11-12. The same quantity of energy is added to 25.0 g pieces of gold (molar heat capacity = 25.41 J/mol °C), magnesium (molar heat capacity 24.79 J/mol °C), and platinum (molar heat capacity = 25.95 J/mol °C). Which piece of metal has the highest final temperature? Calculate the temperature of this piece of metal assuming 1.0 kJ of energy was added to the metal and it was originally at 25 °C.
11-12. The same quantity of energy is added to 25.0 g pieces of gold (molar heat capacity = 25.41 J/mol °C), magnesium (molar heat capacity 24.79 J/mol °C), and platinum (molar heat capacity = 25.95 J/mol °C). Which piece of metal has the highest final temperature? Calculate the temperature of this piece of metal assuming 1.0 kJ of energy was added to the metal and it was originally at 25 °C.
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![**Title: Thermal Properties and Heat Transfer in Metals**
**Question 11-12:**
When the same quantity of energy is added to 25.0 g samples of metals, including gold, magnesium, and platinum, their temperature changes depending on their molar heat capacities. Here are the details provided for each metal:
- **Gold:** Molar heat capacity = 25.41 J/mol °C
- **Magnesium:** Molar heat capacity = 24.79 J/mol °C
- **Platinum:** Molar heat capacity = 25.95 J/mol °C
**Problem:**
Determine which piece of metal reaches the highest final temperature. Calculate the change in temperature for each sample when 1.0 kJ of energy is added. Assume the initial temperature is 25 °C.
**Explanation:**
To find the final temperature, use the formula:
\[ q = n \cdot C \cdot \Delta T \]
Where:
- \( q \) is the heat added (1.0 kJ = 1000 J),
- \( n \) is the number of moles of the metal,
- \( C \) is the molar heat capacity,
- \( \Delta T \) is the change in temperature.
For each metal:
1. Calculate moles (\( n \)) using the metal's molar mass.
2. Rearrange the formula to solve for \( \Delta T \).
This allows us to determine which metal's temperature rises the most. Thus, identifying the metal with the highest final temperature post energy addition.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf266520-407e-4b51-839c-e1d92d759be6%2F33b0027c-54fd-43b3-bea9-af72dacedbbe%2F4spcn5g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Thermal Properties and Heat Transfer in Metals**
**Question 11-12:**
When the same quantity of energy is added to 25.0 g samples of metals, including gold, magnesium, and platinum, their temperature changes depending on their molar heat capacities. Here are the details provided for each metal:
- **Gold:** Molar heat capacity = 25.41 J/mol °C
- **Magnesium:** Molar heat capacity = 24.79 J/mol °C
- **Platinum:** Molar heat capacity = 25.95 J/mol °C
**Problem:**
Determine which piece of metal reaches the highest final temperature. Calculate the change in temperature for each sample when 1.0 kJ of energy is added. Assume the initial temperature is 25 °C.
**Explanation:**
To find the final temperature, use the formula:
\[ q = n \cdot C \cdot \Delta T \]
Where:
- \( q \) is the heat added (1.0 kJ = 1000 J),
- \( n \) is the number of moles of the metal,
- \( C \) is the molar heat capacity,
- \( \Delta T \) is the change in temperature.
For each metal:
1. Calculate moles (\( n \)) using the metal's molar mass.
2. Rearrange the formula to solve for \( \Delta T \).
This allows us to determine which metal's temperature rises the most. Thus, identifying the metal with the highest final temperature post energy addition.
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