The change in internal energy of two moles of a gas during adiabatic expansion is found to be -100 Joule. The work done during the process is

Options

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

Explanation

To solve the problem, we need to determine the work done during the adiabatic expansion of a gas when the change in internal energy is given. Here's a step-by-step solution:

### Step 1: Understand the given information
We are given:
- Change in internal energy (ΔU) = -100 Joules
- The process is adiabatic, which means there is no heat exchange (Q = 0).

### Step 2: Apply the First Law of Thermodynamics
The First Law of Thermodynamics states:
\[ \Delta U = Q + W \]
Where:
- ΔU = Change in internal energy
- Q = Heat added to the system
- W = Work done by the system

### Step 3: Substitute the known values
Since the process is adiabatic, we have:
\[ Q = 0 \]
Thus, the equation simplifies to:
\[ \Delta U = W \]

### Step 4: Rearranging the equation
From the equation, we can express work done (W) as:
\[ W = \Delta U \]

### Step 5: Substitute the value of ΔU
Now, substituting the value of ΔU:
\[ W = -100 \, \text{Joules} \]

### Step 6: Interpret the result
Since the work done is negative, it indicates that work is done by the system on the surroundings. However, we are often interested in the magnitude of work done:
\[ |W| = 100 \, \text{Joules} \]

### Final Answer
The work done during the adiabatic expansion is:
\[ W = 100 \, \text{Joules} \]

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