To find the final temperature of the water, we can follow these steps:
1. Identify the given data:
- Initial mass of water, [tex]\( m = 40.0 \)[/tex] grams.
- Initial temperature, [tex]\( T_{\text{initial}} = 91.0^\circ \text{C} \)[/tex].
- Heat released, [tex]\( Q = 1300 \)[/tex] joules.
- Specific heat capacity of water, [tex]\( c = 4.18 \)[/tex] J/g°C.
2. Write the formula for heat transfer:
The formula to calculate heat transfer is:
[tex]\[
Q = m \cdot c \cdot \Delta T
\][/tex]
where [tex]\( \Delta T \)[/tex] is the change in temperature.
3. Rearrange the formula to find the temperature change:
[tex]\[
\Delta T = \frac{Q}{m \cdot c}
\][/tex]
4. Substitute the given values into the formula:
[tex]\[
\Delta T = \frac{1300 \text{ joules}}{40.0 \text{ grams} \cdot 4.18 \text{ J/g°C}}
\][/tex]
5. Calculate the temperature change:
[tex]\[
\Delta T \approx 7.7751^\circ \text{C}
\][/tex]
6. Determine the final temperature:
The initial temperature was [tex]\( 91.0^\circ \text{C} \)[/tex]. Since the water is cooling, the final temperature will be less than the initial temperature. Thus:
[tex]\[
T_{\text{final}} = T_{\text{initial}} - \Delta T
\][/tex]
[tex]\[
T_{\text{final}} = 91.0^\circ \text{C} - 7.7751^\circ \text{C}
\][/tex]
[tex]\[
T_{\text{final}} \approx 83.2249^\circ \text{C}
\][/tex]
From the given answer choices, the final temperature closest to this value is:
[tex]\[
\boxed{83^\circ \text{C}}
\][/tex]
