If an ideal gas does the work of expansion solely at the cost of its internal energy, the process is

Options

A. reversible
B. irrerversible
C. isothermal
D. adiabatic

Answer

To solve the question, we need to analyze the relationship between internal energy, heat, and work done by an ideal gas during an expansion process.

### Step-by-Step Solution:

1. **Understand the First Law of Thermodynamics**: The first law states that the change in internal energy (dU) of a system is equal to the heat added to the system (dQ) minus the work done by the system (dW). Mathematically, this is expressed as:
\[ dU = dQ - dW \]

2. **Identify the Conditions of the Process**: The question states that the work of expansion is done solely at the cost of internal energy. This implies that there is no heat exchange with the surroundings during the process. Therefore, we can assume:
\[ dQ = 0 \]

3. **Substitute into the First Law**: If we substitute \(dQ = 0\) into the first law equation, we get:
\[ dU = 0 - dW \implies dU = -dW \]

4. **Interpret the Result**: The equation \(dU = -dW\) indicates that any decrease in internal energy (dU) is equal to the work done by the gas (dW) during expansion. This means that the internal energy of the gas is being used entirely to do work.

5. **Identify the Type of Process**: The process described, where the gas expands and does work at the expense of its internal energy without any heat exchange, is characteristic of an **adiabatic process**. In an adiabatic process, the system is thermally insulated, and there is no heat transfer (dQ = 0).

6. **Conclusion**: Therefore, the process in which an ideal gas does work of expansion solely at the cost of its internal energy is an **adiabatic process**.

### Final Answer:
The process is **adiabatic**.