ANS:C - D ∝ T^1.5

The relationship between diffusivity (D) in a binary gas mixture and temperature (T) is typically described by the Stokes-Einstein equation. This equation establishes a relationship between diffusivity, temperature, and the viscosity of the gas mixture. The Stokes-Einstein equation states that the diffusivity of a particle in a fluid is inversely proportional to the temperature of the fluid and the viscosity of the fluid. It is expressed as: 𝐷∝𝑇𝜇D∝μT​ where:

• 𝐷D is the diffusivity,
• 𝑇T is the absolute temperature,
• 𝜇μ is the dynamic viscosity of the fluid.

In the case of a binary gas mixture, the viscosity of the mixture can be related to the temperature through the kinetic theory of gases. According to the kinetic theory of gases, the viscosity of a gas is proportional to the square root of its temperature. Therefore, we have: 𝜇∝𝑇μ∝T​ Substituting this relationship into the Stokes-Einstein equation, we get: 𝐷∝𝑇𝑇=𝑇0.5D∝T​T​=T0.5 So, the correct relationship between diffusivity (D) and temperature (T) in a binary gas mixture is 𝐷∝𝑇0.5D∝T0.5.