In an isothermal process for ideal gas.

Options

A. q=0 and `DeltaE=0`
B. `q ne 0` and `DeltaE=0`
C. q=0 and `DeltaE ne 0`
D. `q ne 0` and `DeltaE ne 0`

Explanation

To solve the question regarding the conditions valid in an isothermal process for an ideal gas, we can analyze each option step by step.

### Step-by-Step Solution:

1. **Understanding Isothermal Process**:
- An isothermal process is one that occurs at a constant temperature. For an ideal gas, this means that the temperature (T) does not change during the process.

2. **Change in Internal Energy (ΔU)**:
- The change in internal energy (ΔU) for an ideal gas is given by the equation:
\[ \Delta U = nC_V\Delta T \]
- Where \(n\) is the number of moles, \(C_V\) is the molar heat capacity at constant volume, and \(\Delta T\) is the change in temperature.
- Since the process is isothermal, \(\Delta T = 0\). Therefore, we have:
\[ \Delta U = nC_V \cdot 0 = 0 \]
- This means that the change in internal energy is zero.

3. **Heat Transfer (Q)**:
- In an isothermal process, although the temperature remains constant, heat can be transferred to or from the system to maintain this constant temperature. Therefore, \(Q\) is not necessarily zero.

4. **Evaluating Each Option**:
- **Option 1**: Heat is zero and change in internal energy is also equal to zero.
- This is incorrect because while \(\Delta U = 0\), \(Q\) is not zero.
- **Option 2**: Heat is not equal to zero and internal energy is equal to zero.
- This is correct. \(Q \neq 0\) and \(\Delta U = 0\).
- **Option 3**: Heat change is zero and internal energy change is not equal to zero.
- This is incorrect because \(\Delta U = 0\) and \(Q\) is not zero.
- **Option 4**: Both heat and internal energy are not equal to 0.
- This is incorrect because while \(Q\) can be non-zero, \(\Delta U = 0\).

5. **Conclusion**:
- The only valid condition for an isothermal process of an ideal gas is **Option 2**: Heat is not equal to zero and internal energy is equal to zero.

### Final Answer:
**Option 2** is the correct answer.