Answer :
The final temperature of the system, after dropping a 3.90 g piece of aluminum at 99.3°C into 10.0 g of water at 22.6°C is approximately 24.6°C.
To determine the final temperature of the system, we can use the principle of conservation of energy. To find the final temperature, we can equate the heat gained by the water to the heat lost by the aluminum. The heat gained or lost by a substance can be calculated using the formula [tex]q = mc\triangle T[/tex] where q represents the heat, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.
For the water, the heat gained ([tex]q_{water[/tex]) is given by:[tex]q_{water} = m_{water}c_{water}\triangle T_{water[/tex]
Substituting the given values, we have:
10.0g×4.18J/g⋅°C×([tex]T_{final } - 22.6)[/tex] =−3.90g×0.897J/g⋅°C×([tex]T_{final} - 99.3)[/tex]
∴ [tex]T_{final[/tex] ≈24.6°C.
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