Total internal energy of an ideal gas remains constant in isothermal process.

Answer

### Step-by-Step Solution:

1. **Understanding Isothermal Process**:
- An isothermal process is defined as a thermodynamic process in which the temperature of the system remains constant throughout the process.
- Mathematically, this can be expressed as \( T = \text{constant} \).

**Hint**: Recall the definition of isothermal processes and remember that temperature does not change.

2. **Internal Energy of an Ideal Gas**:
- The internal energy (\( U \)) of an ideal gas is primarily a function of its temperature. For an ideal gas, the internal energy is considered to be the sum of the kinetic energies of its molecules.
- In an ideal gas, there are no intermolecular forces, which means potential energy is negligible, and thus the internal energy is purely kinetic.

**Hint**: Consider the relationship between internal energy and temperature for an ideal gas.

3. **Relation Between Internal Energy and Temperature**:
- For an ideal gas, the internal energy can be expressed as:
\[ U = f(T) \]
- This indicates that the internal energy is a function of temperature alone.

**Hint**: Remember that changes in internal energy depend on changes in temperature.

4. **Change in Internal Energy During Isothermal Process**:
- Since the temperature remains constant during an isothermal process, there is no change in temperature (\( dT = 0 \)).
- Therefore, the change in internal energy (\( dU \)) can be expressed as:
\[ dU = \frac{dU}{dT} \cdot dT = 0 \]
- This implies that:
\[ dU = 0 \]

**Hint**: Think about how a constant temperature affects the change in internal energy.

5. **Conclusion**:
- Since \( dU = 0 \), it indicates that the total internal energy of the ideal gas remains constant during an isothermal process.
- Thus, the statement "Total internal energy of an ideal gas remains constant in isothermal process" is **true**.

**Hint**: Summarize the findings to confirm the statement's validity.