To find the heat change of copper, you use the fundamental formula for heat transfer: q = mCΔT. This equation quantifies the amount of heat energy absorbed or released by a substance during a temperature change.
Understanding the Heat Change Formula
The formula q = mCΔT is crucial for calculating thermal energy changes in materials like copper. Let's break down each component:
- q (Heat Change): Represents the amount of heat energy transferred, typically measured in Joules (J). A positive 'q' indicates heat absorbed by the copper (an endothermic process), while a negative 'q' indicates heat released by the copper (an exothermic process).
- m (Mass): This is the mass of the copper sample, usually measured in grams (g) or kilograms (kg). The unit must be consistent with the specific heat capacity.
- C (Specific Heat Capacity): This is a material-specific property that indicates the amount of heat energy required to raise the temperature of 1 unit of mass of the substance by 1 degree Celsius (or Kelvin). For copper, its specific heat capacity is approximately 0.385 J/g·°C. This means it takes 0.385 Joules of energy to raise 1 gram of copper by 1 degree Celsius.
- ΔT (Change in Temperature): This is the difference between the final temperature ($T{final}$) and the initial temperature ($T{initial}$) of the copper. It is calculated as $T{final} - T{initial}$. A positive ΔT means the temperature increased, and a negative ΔT means the temperature decreased.
Applying the Formula: A Practical Example
Let's consider an example to illustrate how to calculate the heat change for a specific copper sample.
Scenario: You have a copper sample with a mass of 0.75 grams. Its temperature changes by 22 °C (for instance, if its temperature increased from 7 °C to 29 °C, or vice versa for the magnitude of change).
Here's how the calculation unfolds:
| Variable | Value | Unit |
|---|---|---|
| Mass (m) | 0.75 | g |
| Specific Heat (C) | 0.385 | J/g·°C |
| Temperature Change (ΔT) | 22 | °C |
Now, substitute these values into the formula:
q = m ⋅ C ⋅ ΔT
q = 0.75 g ⋅ 0.385 J/g·°C ⋅ 22 °C
Calculation:
q = 6.3525 J
Therefore, in this example, the heat change (amount of heat transferred) for the copper sample is 6.3525 Joules. If the temperature increased, this is the heat absorbed; if it decreased, this is the heat released (the calculation provides the magnitude).
