During the adiabatic expansion of 2 moles of a gas, the internal energy of the gas is found to decrease by 2 joules , the work done during the process on the gas will be equal to

Answer

To solve the problem, we will use the first law of thermodynamics and the properties of an adiabatic process. Here’s the step-by-step solution:

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

### Step 2: Recognize the Nature of the Process
In an adiabatic process, there is no heat exchange with the surroundings. Therefore:
\[ \Delta Q = 0 \]

### Step 3: Simplify the First Law for Adiabatic Process
Substituting \(\Delta Q = 0\) into the first law equation gives:
\[ 0 = \Delta U + \Delta W \]
This can be rearranged to find the work done:
\[ \Delta W = -\Delta U \]

### Step 4: Identify the Change in Internal Energy
The problem states that the internal energy of the gas decreases by 2 joules. Thus:
\[ \Delta U = -2 \, \text{J} \]

### Step 5: Calculate the Work Done
Now, substituting the value of \(\Delta U\) into the equation for work done:
\[ \Delta W = -(-2 \, \text{J}) = 2 \, \text{J} \]

### Conclusion
The work done during the adiabatic expansion of the gas is:
\[ \Delta W = 2 \, \text{J} \]