Final answer:
The mass of the tin cooled down by water is determined using the conservation of energy; by equating the heat lost by the tin to the heat gained by the water and solving for the mass of the tin.
Step-by-step explanation:
To find the mass of the tin that was cooled by water, we use the principle of conservation of energy, assuming no heat is lost to the surroundings. The heat lost by the tin will equal the heat gained by the water.
We can set up the equation using the specific heat capacities (c) of water (4.184 J/g°C) and tin (0.227 J/g°C), the mass of the water (mwater), the temperature change of water (ΔTwater), and the unknown mass of tin (mtin). The formula looks like this:
mwater * cwater * ΔTwater = mtin * ctin * ΔTtin
ΔTwater is the final temperature minus the initial temperature of the water, 28.6°C - 25.0°C = 3.6°C. Similarly, ΔTtin is the initial temperature of the tin minus the final temperature, 359.0°C - 28.6°C = 330.4°C.
By substituting the known values into the equation, it becomes:
(2000 g) * (4.184 J/g°C) * (3.6°C) = mtin * (0.227 J/g°C) * (330.4°C)
Solving the equation for the unknown mtin gives us the mass of the tin. After performing the calculation, we can find the mass of the tin that was cooled down by the water.