A given system undergoes a change in which up workdone by the system equal the decrease in its internal energy. The system must have undergone an

Options

A. isothermal changes
B. adiabatic change
C. isobaric change
D. isochoric change

Answer

To solve the problem, we need to analyze the relationship between work done by the system, the change in internal energy, and the heat exchange according to the first law of thermodynamics.

### Step-by-Step Solution:

1. **Understand the Given Information**:
We know that the work done by the system (W) is equal to the decrease in its internal energy (ΔU). This can be expressed mathematically as:
\[ W = -\Delta U \]
Here, ΔU is negative because it is a decrease in internal energy.

2. **Apply the First Law of Thermodynamics**:
The first law of thermodynamics states:
\[ \Delta Q = \Delta U + W \]
Where:
- ΔQ is the heat added to the system,
- ΔU is the change in internal energy,
- W is the work done by the system.

3. **Substitute the Expression for W**:
Since we have established that \( W = -\Delta U \), we can substitute this into the first law equation:
\[ \Delta Q = \Delta U + (-\Delta U) \]
This simplifies to:
\[ \Delta Q = 0 \]

4. **Interpret the Result**:
A change in heat (ΔQ) equal to zero indicates that there is no heat exchange with the surroundings. This condition is characteristic of an adiabatic process, where the system is insulated from heat transfer.

5. **Conclusion**:
Since the work done by the system equals the decrease in internal energy, and there is no heat exchange, we conclude that the system must have undergone an **adiabatic process**.

### Final Answer:
The system must have undergone an **adiabatic process**.

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