For free expansion of a gas in an adiabatic container which of the following is true?

Options

A. `Q=W=0 and triangleU=0`
B. `Q=0, W gt 0 and triangleU=0`
C. `W=0, Q gt 0 and triangleU=Q`
D. `W=0, Q lt 0 and triangleU=0`

Explanation

To solve the question regarding the free expansion of a gas in an adiabatic container, we will analyze the concepts of adiabatic processes and free expansion step by step.

### Step-by-Step Solution:

1. **Understanding Adiabatic Process**:
- An adiabatic process is one in which no heat is exchanged with the surroundings. This means that the heat transfer (Q) is equal to zero (Q = 0).

**Hint**: Remember that in an adiabatic process, the system is thermally insulated from its surroundings.

2. **Understanding Free Expansion**:
- Free expansion refers to the expansion of a gas into a vacuum or a larger volume without doing work against an external pressure. In this case, the gas expands freely without any opposing force.

**Hint**: In free expansion, the gas does not perform work on the surroundings, as there is no external pressure.

3. **Applying the First Law of Thermodynamics**:
- The First Law of Thermodynamics states that:
\[ \Delta U = Q - W \]
where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system.

4. **Substituting Values**:
- Since we have established that Q = 0 (adiabatic process) and W = 0 (no work done in free expansion), we can substitute these values into the equation:
\[ \Delta U = 0 - 0 \]
This simplifies to:
\[ \Delta U = 0 \]

**Hint**: The change in internal energy is directly related to heat and work done. If both are zero, the internal energy remains unchanged.

5. **Conclusion**:
- From the above analysis, we can conclude that during the free expansion of a gas in an adiabatic container:
- The heat exchange (Q) is zero.
- The work done (W) is zero.
- The change in internal energy (ΔU) is also zero.

Therefore, the correct statement is that the internal energy of the gas does not change during this process.

**Final Answer**: For free expansion of a gas in an adiabatic container, the correct statement is that the change in internal energy (ΔU) is zero.