During an adiabatic expansion of 2 moles of a gas the chang in internal energy was found to be equal to -100 J. The work done during the process will be equal to

Options

A. zero
B. `-100` joule
C. 200 joule
D. 100 joule

Explanation

To solve the problem, we will use the first law of thermodynamics, which is given by the equation:

\[ \Delta Q = \Delta U + \Delta W \]

Where:
- \(\Delta Q\) is the heat added to the system,
- \(\Delta U\) is the change in internal energy,
- \(\Delta W\) is the work done by the system.

### Step 1: Identify the given values
From the problem, we know:
- The process is adiabatic, which means \(\Delta Q = 0\).
- The change in internal energy \(\Delta U = -100 \, \text{J}\).

### Step 2: Substitute the known values into the first law of thermodynamics
Since \(\Delta Q = 0\), we can rewrite the first law of thermodynamics as:

\[ 0 = \Delta U + \Delta W \]

### Step 3: Rearrange the equation to solve for \(\Delta W\)
Now, we can rearrange the equation to find the work done \(\Delta W\):

\[ \Delta W = -\Delta U \]

### Step 4: Substitute the value of \(\Delta U\)
Now, substituting the value of \(\Delta U\):

\[ \Delta W = -(-100 \, \text{J}) = 100 \, \text{J} \]

### Conclusion
Thus, the work done during the adiabatic expansion is:

\[ \Delta W = 100 \, \text{J} \]

### Final Answer
The work done during the process will be equal to **100 J**.

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