Select the correct statement for work, heat and change in internal energy

Options

A. Heat supplied and work done depend on initial and final states
B. Change ininternal energy depends on the initial and final states only
C. Heat and work depend on the path between the two points
D. All of these

Answer

To solve the question regarding the relationships between work, heat, and change in internal energy, we will analyze each statement provided in the options.

### Step-by-Step Solution:

1. **Understanding Work (W)**:
- Work done in a thermodynamic process can be expressed as \( W = P \cdot dV \), where \( P \) is pressure and \( dV \) is the change in volume.
- Work depends on the initial and final states of the system, as well as the path taken between these states.

2. **Understanding Heat (Q)**:
- Heat can be expressed as \( Q = nC \Delta T \), where \( n \) is the number of moles, \( C \) is the heat capacity, and \( \Delta T \) is the change in temperature.
- Similar to work, heat also depends on the initial and final states of the system and the path taken during the process.

3. **Understanding Change in Internal Energy (ΔU)**:
- The change in internal energy can be expressed as \( \Delta U = nC_v \Delta T \), where \( C_v \) is the molar heat capacity at constant volume.
- The change in internal energy is a state function, meaning it only depends on the initial and final states of the system, not the path taken.

4. **Analyzing the Statements**:
- **Option A**: "Heat supplied and work done depend on initial and final states."
- This statement is **true** because both heat and work are path-dependent and require knowledge of the initial and final states to be defined.

- **Option B**: "Change in internal energy depends on initial and final states only."
- This statement is also **true** because the change in internal energy is a state function and is determined solely by the initial and final states.

- **Option C**: "Heat and work done depend on the path between the two points."
- This statement is **true** as well, since the amount of work done and heat transferred can vary depending on the specific path taken during the process.

5. **Conclusion**:
- Since all three statements (A, B, and C) are correct, the final answer is that all the given options are true.

### Final Answer:
All of the statements regarding work, heat, and change in internal energy are correct.

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