Under which of the following conditions is the law PV = RT obeyed most closely by a real gas

The correct option is Low pressure and high temperature.

Explanation:
The equation:

$PV=RT$

represents the ideal gas equation. Real gases do not obey this equation perfectly under all conditions due to two assumptions of the kinetic theory of ideal gases that do not hold true for real gases under ordinary conditions:
1. There are no intermolecular forces of attraction between the gas molecules.
2. The volume occupied by the gas molecules themselves is negligible compared to the total volume of the container.

A real gas behaves most like an ideal gas under the following conditions:

1. Low Pressure:
At low pressures, the volume occupied by the gas is very large. Consequently, the actual volume of the gas molecules becomes negligible compared to the total volume of the container. Furthermore, because the molecules are spaced far apart, the intermolecular forces of attraction between them become negligible.

2. High Temperature:
At high temperatures, the average kinetic energy of the gas molecules is very high. Because the molecules move at very high speeds, they easily overcome the intermolecular forces of attraction during collisions, making these forces negligible.

Therefore, a real gas obeys the ideal gas law:

$PV=RT$

most closely under the conditions of low pressure and high temperature.