To determine the heat value and whether heat is absorbed or lost, let's follow these steps:
1. Identify the given values:
- Mass of iron ([tex]\(m\)[/tex]): [tex]\(9.0 \, \text{g}\)[/tex]
- Specific heat capacity ([tex]\(c\)[/tex]): [tex]\(0.44 \, \text{J/g}^\circ\text{C}\)[/tex]
- Initial temperature ([tex]\(T_i\)[/tex]): [tex]\(60^\circ\text{C}\)[/tex]
- Final temperature ([tex]\(T_f\)[/tex]): [tex]\(30^\circ\text{C}\)[/tex]
2. Calculate the change in temperature ([tex]\(\Delta T\)[/tex]):
[tex]\[
\Delta T = T_f - T_i
\][/tex]
[tex]\[
\Delta T = 30^\circ\text{C} - 60^\circ\text{C}
\][/tex]
[tex]\[
\Delta T = -30^\circ\text{C}
\][/tex]
3. Use the formula for heat transfer ([tex]\(q\)[/tex]):
[tex]\[
q = m \cdot c \cdot \Delta T
\][/tex]
Substitute the values into the formula:
[tex]\[
q = 9.0 \, \text{g} \times 0.44 \, \text{J/g}^\circ\text{C} \times (-30^\circ\text{C})
\][/tex]
4. Calculate the heat value ([tex]\(q\)[/tex]):
[tex]\[
q = 9.0 \times 0.44 \times (-30)
\][/tex]
[tex]\[
q = 9.0 \times (-13.2)
\][/tex]
[tex]\[
q = -118.8 \, \text{J}
\][/tex]
5. Interpret the result:
- The heat value is [tex]\(-118.8 \, \text{J}\)[/tex].
- The negative sign indicates that heat is lost, not absorbed.
Conclusion:
The heat value is [tex]\(-118.8 \, \text{J}\)[/tex]. The negative sign of [tex]\(q\)[/tex] indicates that the heat is lost.
