The process `DeltaU = 0`, for an ideal gas can be best represented in the form of a graph:

Options

A.
B.
C.
D.

Explanation

To solve the question regarding the process where the change in internal energy (ΔU) for an ideal gas is zero, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding ΔU for an Ideal Gas**:
- The change in internal energy (ΔU) for an ideal gas is given by the formula:
\[ \Delta U = nC \Delta T \]
where \( n \) is the number of moles, \( C \) is the molar heat capacity, and \( \Delta T \) is the change in temperature.

2. **Setting ΔU to Zero**:
- According to the question, we have ΔU = 0. This implies:
\[ nC \Delta T = 0 \]
For this equation to hold true, either \( n \) or \( C \) must be zero, or \( \Delta T \) must be zero. Since \( n \) and \( C \) cannot be zero for an ideal gas, we conclude that:
\[ \Delta T = 0 \]

3. **Interpreting ΔT = 0**:
- If ΔT = 0, it means that the temperature of the gas remains constant throughout the process. A process in which the temperature remains constant is known as an **isothermal process**.

4. **Graphical Representation**:
- In an isothermal process for an ideal gas, the relationship between pressure (P) and volume (V) can be represented graphically. The equation for an isothermal process is given by:
\[ PV = nRT \]
This indicates that for a constant temperature (T), the product of pressure and volume remains constant.

5. **Shape of the Graph**:
- The graph of an isothermal process is a rectangular hyperbola when plotted with pressure (P) on the y-axis and volume (V) on the x-axis. As volume increases, pressure decreases, and vice versa, maintaining the product \( PV \) constant.

6. **Conclusion**:
- Therefore, the best representation of the process ΔU = 0 for an ideal gas is a rectangular hyperbola graph, which corresponds to an isothermal process.

### Final Answer:
The process ΔU = 0 for an ideal gas can be best represented by a rectangular hyperbola graph.

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