In an isothermal expansion of an ideal gas. Select wrong statement:

Options

A. there is no change in the temperature of the gas
B. there is no change in the internal energy of the gas
C. the work done by the gas is equal to the heat supplied to the gas
D. the work done by the gas is equal to the changes in its internal energy

Answer

To solve the question regarding the isothermal expansion of an ideal gas and to identify the wrong statement, we will analyze each option step by step.

### Step-by-Step Solution:

1. **Understanding Isothermal Process**:
- An isothermal process is one where the temperature (T) remains constant throughout the process. Therefore, the change in temperature (ΔT) is equal to 0.
- Since the temperature is constant, the internal energy of an ideal gas, which depends only on temperature, also remains constant.

2. **Analyzing the Options**:
- **Option 1**: "There is no change in temperature of the gas."
- This statement is true because, by definition of an isothermal process, the temperature does not change.

- **Option 2**: "There is no change in internal energy of the gas."
- This statement is also true. For an ideal gas, the internal energy (U) depends only on temperature. Since ΔT = 0, ΔU = 0.

- **Option 3**: "The work done by the gas is equal to the heat supplied to the gas."
- This statement is true as well. According to the first law of thermodynamics, ΔU = ΔQ - ΔW. Since ΔU = 0 in an isothermal process, it follows that ΔQ = ΔW.

- **Option 4**: "The work done by the gas is equal to the change in its internal energy."
- This statement is false. In an isothermal expansion, the work done by the gas is not equal to the change in internal energy because the change in internal energy is zero (ΔU = 0), while work done (ΔW) is not zero.

3. **Conclusion**:
- The wrong statement among the options given is Option 4: "The work done by the gas is equal to the change in its internal energy."

### Final Answer:
The wrong statement is: "The work done by the gas is equal to the change in its internal energy."