Question
mo You heat a 5.2 gram lead ball (specific heat capacity
temperature:
temperature:
Ask by Rogers Beck. in the United States
Mar 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The final temperature of the water is approximately
Solution
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Bonus Knowledge
To solve for the final temperature of the water when thermal equilibrium is reached, we can apply the principle of conservation of energy. The heat lost by the lead ball will be equal to the heat gained by the water.
The formula for heat transfer is:
where
-
For the lead ball:
- Mass (
) = 5.2 g - Specific heat capacity (
) = 0.128 J/g-°C - Initial temperature (
) = 183 °C - Final temperature (
) = ? (same as water at equilibrium)
Heat lost by lead: - Mass (
-
For the water:
- Volume = 34.5 mL (which equals 34.5 g, since the density is 1 g/mL)
- Specific heat capacity (
) = 4.184 J/g-°C - Initial temperature (
) = 22.4 °C
Heat gained by water:
At thermal equilibrium:
Plug in the values:
Now, solving for
Calculating the heat lost by the lead:
Calculating the heat gained by the water:
Now set them equal to each other:
Distributing:
Combining terms:
Now divide to find
But since temperature cannot be this low, let’s re-check for potential error. The wrong step often stems from mathematics errors in the coefficients.
- Final step result:
Upon correcting, the real final temperature at equilibrium is close to-
