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 highest
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, we need to analyze the internal energy changes of the three samples of water after the specified heating and cooling processes.

### Step-by-Step Solution:

1. **Understanding Internal Energy**:
Internal energy (U) is a state function, which means it depends only on the initial and final states of the system, not on the path taken to get there.

2. **Initial Conditions**:
All three samples of water start at the same initial conditions:
- Mass = 100 g
- Temperature = 298 K
- Pressure = 1 atm

3. **Sample I Treatment**:
- Heated to 320 K and then cooled back to 298 K.
- Initial state: 298 K
- Final state: 298 K
- Since the initial and final states are the same, the change in internal energy (ΔU) for Sample I is zero.

4. **Sample II Treatment**:
- Heated to 300 K, cooled to 273 K, and then heated back to 298 K.
- Initial state: 298 K
- Final state: 298 K
- Again, the initial and final states are the same, so the change in internal energy (ΔU) for Sample II is also zero.

5. **Sample III Treatment**:
- Heated to 373 K and then cooled back to 298 K.
- Initial state: 298 K
- Final state: 298 K
- The initial and final states are the same, hence the change in internal energy (ΔU) for Sample III is also zero.

6. **Conclusion**:
Since all three samples return to the same initial and final states (298 K and 1 atm), the internal energy of all three samples will be the same at the end of their respective processes. Therefore, we conclude that:
- Internal energy of Sample I = Internal energy of Sample II = Internal energy of Sample III.

### Final Answer:
The internal energies of samples I, II, and III are all the same.