A cube of iron ( [tex]$C_p = 0.450 \, \text{J/g} \cdot { }^{\circ}\text{C}$[/tex] ) with a mass of [tex]$55.8 \, \text{g}$[/tex] is heated from [tex]$25.0^{\circ}\text{C}$[/tex] to [tex]$75.0^{\circ}\text{C}$[/tex].

How much heat is required for this process? Round your answer to three significant figures.

Use the formula [tex]$q = m C_p \Delta T$[/tex].

[tex]$\square$[/tex] J



Answer :

To determine the amount of heat energy required to heat a cube of iron, we follow these steps:

1. Identify the given values:
- Specific heat capacity ([tex]\(C_p\)[/tex]): [tex]\(0.450 \, \text{J/g}^\circ\text{C}\)[/tex]
- Mass ([tex]\(m\)[/tex]): [tex]\(55.8 \, \text{g}\)[/tex]
- Initial temperature ([tex]\(T_{\text{initial}}\)[/tex]): [tex]\(25.0^\circ\text{C}\)[/tex]
- Final temperature ([tex]\(T_{\text{final}}\)[/tex]): [tex]\(175.0^\circ\text{C}\)[/tex]

2. Calculate the temperature change ([tex]\(\Delta T\)[/tex]):
[tex]\[ \Delta T = T_{\text{final}} - T_{\text{initial}} \][/tex]
Substituting the given values:
[tex]\[ \Delta T = 175.0^\circ\text{C} - 25.0^\circ\text{C} = 150.0^\circ\text{C} \][/tex]

3. Use the formula for heat energy ([tex]\(q\)[/tex]):
[tex]\[ q = m \cdot C_p \cdot \Delta T \][/tex]
Where:
- [tex]\(q\)[/tex] is the heat energy
- [tex]\(m\)[/tex] is the mass
- [tex]\(C_p\)[/tex] is the specific heat capacity
- [tex]\(\Delta T\)[/tex] is the temperature change

4. Substitute the known values into the formula:
[tex]\[ q = 55.8 \, \text{g} \cdot 0.450 \, \text{J/g}^\circ\text{C} \cdot 150.0^\circ\text{C} \][/tex]

5. Perform the calculation:
[tex]\[ q = 55.8 \times 0.450 \times 150.0 \][/tex]
[tex]\[ q = 3766.5 \, \text{J} \][/tex]

Therefore, the heat energy required to heat the cube of iron is [tex]\(3766.5 \, \text{J}\)[/tex]. Rounded to three significant figures, the answer is:
[tex]\[ \boxed{3766.5 \, \text{J}} \][/tex]