Three samples of 100 g of water (samples I, II and III), initially kept at 1 atm pressure and 298 K were given the following treatments.
Sample I was heated to 320 K and cooled to 298 K
Sample II was heated to 300 K, cooled to 273 K and heated to 298 K
Sample III was heated to 373 K and cooled to 298 K
At the end of these processes, the internal energy of

Options

A. III is the highest
B. II is the highst
C. I and III are the same, II is lower than that of I and III
D. I, II and III are the same

Answer

To solve the problem regarding the internal energy of the three samples of water after undergoing various heating and cooling processes, we will follow these steps:

### Step-by-Step Solution:

1. **Understanding Internal Energy**:
Internal energy (U) is a state function, meaning it depends only on the state of the system (temperature, pressure, and composition) and not on how the system reached that state.

2. **Initial Conditions**:
All three samples (I, II, and III) start at the same conditions: 100 g of water at 1 atm pressure and 298 K.

3. **Sample I Treatment**:
- Heated to 320 K and then cooled back to 298 K.
- Final state: 298 K, 1 atm.
- Since the final state is the same as the initial state, the internal energy remains unchanged.

4. **Sample II Treatment**:
- Heated to 300 K, cooled to 273 K, and then heated back to 298 K.
- Final state: 298 K, 1 atm.
- Again, the final state is the same as the initial state, so the internal energy remains unchanged.

5. **Sample III Treatment**:
- Heated to 373 K and then cooled back to 298 K.
- Final state: 298 K, 1 atm.
- The final state is the same as the initial state, thus the internal energy remains unchanged.

6. **Conclusion**:
Since all three samples return to the same final state (298 K and 1 atm), the internal energy for all three samples remains the same.

### Final Answer:
The internal energy of the three samples (I, II, and III) at the end of their respective processes is the same.

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