Introduction:
In order to understand why the thermal conductivity of a gas increases as the temperature increases, it is important to first define what thermal conductivity is. Thermal conductivity is a property of a material that describes its ability to conduct heat. It is defined as the amount of heat that can pass through a unit area of a material in a unit time when a temperature gradient exists across the material. In other words, it is a measure of how easily heat can be transferred through a material.

Explanation:
When the temperature of a gas increases, the thermal conductivity also increases. This can be explained by the behavior of gas molecules at different temperatures.

1. Molecular Motion:
At higher temperatures, the molecules in a gas move faster and have higher kinetic energy. This increased molecular motion leads to more frequent collisions between the gas molecules, which in turn increases the number of collisions with neighboring molecules. These collisions transfer energy from one molecule to another, facilitating the conduction of heat.

2. Increased Energy Transfer:
With higher temperatures, the molecules gain more energy, resulting in increased energy transfer between them. As a result, the gas molecules can transfer heat more efficiently, leading to an increase in thermal conductivity.

3. Enhanced Vibrational Modes:
At higher temperatures, the gas molecules can also undergo additional vibrational modes. These additional modes allow the molecules to absorb and transfer more heat, thereby increasing the thermal conductivity of the gas.

4. Decreased Mean Free Path:
Another factor that contributes to the increase in thermal conductivity with temperature is the decrease in the mean free path of the gas molecules. The mean free path is the average distance a molecule travels between collisions. As the temperature increases, the gas molecules move faster and collide more frequently, reducing the mean free path. This reduction in the mean free path allows for more efficient heat transfer through the gas, resulting in higher thermal conductivity.

Conclusion:
In summary, as the temperature of a gas increases, the thermal conductivity also increases. This is due to the increased molecular motion, enhanced energy transfer, additional vibrational modes, and decreased mean free path of the gas molecules at higher temperatures. These factors collectively contribute to a higher thermal conductivity, allowing the gas to conduct heat more effectively.