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 correct statement for work, heat, and change in internal energy, we will analyze each option step by step.

### Step 1: Understanding Work and Heat
- Work (W) and heat (Q) are forms of energy transfer.
- They are not state functions, meaning their values depend on the path taken between the initial and final states of a system.

**Hint:** Remember that state functions depend only on the state of the system, not how it got there.

### Step 2: Analyzing the First Law of Thermodynamics
- According to the first law of thermodynamics, we have:
\[ \Delta U = Q - W \]
where \(\Delta U\) is the change in internal energy, Q is the heat added to the system, and W is the work done by the system.
- Here, \(\Delta U\) is a state function, meaning it only depends on the initial and final states of the system, not the path taken.

**Hint:** The first law of thermodynamics is crucial for understanding the relationship between heat, work, and internal energy.

### Step 3: Evaluating Each Option
1. **Option 1:** "Heat supply and work done depend on initial and final state."
- This statement is partially correct. While heat and work do depend on the initial and final states, they also depend on the path taken. Therefore, this option is not entirely accurate.

2. **Option 2:** "Change in internal energy depends on initial and final state only."
- This statement is correct. The change in internal energy is indeed a state function and depends only on the initial and final states.

3. **Option 3:** "Heat and work depend on the path between the two points."
- This statement is correct. Since heat and work are not state functions, they depend on the specific path taken between the initial and final states.

### Step 4: Conclusion
- Since we have evaluated all options, we find that:
- Option 2 and Option 3 are correct.
- Option 1 is misleading as it does not fully capture the dependence on the path.
- Therefore, the correct conclusion is that Options 2 and 3 are valid statements regarding work, heat, and change in internal energy.

**Final Answer:** The correct statements are:
- Change in internal energy depends on initial and final state only.
- Heat and work depend on the path between the two points.