A system is expanded under adiabatic process

Options

A. Temp. increase
B. `DeltaE` decreases
C. `DeltaE` increases
D. None of these

Answer

To solve the problem of whether the internal energy (ΔU) of a system decreases, increases, or remains the same during an adiabatic expansion, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Adiabatic Process**:
- In an adiabatic process, there is no heat exchange with the surroundings. This means that the heat (Q) is equal to zero.

**Hint**: Remember that in an adiabatic process, Q = 0.

2. **Apply the First Law of Thermodynamics**:
- The first law of thermodynamics states:
\[ \Delta U = Q + W \]
- Since Q = 0 in an adiabatic process, the equation simplifies to:
\[ \Delta U = W \]

**Hint**: The first law of thermodynamics relates changes in internal energy to heat and work.

3. **Determine the Work Done (W)**:
- For an expansion, the work done by the system is given by:
\[ W = -\int P \, dV \]
- When the system expands, the volume increases (V2 > V1), which means dV is positive. Therefore, the work done (W) is negative.

**Hint**: Remember that work done by the system during expansion is considered negative.

4. **Substitute Work into the First Law**:
- Since W is negative, we can substitute it back into the first law:
\[ \Delta U = W < 0 \]
- This indicates that the internal energy (ΔU) of the system decreases.

**Hint**: A negative work done implies a decrease in internal energy.

5. **Conclusion**:
- Therefore, during an adiabatic expansion, the internal energy of the system decreases.

### Final Answer:
The internal energy (ΔU) of the system decreases during an adiabatic expansion.