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Given Problem: A block of Aluminum has a mass of 32.5 grams and is at 45.8° C. It’s placed in 105.3 grams of water at 15.4° C. What’s the final temperature for both the aluminum and water?

1.  These are the equations we’re going to use. Because we have two equations for q, we can substitute one with another. It should also be noted that ΔT can also be written as (T*final-T*initial). This is important because we can now use that to eventually find Tf.

2. This step just shows how to set up the equation. As stated before, q system/surroundings can be substituted with mass*Cs*T.

3. Plug in the given values and keep Tf as a variable. This way we can solve for it later on.

4. Multiply the masses and specific heats together, and keep the temperature where it is mathematically. After this, it’d be the best to distribute as shown with the arrows.

5. After everything is distributed and organized, distribute your negative sign on the surrounding side of the equation. This way hopefully there isn’t any confusion about how to enter values in to a calculator.

6. After this, combine like terms. Remember, we’re still solving for Tf, so don’t lose it in all your calculations.

7. Divide through to find the final temperature.

It makes sense that we’re only solving for one variable, and that the end temperature would be the same for both the aluminum and the water. This is because heat goes to equilibrium when there’s an imbalance of energy. That means that both the water and the aluminum are going to have the same amount of heat, or same temperature, at the end of the reaction.

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