Answer :
Final answer:
We can use the principle of conservation of energy to set up an equation based on the specific heat capacities of water and aluminum and the initial and final temperatures. Solving this equation will give us the final temperature when a piece of aluminum is dropped into water.
Explanation:
To solve this problem, we can employ the first law of thermodynamics, which is also known as the conservation of energy. This law states that in a closed system, energy cannot be created or destroyed; it can only change from one form to another.
We also need to take into account the specific heat capacities of both water and aluminum. The specific heat capacity (C) of a substance is the amount of heat energy required to raise the temperature of a certain amount of the substance by one degree. In this case, the specific heat capacity of water (Cw) is about 1 cal/g°C, or 1 btu/lb°F, and the specific heat capacity of aluminum (Ca) is about 0.215 btu/lb°F.
Let's let T be the final temperature. We can set up the following equation based on the conservation of energy:
159 lb * 0.215 Btu/lb°F * (500°F - T) = 400 lb * 1 btu/lb°F * (T - 600°F)
We can solve this equation algebraically for T to find the final temperature in degrees Fahrenheit. It is a linear algebra problem.
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