To find the heat capacity of the calorimeter, we need to use the relationship between the energy released, the temperature rise, and the heat capacity. The specific formula used for this calculation is:
[tex]\[
C_{\text{cal}} = \frac{\text{energy released}}{\text{temperature rise}}
\][/tex]
Given data:
- Energy released during the reaction is [tex]\( 143 \text{ kJ} \)[/tex]
- Temperature rise of the calorimeter is [tex]\( 51.2\,^{\circ}\text{C} \)[/tex]
We substitute the given values into the formula:
[tex]\[
C_{\text{cal}} = \frac{143 \text{ kJ}}{51.2\,^{\circ}\text{C}}
\][/tex]
Now, let's carry out the division:
[tex]\[
C_{\text{cal}} = 2.79296875 \text{ kJ}/\,^{\circ}\text{C}
\][/tex]
Therefore, the heat capacity of the calorimeter is:
[tex]\[
C_{\text{cal}} = 2.79296875 \text{ kJ}/\,^{\circ}\text{C}
\][/tex]
This result means the calorimeter requires 2.79296875 kJ of energy to raise its temperature by [tex]\( 1\,^{\circ}\text{C} \)[/tex].
