Certainly! Let's solve this problem step-by-step.
1. Given Information:
- Mass of water ([tex]\( m \)[/tex]) = [tex]\( 8.0 \times 10^2 \)[/tex] grams = 800 grams
- Initial temperature ([tex]\( T_{\text{initial}} \)[/tex]) = [tex]\( 21^{\circ}C \)[/tex]
- Final temperature ([tex]\( T_{\text{final}} \)[/tex]) = [tex]\( 85^{\circ}C \)[/tex]
- Specific heat capacity of water ([tex]\( c \)[/tex]) = [tex]\( 4.184 \, \text{J/g}^{\circ}\text{C} \)[/tex]
2. Calculate the Temperature Change:
[tex]\[
\Delta T = T_{\text{final}} - T_{\text{initial}} = 85^{\circ}C - 21^{\circ}C = 64^{\circ}C
\][/tex]
3. Use the formula to calculate heat absorbed (Q):
The formula to calculate the amount of heat absorbed or released is:
[tex]\[
Q = mc\Delta T
\][/tex]
where
- [tex]\( Q \)[/tex] is the heat absorbed or released,
- [tex]\( m \)[/tex] is the mass of the substance,
- [tex]\( c \)[/tex] is the specific heat capacity, and
- [tex]\( \Delta T \)[/tex] is the change in temperature.
4. Substitute the values into the formula:
[tex]\[
Q = (800 \, \text{g}) \times (4.184 \, \text{J/g}^{\circ}\text{C}) \times (64^{\circ}C)
\][/tex]
5. Calculate the result:
[tex]\[
Q = 800 \times 4.184 \times 64 = 214220.8 \, \text{J}
\][/tex]
Summary and Comment on the Sign:
The water absorbed [tex]\( 214220.8 \)[/tex] Joules of heat. The positive sign of the heat value indicates that the water absorbed energy, as expected when the temperature of the water increases.
Therefore, the total heat absorbed by the water is [tex]\( 214220.8 \)[/tex] Joules.
