To find the energy change for the calorimeter, we need to use the formula for heat transfer, which is given by \( q = C \Delta T \), where \( q \) is the heat transferred, \( C \) is the heat capacity of the calorimeter, and \( \Delta T \) is the change in temperature.
Given values:
- Heat capacity of the calorimeter, \( C = 8.2 \, \text{J/°C} \)
- Initial temperature of the water/calorimeter, \( T_i = 15.0 \, \text{°C} \)
- Final temperature, \( T_f = 19.3 \, \text{°C} \)
First, calculate the change in temperature \( \Delta T \):
[tex]\[
\Delta T = T_f - T_i = 19.3 \, \text{°C} - 15.0 \, \text{°C} = 4.3 \, \text{°C}
\][/tex]
Next, calculate the energy change for the calorimeter using the formula:
[tex]\[
q_{\text{cal}} = C \Delta T = 8.2\, \text{J/°C} \times 4.3 \, \text{°C} = 35.26 \, \text{J}
\][/tex]
Therefore, the energy change for the calorimeter is:
[tex]\[
q_{\text{cal}} = +35.26 \, \text{J}
\][/tex]
