To find the specific heat ([tex]\(C_p\)[/tex]) of copper, we can use the formula:
[tex]\[ q = m \cdot C_p \cdot \Delta T \][/tex]
where:
- [tex]\( q \)[/tex] is the heat added (in Joules),
- [tex]\( m \)[/tex] is the mass of the substance (in grams),
- [tex]\( \Delta T \)[/tex] is the change in temperature (in Celsius),
- [tex]\( C_p \)[/tex] is the specific heat (in J/g°C).
Let's go through this step-by-step:
1. Identify the given values:
- Heat added ([tex]\( q \)[/tex]) = 1,540 Joules
- Mass ([tex]\( m \)[/tex]) = 200.0 grams
- Initial temperature ([tex]\( T_{\text{initial}} \)[/tex]) = 20.0°C
- Final temperature ([tex]\( T_{\text{final}} \)[/tex]) = 40.0°C
2. Calculate the change in temperature ([tex]\( \Delta T \)[/tex]):
[tex]\[ \Delta T = T_{\text{final}} - T_{\text{initial}} \][/tex]
Thus,
[tex]\[ \Delta T = 40.0°C - 20.0°C = 20.0°C \][/tex]
3. Rearrange the formula to solve for [tex]\( C_p \)[/tex]:
[tex]\[ C_p = \frac{q}{m \cdot \Delta T} \][/tex]
4. Substitute the values into the formula:
[tex]\[ C_p = \frac{1,540 \, \text{J}}{200.0 \, \text{g} \cdot 20.0 \, \text{°C}} \][/tex]
[tex]\[ C_p = \frac{1,540}{4,000} \][/tex]
5. Calculate the result:
[tex]\[ C_p = 0.385 \, \text{J/g°C} \][/tex]
The specific heat of copper is [tex]\( 0.385 \, \text{J/g°C} \)[/tex].
So the correct answer is:
[tex]\[ 0.385 \, \text{J/g°C} \][/tex]
