To calculate the specific heat ($c$) of the metal, we'll again use the principle of conservation of energy, where the heat lost by the metal is equal to the heat gained by the water.

Given:

• Mass of metal ($m_{\text{metal}}$) = 19.4 g
• Initial temperature of metal ($T_{\text{initial, metal}}$) = 88.5 °C
• Final temperature ($T_{\text{final}}$) = 28.0 °C
• Mass of water ($m_{\text{water}}$) = 41 g
• Initial temperature of water ($T_{\text{initial, water}}$) = 23.5 °C
• Specific heat of water ($c_{\text{water}}$) = 4.18 J/g°C

Steps:

1. Calculate the temperature changes: $\Delta T_{\text{metal}} = T_{\text{final}} - T_{\text{initial, metal}} = 28.0 - 88.5 = -60.5 \, \text{°C}$ $\Delta T_{\text{water}} = T_{\text{final}} - T_{\text{initial, water}} = 28.0 - 23.5 = 4.5 \, \text{°C}$

2. Calculate the heat gained by the water: $q_{\text{water}} = m_{\text{water}} \cdot c_{\text{water}} \cdot \Delta T_{\text{water}}$ $q_{\text{water}} = 41 \, \text{g} \cdot 4.18 \, \text{J/g°C} \cdot 4.5 \, \text{°C}$ $q_{\text{water}} = 770.01 \, \text{J}$

   The heat lost by the metal ($q_{\text{metal}}$) equals the heat gained by the water: $q_{\text{metal}} = -q_{\text{water}} = -770.01 \, \text{J}$

3. Calculate the specific heat of the metal: $q_{\text{metal}} = m_{\text{metal}} \cdot c_{\text{metal}} \cdot \Delta T_{\text{metal}}$ $-770.01 \, \text{J} = 19.4 \, \text{g} \cdot c_{\text{metal}} \cdot (-60.5 \, \text{°C})$

   Simplify to solve for $c_{\text{metal}}$: $c_{\text{metal}} = \frac{-770.01 \, \text{J}}{19.4 \, \text{g} \cdot (-60.5 \, \text{°C})}$ $c_{\text{metal}} \approx \frac{770.01 \, \text{J}}{1173.7 \, \text{g°C}} \approx 0.656 \, \text{J/g°C}$

   Rounded to two significant figures: $c_{\text{metal}} \approx 0.66 \, \text{J/g°C}$

The specific heat of the metal is approximately 0.66 J/g°C.

Would you like more details, or do you have any questions?

Here are five related questions:

1. How does the specific heat of a substance relate to its atomic or molecular structure?
2. What is the significance of a substance having a high specific heat compared to a low one?
3. How would the result change if the water had a different initial temperature?
4. Can you calculate the amount of heat required to raise the temperature of the metal by a certain number of degrees?
5. How would you experimentally determine the specific heat of a substance in a laboratory?

Tip: Always ensure you use the correct number of significant figures in your final answer, matching the precision of the given data.