To determine the heat capacity of the calorimeter, we need to follow the formula for calculating calorimeter heat capacity given the heat of combustion and the observed temperature increase in the calorimeter. The formula is:
[tex]\[ C_{\text{cal}} = \frac{-q_{\text{comb}}}{\Delta T} \][/tex]
Where:
- [tex]\( q_{\text{comb}} \)[/tex] is the heat of combustion, given as [tex]\(-840 \text{ J}\)[/tex] (negative because it is exothermic).
- [tex]\(\Delta T\)[/tex] is the temperature increase, given as [tex]\(3.4^{\circ} \text{C}\)[/tex].
Step by step solution:
1. Identify the given values:
- Heat of combustion, [tex]\( q_{\text{comb}} = -840 \text{ J} \)[/tex]
- Temperature increase, [tex]\( \Delta T = 3.4^{\circ} \text{C} \)[/tex]
2. Substitute these values into the formula:
[tex]\[ C_{\text{cal}} = \frac{-q_{\text{comb}}}{\Delta T} \][/tex]
[tex]\[ C_{\text{cal}} = \frac{-(-840 \text{ J})}{3.4^{\circ} \text{C}} \][/tex]
3. Simplify the expression:
[tex]\[ C_{\text{cal}} = \frac{840 \text{ J}}{3.4^{\circ} \text{C}} \][/tex]
4. Perform the division:
[tex]\[ C_{\text{cal}} = 247.05882352941177 \text{ J/}^{\circ}\text{C} \][/tex]
Therefore, the heat capacity of the calorimeter, [tex]\( C_{\text{cal}} \)[/tex], is [tex]\(\boxed{247.05882352941177} \text{ J/}^{\circ}\text{C}\)[/tex] without rounding for significant figures.
