To calculate the heat released when 37.0 grams of copper cools from 55.5°C to 22.5°C, follow these steps:
1. Identify and write down the known values:
- Mass of the copper (m): \( 37.0 \, \text{g} \)
- Specific heat capacity of copper (c): \( 0.0920 \, \text{Cal/g} \cdot {}^\circ \text{C} \)
- Initial temperature (T\(_\text{initial}\)): \( 55.5 \, {}^\circ \text{C} \)
- Final temperature (T\(_\text{final}\)): \( 22.5 \, {}^\circ \text{C} \)
2. Calculate the change in temperature (\(\Delta T\)):
[tex]\[
\Delta T = \text{T}_\text{initial} - \text{T}_\text{final}
\][/tex]
[tex]\[
\Delta T = 55.5 \, {}^\circ \text{C} - 22.5 \, {}^\circ \text{C}
\][/tex]
[tex]\[
\Delta T = 33.0 \, {}^\circ \text{C}
\][/tex]
3. Use the formula for heat transfer:
[tex]\[
Q = m \times c \times \Delta T
\][/tex]
where
- \( Q \) is the heat released,
- \( m \) is the mass,
- \( c \) is the specific heat capacity,
- \( \Delta T \) is the change in temperature.
4. Substitute the known values into the formula:
[tex]\[
Q = 37.0 \, \text{g} \times 0.0920 \, \text{Cal/g} \cdot {}^\circ \text{C} \times 33.0 \, {}^\circ \text{C}
\][/tex]
5. Calculate the heat released:
[tex]\[
Q = 37.0 \times 0.0920 \times 33.0
\][/tex]
[tex]\[
Q \approx 112.332 \, \text{Cal}
\][/tex]
Therefore, the heat released as 37.0 grams of copper cools from 55.5°C to 22.5°C is approximately 112.332 Calories.
