`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 calculating the change in internal energy when 200 g of water is heated from 40°C to 60°C, we can follow these steps:

### Step 1: Convert mass from grams to kilograms
The mass of water is given as 200 g. Since the specific heat is given in Joules per kg per Kelvin, we need to convert grams to kilograms.

\[ m = 200 \, \text{g} = \frac{200}{1000} \, \text{kg} = 0.2 \, \text{kg} \]

**Hint:** Remember that 1 kg = 1000 g.

### Step 2: Determine the change in temperature (ΔT)
The initial temperature (T1) is 40°C and the final temperature (T2) is 60°C. The change in temperature can be calculated as:

\[ \Delta T = T2 - T1 = 60°C - 40°C = 20°C \]

**Hint:** The change in temperature can be expressed in Celsius or Kelvin since the difference is the same.

### Step 3: Use the formula for change in internal energy (ΔU)
The change in internal energy (ΔU) can be calculated using the formula:

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

where:
- \( m \) is the mass in kg,
- \( s \) is the specific heat capacity of water (given as 4184 J/kg/K),
- \( \Delta T \) is the change in temperature in Kelvin.

### Step 4: Substitute the values into the formula
Now, substituting the values we have:

\[ \Delta U = 0.2 \, \text{kg} \cdot 4184 \, \text{J/kg/K} \cdot 20 \, \text{K} \]

### Step 5: Calculate ΔU
Now we perform the calculation:

\[ \Delta U = 0.2 \cdot 4184 \cdot 20 \]

Calculating step-by-step:

1. Calculate \( 0.2 \cdot 4184 = 836.8 \, \text{J/K} \)
2. Then multiply by 20:
\[ 836.8 \cdot 20 = 16736 \, \text{J} \]

### Step 6: Convert Joules to Kilojoules
Since 1 kJ = 1000 J, we convert the energy from Joules to Kilojoules:

\[ \Delta U = \frac{16736 \, \text{J}}{1000} = 16.736 \, \text{kJ} \approx 16.7 \, \text{kJ} \]

### Conclusion
The change in internal energy when 200 g of water is heated from 40°C to 60°C is approximately **16.7 kJ**.

**Final Answer:** 16.7 kJ

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