To find the specific heat [tex]\( C_p \)[/tex] of a substance given a mass, a change in temperature, and the amount of heat added, we can follow these steps:
1. Identify the given values:
- Mass ([tex]\( m \)[/tex]): [tex]\( 10.0 \, \text{kg} \)[/tex]
- Initial temperature ([tex]\( T_{initial} \)[/tex]): [tex]\( 10.0 \, ^\circ \text{C} \)[/tex]
- Final temperature ([tex]\( T_{final} \)[/tex]): [tex]\( 70.0 \, ^\circ \text{C} \)[/tex]
- Heat added ([tex]\( q \)[/tex]): [tex]\( 2520 \, \text{J} \)[/tex]
2. Calculate the temperature change (ΔT):
[tex]\[
\Delta T = T_{final} - T_{initial}
\][/tex]
Substituting the given values:
[tex]\[
\Delta T = 70.0 \, ^\circ \text{C} - 10.0 \, ^\circ \text{C} = 60.0 \, ^\circ \text{C}
\][/tex]
3. Apply the specific heat formula:
The formula for specific heat is:
[tex]\[
q = m C_p \Delta T
\][/tex]
Rearrange this formula to solve for [tex]\( C_p \)[/tex]:
[tex]\[
C_p = \frac{q}{m \Delta T}
\][/tex]
4. Substitute the known values into the rearranged formula:
[tex]\[
C_p = \frac{2520 \, \text{J}}{10.0 \, \text{kg} \times 60.0 \, ^\circ \text{C}}
\][/tex]
[tex]\[
C_p = \frac{2520 \, \text{J}}{600.0 \, \text{kg} \cdot \, ^\circ \text{C}}
\][/tex]
[tex]\[
C_p = 4.2 \, \frac{\text{J}}{\text{kg} \cdot \, ^\circ \text{C}}
\][/tex]
The specific heat [tex]\( C_p \)[/tex] of the substance is [tex]\( 4.2 \, \frac{\text{J}}{\text{kg} \cdot \, ^\circ \text{C}} \)[/tex].
