Which of the following statement/expression is/are correct?

Options

A. `DeltaU=W_("adiabatic")`
B. `W_(ad)=+ve`, when work is done on the system
C. `W_(ad)=-ve`, when work is done by the system
D. All of these

Explanation

To determine which of the statements regarding thermodynamics are correct, let’s analyze each statement step by step.

### Step 1: Analyze the First Statement
**Statement:** ΔU = ΔW (Adiabatic Process)

In an adiabatic process, there is no heat exchange with the surroundings. According to the first law of thermodynamics, we have:
\[ \Delta U = Q + W \]
Since the process is adiabatic, \( Q = 0 \). Therefore, the equation simplifies to:
\[ \Delta U = W \]
This means that the change in internal energy (ΔU) is equal to the work done (W) in an adiabatic process. Thus, the first statement is **correct**.

### Step 2: Analyze the Second Statement
**Statement:** Work is positive when done on the system and negative when done by the system.

In thermodynamics, the sign convention for work is as follows:
- Work done **on** the system is considered **positive**.
- Work done **by** the system is considered **negative**.

This aligns with the statement provided. Therefore, the second statement is also **correct**.

### Step 3: Analyze the Third Statement
**Statement:** Work done is negative when work is done by the system.

As established in the previous step, when the system does work on the surroundings, it is considered negative. Thus, this statement is also **correct**.

### Step 4: Analyze the Fourth Statement
**Statement:** All of these.

Since we have established that the first, second, and third statements are all correct, it follows that the fourth statement, which claims that all of the previous statements are correct, is also **correct**.

### Conclusion
All the statements provided in the question are correct.

### Final Answer
The correct answer is: **All of these**.

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