How many kilograms of copper will experience the same temperature rises as 10 kg of water when the same amount of heat is absorbed? `(S_(cu)=0.09"cal"//g.^(@)C`)

Answer

To find out how many kilograms of copper will experience the same temperature rise as 10 kg of water when the same amount of heat is absorbed, we can use the formula for heat transfer:

\[ Q = m \cdot s \cdot \Delta T \]

Where:
- \( Q \) is the heat absorbed,
- \( m \) is the mass,
- \( s \) is the specific heat capacity,
- \( \Delta T \) is the change in temperature.

### Step-by-Step Solution:

1. **Identify the known values:**
- Mass of water, \( m_w = 10 \, \text{kg} = 10,000 \, \text{g} \) (since \( 1 \, \text{kg} = 1000 \, \text{g} \))
- Specific heat of water, \( s_w = 1 \, \text{cal/g°C} \)
- Specific heat of copper, \( s_{cu} = 0.09 \, \text{cal/g°C} \)

2. **Set up the heat equation for both substances:**
Since the heat absorbed is the same for both water and copper, we can write:
\[ Q_{cu} = Q_{w} \]
This gives us:
\[ m_{cu} \cdot s_{cu} \cdot \Delta T = m_w \cdot s_w \cdot \Delta T \]

3. **Cancel out the common term \( \Delta T \):**
Since \( \Delta T \) is the same for both substances, we can cancel it out:
\[ m_{cu} \cdot s_{cu} = m_w \cdot s_w \]

4. **Substitute the known values:**
\[ m_{cu} \cdot 0.09 = 10,000 \cdot 1 \]

5. **Solve for \( m_{cu} \):**
\[ m_{cu} \cdot 0.09 = 10,000 \]
\[ m_{cu} = \frac{10,000}{0.09} \]
\[ m_{cu} = 111,111.11 \, \text{g} \]

6. **Convert grams to kilograms:**
\[ m_{cu} = \frac{111,111.11}{1000} = 111.11 \, \text{kg} \]

### Final Answer:
The mass of copper that will experience the same temperature rise as 10 kg of water when the same amount of heat is absorbed is approximately **111.11 kg**.