To determine the specific heat capacity of the unknown metal, follow these steps:
1. Determine the change in temperature \(\Delta T\):
- Initial temperature (\( T_{\text{initial}} \)) = \( 225.0^\circ C \)
- Final temperature (\( T_{\text{final}} \)) = \( 19.3^\circ C \)
- \(\Delta T = T_{\text{initial}} - T_{\text{final}} = 225.0^\circ C - 19.3^\circ C\)
- \(\Delta T = 205.7^\circ C\)
2. Identify the given values:
- Thermal energy (\( q \)) = 2020 J
- Mass (\( m \)) = 50.0 g
3. Recall the formula for specific heat capacity (c):
[tex]\[
q = m \cdot c \cdot \Delta T
\][/tex]
In this formula, \( q \) is the thermal energy absorbed or released, \( m \) is the mass of the substance, \( c \) is the specific heat capacity, and \( \Delta T \) is the change in temperature.
4. Rearrange the formula to solve for the specific heat capacity (c):
[tex]\[
c = \frac{q}{m \cdot \Delta T}
\][/tex]
5. Plug in the known values into the rearranged formula:
[tex]\[
c = \frac{2020 \, \text{J}}{50.0 \, \text{g} \cdot 205.7^\circ C}
\][/tex]
6. Calculate the specific heat capacity (c):
[tex]\[
c = \frac{2020}{50.0 \times 205.7}
\][/tex]
[tex]\[
c \approx 0.1964 \, \text{J/(g} \cdot \text{°C)}
\][/tex]
Thus, the specific heat capacity of the unknown metal is approximately [tex]\( 0.1964 \, \text{J/(g} \cdot \text{°C)} \)[/tex].
