`200` g of water is heated from `40^(@)C "to" 60^(@)C` . Ignoring the slight expansion of water , the change in its internal energy is closed to (Given specific heat of water = `4184 J//kg//K`):

Options

A. `4.2kJ`
B. `8.4kJ`
C. `167.4kJ`
D. `16.7kJ`

Answer

To solve the problem of finding the change in internal energy of 200 g of water heated from 40°C to 60°C, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Mass of water (m) = 200 g = 0.2 kg (since 1 kg = 1000 g)
- Initial temperature (T1) = 40°C
- Final temperature (T2) = 60°C
- Specific heat of water (c) = 4184 J/(kg·K)

2. **Calculate the Change in Temperature (ΔT):**
\[ \Delta T = T2 - T1 = 60°C - 40°C = 20°C \]
Note: The change in temperature in Celsius is equivalent to Kelvin for this calculation.

3. **Use the Formula for Heat Supplied (Q):**
The formula for the heat supplied (which is equal to the change in internal energy when expansion is ignored) is:
\[ Q = m \cdot c \cdot \Delta T \]

4. **Substitute the Values into the Formula:**
\[ Q = 0.2 \, \text{kg} \cdot 4184 \, \text{J/(kg·K)} \cdot 20 \, \text{K} \]

5. **Perform the Calculation:**
\[ Q = 0.2 \cdot 4184 \cdot 20 = 16736 \, \text{J} \]

6. **Convert the Result to Kilojoules:**
\[ Q = 16736 \, \text{J} = 16.736 \, \text{kJ} \approx 16.7 \, \text{kJ} \]

7. **Conclusion:**
The change in internal energy (ΔU) is approximately 16.7 kJ.

### Final Answer:
The change in internal energy is approximately **16.7 kJ**.

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