ANS:B - increases

Thermal conductivity of a gas at low density typically increases with an increase in temperature. Here's why:

1. Increase in Molecular Velocity: At low densities, the molecules in the gas have relatively large mean free paths and move at high speeds. When the temperature of the gas increases, the kinetic energy of the molecules also increases, leading to higher molecular velocities.
2. Impact on Collisions: The increase in molecular velocity results in more frequent collisions between gas molecules. These collisions lead to greater transfer of kinetic energy between molecules, which enhances thermal conductivity.
3. Effect on Mean Free Path: While the mean free path of gas molecules tends to decrease with increasing temperature due to increased molecular collisions, the overall effect of increased molecular velocity dominates, leading to an increase in thermal conductivity.
4. Temperature Dependent Properties: Additionally, factors such as specific heat capacity and viscosity, which influence thermal conductivity, may also change with temperature. However, the dominant effect at low gas densities is the increase in molecular velocity, which leads to an overall increase in thermal conductivity with increasing temperature.