During the adiabatic expansion of 2 moles of a gas, the internal energy was found to have decreased by 100 J . The work done by the gas in this process is

Options

A. Zero
B. `-100j`
C. `200j`
D. `100j`

Answer

To solve the problem, we will use the first law of thermodynamics, which states:

\[ \Delta U = Q - W \]

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

In the case of adiabatic processes, there is no heat exchange with the surroundings, which means:

\[ Q = 0 \]

Thus, the equation simplifies to:

\[ \Delta U = -W \]

Given that the internal energy decreases by 100 J, we can express this as:

\[ \Delta U = -100 \, \text{J} \]

Substituting this value into the simplified first law equation gives:

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

From this, we can solve for \(W\):

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

This means that the work done by the gas during the adiabatic expansion is 100 J.

### Final Answer:
The work done by the gas in this process is **100 J**.

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