in temperature, the volume of coffee will expand proportionally by this coefficient. This property is crucial in calculating how much liquid will spill out when heated in a full container.

Temperature change is a straightforward concept that refers to the difference between the final and initial temperatures of a substance. It is usually the result of transferring energy to or from the substance, leading to a measurable change in temperature. - The temperature change, represented as \( \Delta T \), is calculated by subtracting the initial temperature from the final temperature.- In our exercise, the initial temperature was \( 18^{\circ} \mathrm{C} \) and the final temperature was \( 92^{\circ} \mathrm{C} \).- Therefore, the temperature change \( \Delta T = 92^{\circ} \mathrm{C} - 18^{\circ} \mathrm{C} = 74^{\circ} \mathrm{C} \).The temperature change informs us about how much the environment around the liquid and beaker has been altered, linking directly to how much the liquid will expand.

The initial volume of a substance is a fundamental factor in determining its behavior when subjected to temperature variations. - It denotes the amount of space occupied by the substance before any external changes, such as heating or cooling.- In our case, the initial volume of the coffee is stated as \( 0.50 \times 10^{-3} \) m鲁. Knowing the initial volume helps us calculate the potential change in volume when temperature changes. It is a key input for applying the volume expansion formula, necessary to determine how much coffee will spill from the beaker during heating.

Volume calculation for thermal expansion involves using a specific mathematical formula to find out how much a liquid's volume changes with temperature.- The formula is: \( \Delta V = \beta V_0 \Delta T \), where \( \Delta V \) is the change in volume, \( \beta \) is the coefficient of volume expansion, \( V_0 \) is the initial volume, and \( \Delta T \) is the temperature change.In our specific example:

• We substitute the values: \( \beta = 207 \times 10^{-6} \) 掳C鈦宦�, \( V_0 = 0.50 \times 10^{-3} \) m鲁, and \( \Delta T = 74 \) 掳C.
• Performing the calculation yields: \( \Delta V = 207 \times 10^{-6} \times 0.50 \times 10^{-3} \times 74 = 7.6419 \times 10^{-6} \) m鲁.

This result shows the additional volume the coffee gains due to the increase in temperature, indicating how much coffee will spill out.