Step 1: Understand ideal gas conditions.
An ideal gas is best approximated when intermolecular forces are negligible and molecular volume is insignificant. This occurs at high temperature and low pressure conditions.
Step 2: Effect of temperature.
At higher temperature, kinetic energy of gas molecules increases, reducing the effect of intermolecular attractions. Therefore, gases behave more ideally at higher temperatures.
Step 3: Effect of pressure.
At lower pressure, molecules are far apart, and intermolecular interactions become negligible. This improves ideal gas behavior significantly.
Step 4: Analyze given options.
We compare conditions:
- 400 K is high temperature
- 0.01 bar is very low pressure
Thus, this combination best satisfies ideal gas assumptions.
Step 5: Eliminate other options.
100 K is low temperature (less ideal behavior), and 1 bar is relatively higher pressure, both of which increase deviation from ideality. Hence those options are less suitable.
Step 6: Final conclusion.
Therefore, the gas behaves most ideally under:
\[
\boxed{400 \, \text{K and } 0.01 \, \text{bar}}
\]