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Calculating heat energy is an essential part of understanding how substances transfer heat. In this process, we use the formula:\[q = m \times c \times \Delta T\]where:

• \(q\) is the heat energy required (in joules).
• \(m\) is the mass of the substance (in grams).
• \(c\) is the specific heat capacity (J/g∙K).
• \(\Delta T\) is the change in temperature (in degrees Celsius or Kelvin).

The formula helps us learn how much energy is necessary to raise the temperature of a certain mass of a substance.
The calculation requires substituting known values into the formula.In this example, \(m = 168 \, \text{g}\), \(c = 0.385 \, \text{J/g} \cdot \text{K}\), and \(\Delta T = 37.8^{\circ} \text{C}\). Substituting these values gives:\[q = 168 \times 0.385 \times 37.8 = 2447.712 \, \text{J}\]This means 2448 J (rounded to three significant figures) of energy is needed to heat the copper.

Understanding temperature change calculations is vital for gauging how much a substance's temperature shifts due to heat absorption or release. Calculating the change in temperature involves the difference between the initial and final temperatures:\[\Delta T = T_{final} - T_{initial}\]In our example, the copper's initial temperature is \(-12.2^{\circ} \text{C}\), and the final temperature is \(+25.6^{\circ} \text{C}\). By subtracting these values, we calculate the change:\[\Delta T = 25.6^{\circ} \text{C} - (-12.2^{\circ} \text{C}) = 37.8^{\circ} \text{C}\]A positive \(\Delta T\) indicates that the copper's temperature increased as it absorbed heat. This change is crucial for understanding how energy shifts manifest as temperature alterations.
By comprehending and calculating temperature changes accurately, you can predict and analyze the thermal properties of different substances in various contexts, such as in environmental sciences and material engineering.