A [tex]$9.0 \, \text{g}$[/tex] sample of iron (specific heat [tex]$=0.44 \, \text{J/g}^{\circ} \text{C}$[/tex]) is heated to [tex]$60^{\circ} \text{C}$[/tex] and eventually cools to [tex]$30^{\circ} \text{C}$[/tex].

What is the heat value?

Does the sign of [tex]$q$[/tex] indicate heat absorbed or lost?



Answer :

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.