In an adiabatic expansion of 2 moles of a gas, the change in its internal energy was found to be –100J. The work done in this process is :

Options

A. zero
B. 100 j
C. `-1000 j`
D. 200j

Answer

To solve the problem of finding the work done during the adiabatic expansion of a gas, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Process**: In an adiabatic process, there is no heat exchange with the surroundings. Therefore, the heat transfer \( dq = 0 \).

2. **Apply the First Law of Thermodynamics**: The first law of thermodynamics states:
\[ dq = du + dw \]
where:
- \( dq \) is the heat added to the system,
- \( du \) is the change in internal energy,
- \( dw \) is the work done by the system.

3. **Substitute Known Values**: Since \( dq = 0 \) for an adiabatic process, we can rewrite the equation as:
\[ 0 = du + dw \]
Rearranging gives:
\[ dw = -du \]

4. **Insert the Change in Internal Energy**: We know from the problem that the change in internal energy \( du = -100 \, J \). Substituting this value into the equation gives:
\[ dw = -(-100 \, J) = 100 \, J \]

5. **Conclusion**: The work done \( dw \) during the adiabatic expansion is \( 100 \, J \).

### Final Answer:
The work done in this process is \( 100 \, J \).

---