Answer :
Final answer:
The final temperature of the metal and water mixture, assuming no heat loss to the surroundings, can be calculated using the principle of conservation of energy. By equating the heat gained by the water to the heat lost by the aluminum pellets, we can determine the final temperature. The final temperature of the mixture is found to be approximately 24.1°C.
Explanation:
To calculate the final temperature, we first find the heat gained by the water and the heat lost by the aluminum pellets. The heat gained by the water can be calculated using the equation q_water = mcΔT, where m is the mass of water, c is the specific heat capacity of water, and ΔT is the change in temperature. Substituting the given values, we find q_water = (97.3 g)(4.18 J/g°C)(T_f - 22.0°C).
Next, we find the heat lost by the aluminum pellets using the same formula, q_aluminum = mcΔT, where m is the mass of aluminum, c is the specific heat capacity of aluminum, and ΔT is the change in temperature. Substituting the given values, we find q_aluminum = (15.00 g)(0.890 J/g°C)(100.0°C - T_f).
Since the total heat gained by the water equals the total heat lost by the aluminum pellets (assuming no heat loss to the surroundings), we set q_water = q_aluminum and solve for the final temperature, denoted as T_f. After substituting the expressions for q_water and q_aluminum, we solve the resulting equation to find T_f, which is approximately 24.1°C.
