It takes 74.7 JJ to raise the temperature of an 12.0 gg piece of unknown metal from 13.0∘C∘C to 24.9 ∘C∘C. What is the specific heat for the metal?

Express your answer with the appropriate units.

To calculate the specific heat capacity (\(c\)) of the unknown metal, we can use the formula:

\[
q = mc\Delta T
\]

Where:
- \(q\) = heat absorbed (in joules, JJ)
- \(m\) = mass of the metal (in grams, gg)
- \(c\) = specific heat capacity (in J/g°C)
- \(\Delta T\) = change in temperature (in °C)

### Given values:
- \(q = 74.7 \, \text{JJ}\)
- \(m = 12.0 \, \text{gg}\)
- Initial temperature (\(T_i\)) = 13.0°C
- Final temperature (\(T_f\)) = 24.9°C

### Step 1: Calculate \(\Delta T\)
\[
\Delta T = T_f - T_i = 24.9°C - 13.0°C = 11.9°C
\]

### Step 2: Rearranging the formula to find \(c\)
\[
c = \frac{q}{m \Delta T}
\]

### Step 3: Plugging in the values
\[
c = \frac{74.7 \, \text{JJ}}{12.0 \, \text{gg} \times 11.9°C}
\]

Calculating:

\[
c = \frac{74.7}{12.0 \times 11.9} = \frac{74.7}{142.8} \approx 0.523 \, \text{J/g°C}
\]

### Final Answer:
The specific heat capacity of the unknown metal is approximately \(0.523 \, \text{J/g°C}\).

Do you want more details on this calculation or have any questions? Here are some related questions you might consider:

1. How does specific heat capacity vary between different materials?
2. What are practical applications of knowing the specific heat of a substance?
3. How can specific heat capacity be experimentally determined?
4. What is the relationship between heat transfer and temperature change?
5. How does the mass of a substance affect its heat capacity? 

**Tip:** Always ensure your units are consistent when performing calculations to avoid errors!

It takes 74.7 JJ to raise the temperature of a 12.0 gg piece of unknown metal from 13.0°C to 24.9°C. What is the specific heat for the metal?

Discover how to calculate the specific heat capacity of an unknown metal using 74.7 JJ of heat to raise its temperature from 13.0°C to 24.9°C. This solution involves key concepts in thermodynamics and heat transfer, suitable for Grades 9-12.

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