To solve Question 1, we need to use the principle of conservation of energy, where the heat lost by the metal is equal to the heat gained by the water:

Formula:

$q_{\text{metal}} = q_{\text{water}}$

Where:

• $q = m \cdot c \cdot \Delta T$
• $m$ is the mass,
• $c$ is the specific heat capacity,
• $\Delta T$ is the change in temperature.

Given Data:

For the water:

• Mass of water $m_{\text{water}} = 60.5 \, \text{g}$
• Specific heat of water $c_{\text{water}} = 4.18 \, \text{J/g°C}$
• Initial temperature of water $T_{\text{initial water}} = 22.0 \, °C$
• Final temperature of water $T_{\text{final water}} = 27.1 \, °C$

For the metal:

• Mass of metal $m_{\text{metal}} = 471.1 \, \text{g}$
• Initial temperature of metal $T_{\text{initial metal}} = 98.2 \, °C$
• Final temperature of metal $T_{\text{final metal}} = 27.1 \, °C$

Step 1: Calculate the heat gained by water.

$q_{\text{water}} = m_{\text{water}} \cdot c_{\text{water}} \cdot (T_{\text{final water}} - T_{\text{initial water}})$

Step 2: Assume heat lost by metal is equal to heat gained by water:

$m_{\text{metal}} \cdot c_{\text{metal}} \cdot (T_{\text{final metal}} - T_{\text{initial metal}}) = q_{\text{water}}$

We can solve for $c_{\text{metal}}$ and compare it to the given specific heat values for copper, zinc, lead, and aluminum to identify the unknown metal.

Let me calculate it for you.The calculated specific heat for the metal is approximately $-0.0385 \, \text{J/g°C}$, which is a negative value. This is physically unrealistic, as specific heat capacity cannot be negative.

This result suggests that there may be a misunderstanding in the calculation setup. Specifically, the temperature change for the metal must be treated carefully. The metal cools down, so the temperature change for the metal should be taken as an absolute positive value.

Let me adjust the calculation and fix this.It seems like I can’t do more advanced data analysis right now. Please try again later. However, I can guide you through the steps so you can solve it manually if you'd like!

Here’s what to do next:

• Use the formula for heat gained by the water:
  ( q_{\text{water}} = 60.5 , \text{g} \times 4.18 , \text{J/g°C} \times (27.1 - 22.0) \