You measure the viscosity of nitrogen gas at 300 K, then again at 1200 K (a factor-of-4 increase in absolute temperature). What do you expect to observe, and why?
AViscosity decreases by roughly half — higher temperature means faster molecules that disrupt ordered flow more chaotically
BViscosity is unchanged — the mean free path shortens in exactly the proportion the speed increases
CViscosity roughly doubles (increases by ~√4) — faster molecules transport momentum across velocity gradients more effectively
DViscosity increases fourfold — viscosity scales directly with absolute temperature in gases
Gas viscosity scales as √T from kinetic theory: η ∝ √T. At 4× the temperature, viscosity increases by √4 = 2×. This contradicts liquid behavior, where viscosity decreases with temperature. In gases, there are no intermolecular attractions to weaken — faster molecules simply carry momentum more effectively across a velocity gradient. Option A describes the liquid case; option D overestimates by confusing √T with T.
Question 2 Multiple Choice
Thermal conductivity (κ) of an ideal gas is proportional to its viscosity (η). Which statement best explains why?
ABoth properties increase with temperature, so they must be proportional to each other
BBoth properties arise from the same microscopic mechanism — molecules traveling a mean free path and carrying a quantity (momentum or energy) between collisions — differing only in what is transported
CThey are related because denser gases have both higher viscosity and higher thermal conductivity
DThe proportionality is empirical and has no theoretical explanation from kinetic theory
The formulas make the connection explicit: η = (1/3)ρc̄λ and κ = (1/3)ρc̄λC_V/M. Both contain the same ρ, c̄, and λ; the only difference is that κ includes the heat capacity per unit mass C_V/M because thermal conductivity transports kinetic energy while viscosity transports momentum. This proportionality is a theoretical prediction, not just an empirical coincidence, and it follows directly from the unified mean-free-path picture of gas transport.
Question 3 True / False
In an ideal gas, viscosity and thermal conductivity both depend on the same mean free path (λ) and mean molecular speed (c̄).
TTrue
FFalse
Answer: True
True. The kinetic theory expressions η = (1/3)ρc̄λ and κ = (1/3)ρc̄λC_V/M share the same c̄λ product. Both properties arise because molecules travel on average a distance λ before colliding, carrying whatever macroscopic quantity varies spatially (momentum for viscosity, kinetic energy for thermal conductivity). Diffusion also shares this structure: D = (1/3)c̄λ. The unified mean-free-path picture is the central insight of gas transport theory.
Question 4 True / False
Like liquids, gases become less viscous when heated, because higher kinetic energy disrupts the intermolecular interactions that cause resistance to flow.
TTrue
FFalse
Answer: False
False — this is the most common misconception in gas transport. Gas viscosity INCREASES with temperature. Gases have negligible intermolecular attractions, so there are no cohesive interactions to disrupt. Instead, gas viscosity arises purely from molecular momentum transfer: faster molecules (higher T) traverse the mean free path more quickly and carry more momentum per molecule, making momentum transport across a velocity gradient more efficient. The result is η ∝ √T. The liquid mechanism described in the question simply does not apply to gases.
Question 5 Short Answer
Why does gas viscosity increase with temperature while liquid viscosity decreases? Explain the different mechanisms responsible.
Think about your answer, then reveal below.
Model answer: In liquids, viscosity arises from intermolecular cohesion — molecules must overcome attractive forces to flow past neighbors, and thermal energy reduces these effective energy barriers, so viscosity drops as T rises. In gases, intermolecular attractions are negligible; viscosity arises entirely from momentum transfer between layers. Molecules randomly crossing from a fast-moving layer to a slower one carry excess momentum, dragging the layers toward the same speed. Faster molecules (higher T) traverse the mean free path more quickly and carry more momentum, so viscous coupling between layers strengthens with temperature. The net result is η ∝ √T for ideal gases.
The key is recognizing that liquid and gas viscosity have fundamentally different physical origins. Liquid viscosity is about overcoming attraction; gas viscosity is about collisional momentum transfer. This also explains why adding a noble gas to a mixture affects viscosity even though noble gases have essentially no intermolecular attractions — what matters is their mass and speed, not their chemistry.