To calculate the temperature change ([tex]\(\Delta T\)[/tex]) when a certain amount of heat ([tex]\(Q\)[/tex]) is added to a substance, we use the formula:
[tex]\[
\Delta T = \frac{Q}{m \cdot c}
\][/tex]
Where:
- [tex]\(Q\)[/tex] is the amount of heat added (in Joules),
- [tex]\(m\)[/tex] is the mass of the substance (in grams),
- [tex]\(c\)[/tex] is the specific heat of the substance (in J/g°C).
Given:
- [tex]\(Q = 100\)[/tex] Joules,
- [tex]\(m = 20\)[/tex] grams,
- [tex]\(c = 0.39\)[/tex] J/g°C.
Let's calculate the temperature change step-by-step:
1. Substitute the given values into the formula:
[tex]\[
\Delta T = \frac{100 \text{ J}}{20 \text{ g} \cdot 0.39 \text{ J/g°C}}
\][/tex]
2. Calculate the denominator ([tex]\(m \cdot c\)[/tex]):
[tex]\[
m \cdot c = 20 \text{ g} \cdot 0.39 \text{ J/g°C} = 7.8 \text{ J/°C}
\][/tex]
3. Divide the numerator ([tex]\(Q\)[/tex]) by the denominator ([tex]\(m \cdot c\)[/tex]):
[tex]\[
\Delta T = \frac{100 \text{ J}}{7.8 \text{ J/°C}} \approx 12.82 \text{ °C}
\][/tex]
Therefore, the temperature change ([tex]\(\Delta T\)[/tex]) when 100 Joules of heat is added to 20 grams of copper is approximately 12.82 °C.
The correct answer is:
12.82 °C
