Question

Which of the following statements about the viscosity of a dilute ideal gas is correct ?

• A. It is independent of pressure at fixed temperature
• B. It increases with increasing pressure at fixed temperature
• C. It is independent of temperature
• D. It decreases with increasing temperature

Answer 1

The Correct Option is A

The question asks about the behavior of the viscosity of a dilute ideal gas under varying conditions. Let's analyze each statement step-by-step:

1. Statement A: "It is independent of pressure at fixed temperature."

In the kinetic theory of gases, the viscosity of a dilute ideal gas is primarily determined by the average velocity of the gas molecules and the mean free path. At a constant temperature, these properties are influenced mostly by molecular characteristics rather than pressure. According to the kinetic theory, for a dilute ideal gas, viscosity remains relatively unaffected by changes in pressure at a fixed temperature. Thus, this statement is correct.

2. Statement B: "It increases with increasing pressure at fixed temperature."

This statement is incorrect for dilute ideal gases because, according to the kinetic theory, at fixed temperature, the viscosity remains practically the same even if the pressure changes. In practice, for ideal gases, viscosity does not significantly vary with pressure in a dilute gas scenario.

3. Statement C: "It is independent of temperature."

This statement is incorrect. Viscosity of gases typically increases with an increase in temperature. This happens because at higher temperatures, molecules move faster and collide more frequently, thus increasing the gas's resistance to flow, i.e., its viscosity. Therefore, viscosity depends on temperature rather than being independent of it.

4. Statement D: "It decreases with increasing temperature."

This statement is also incorrect because, as mentioned, the viscosity of a dilute gas actually increases with an increase in temperature due to higher molecular activity and more frequent collisions.

After analyzing all the options, the only correct statement is that the viscosity of a dilute ideal gas is independent of pressure at a fixed temperature.

Thus, the correct answer is: It is independent of pressure at fixed temperature.