The combination of plots which does not represent isothermal expansion of an ideal gas is :

Options

A.
B.
C.
D.

Explanation

To determine which combination of plots does not represent the isothermal expansion of an ideal gas, we need to analyze the properties of isothermal processes and the ideal gas law.

### Step-by-Step Solution:

1. **Understand Isothermal Process**:
- An isothermal process is one where the temperature (T) remains constant. For an ideal gas, this means that any change in volume (V) will result in a corresponding change in pressure (P) such that the product PV remains constant.

2. **Ideal Gas Law**:
- The ideal gas law is given by the equation:
\[ PV = nRT \]
- For an isothermal process, since T is constant, we can express this as:
\[ PV = C \]
- where C is a constant (since n and R are also constants).

3. **Analyze the Plots**:
- **Plot 1**: If we plot pressure (P) against the reciprocal of volume (1/V), we expect a linear relationship because \( P = C/V \). This plot is valid for isothermal expansion.
- **Plot 2**: If we plot P against V, we expect a hyperbolic curve (since PV = constant). This plot is valid for isothermal expansion.
- **Plot 3**: If we plot PV against a constant, it should be a horizontal line since PV remains constant. This plot is valid for isothermal expansion.
- **Plot 4**: If we plot internal energy (U) against volume (V), we need to consider that for an ideal gas, the internal energy is a function of temperature alone. Since temperature is constant in an isothermal process, the change in internal energy (ΔU) is zero. Thus, this plot would be a horizontal line at zero change, which does not represent an isothermal expansion.

4. **Conclusion**:
- The combination of plots that does not represent the isothermal expansion of an ideal gas is the one that shows a change in internal energy (U vs. V), as U remains constant during an isothermal process.

### Final Answer:
The combination of plots which does not represent isothermal expansion of an ideal gas is the plot of internal energy (U) versus volume (V).

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