In an adiabatic expansion of an ideal gas -

Options

A. (a) `W=-DeltaU`
B. (b) `W=DeltaU`
C. (c) `DeltaU=0`
D. (d) `W = 0 `

Explanation

To solve the question regarding the adiabatic expansion of an ideal gas, we can follow these steps:

### Step 1: Understand the First Law of Thermodynamics
The first law of thermodynamics states that:
\[ Q + W = \Delta U \]
where:
- \( Q \) is the heat exchanged,
- \( W \) is the work done on the system,
- \( \Delta U \) is the change in internal energy of the system.

### Step 2: Identify Conditions for Adiabatic Process
In an adiabatic process, there is no heat exchange with the surroundings. Therefore, we have:
\[ Q = 0 \]

### Step 3: Substitute into the First Law
Substituting \( Q = 0 \) into the first law equation gives:
\[ 0 + W = \Delta U \]
or simply:
\[ W = \Delta U \]

### Step 4: Analyze Work Done in Expansion
For an adiabatic expansion of an ideal gas, the gas does work on the surroundings. By convention, the work done by the system (the gas) is considered negative. Thus, we can write:
\[ W = -\Delta U \]

### Step 5: Conclusion
From the above analysis, we conclude that during an adiabatic expansion of an ideal gas, the work done by the gas is equal to the negative change in internal energy:
\[ W = -\Delta U \]

Thus, the correct condition for the adiabatic expansion of an ideal gas is that the work done by the gas is equal to the negative change in internal energy.

### Final Answer
The correct option is:
\[ W = -\Delta U \]

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