If one kilogram water at `100^(@)C` is vapourised in open atmosphere. The correct statement is

Options

A. increase in internal energy is equal to L (L is latent heat of vaporisation for 1 Kg)
B. increase in internal energy is zero
C. increase in internal energy is less than L
D. none of the above

Explanation

To solve the problem, we need to analyze the process of vaporization of water at 100°C and determine the correct statement regarding the increase in internal energy.

### Step-by-Step Solution:

1. **Identify Given Data:**
- Mass of water, \( m = 1 \, \text{kg} \)
- Temperature of water, \( T = 100^\circ C \)
- Latent heat of vaporization of water, \( L \) (approximately \( 2260 \, \text{kJ/kg} \) or \( 2.26 \times 10^6 \, \text{J/kg} \))

2. **Calculate Heat Supplied (Q):**
- The heat supplied to vaporize the water can be calculated using the formula:
\[ Q = m \times L \]
- Substituting the values:
\[ Q = 1 \, \text{kg} \times L \]
- Thus, \( Q = L \).

3. **Understand the Work Done (W):**
- When water vaporizes, it expands against the atmospheric pressure. The work done during this expansion is given by:
\[ W = P \Delta V \]
- Here, \( P \) is the atmospheric pressure and \( \Delta V \) is the change in volume when water turns into steam.

4. **Apply the First Law of Thermodynamics:**
- According to the first law of thermodynamics:
\[ \Delta U = Q - W \]
- Where \( \Delta U \) is the change in internal energy.

5. **Substituting Values:**
- Since \( Q = L \), we can substitute this into the equation:
\[ \Delta U = L - W \]

6. **Analyze the Relationship:**
- Since the work done \( W \) is positive (because the system does work on the surroundings during expansion), it follows that:
\[ \Delta U < L \]
- This means the increase in internal energy is less than the latent heat of vaporization.

7. **Conclusion:**
- The correct statement regarding the increase in internal energy when 1 kg of water at \( 100^\circ C \) is vaporized in open atmosphere is that the increase in internal energy is less than the latent heat of vaporization.

### Final Answer:
The correct statement is: The increase in internal energy is less than the latent heat of vaporization.

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