A gas is compressed to five times its original pressure at constant temperature. What happens to its viscosity?
AIt increases five-fold because there are five times as many molecules per unit volume to transfer momentum between layers
BIt remains essentially unchanged because the increase in density is exactly offset by a decrease in mean free path
CIt decreases because molecules collide more frequently and cannot travel far enough between layers to transfer momentum
DIt doubles because both density and collision frequency increase proportionally with pressure
This is Maxwell's counterintuitive result from 1860. At higher pressure, gas density ρ increases (more molecules per volume), but mean free path λ decreases by the same factor — molecules collide more often and travel shorter distances. In the kinetic theory expression η = ⅓ρ⟨c⟩λ, the product ρλ stays constant, so η is independent of pressure. This was a testable prediction that Maxwell made before experimental confirmation, and its verification was a major triumph of kinetic theory.
Question 2 Multiple Choice
Why does raising temperature increase gas viscosity but decrease liquid viscosity?
ATemperature increases molecular spacing in both phases, but viscosity depends on spacing only in gases
BIn gases, faster-moving molecules carry momentum more effectively between layers; in liquids, higher thermal energy helps molecules overcome attractive forces that impede flow
CGas viscosity decreases at high temperature due to reduced collision frequency; liquid viscosity increases because thermal expansion reduces molecular mobility
DTemperature affects only polar molecules; the difference between gas and liquid behavior reflects differences in molecular polarity
The mechanisms are fundamentally different. In gases, viscosity comes from momentum transport — molecules jumping between layers carry momentum with them. Faster molecules (higher T) carry momentum more effectively, so η increases as roughly T^(1/2). In liquids, molecules are densely packed and viscosity arises from needing to overcome intermolecular attractions to flow past neighbors. Higher temperature gives molecules energy to clear these barriers, so η decreases following an Arrhenius relation η = A·exp(Eₐ/RT). The opposite temperature dependencies reflect completely different physical origins.
Question 3 True / False
The viscosity of a gas increases with temperature because faster-moving molecules are more effective at transferring momentum between adjacent fluid layers.
TTrue
FFalse
Answer: True
In kinetic theory, viscosity arises from molecules exchanging momentum between layers moving at different speeds. Molecules from a fast-moving layer carry extra forward momentum when they collide with a slow-moving layer, and vice versa. Higher temperature means higher mean molecular speed, which means more effective momentum transfer — so gas viscosity increases with temperature. This is opposite to everyday intuition built on liquids (which thin when heated), so it surprises many students on first encounter.
Question 4 True / False
Since liquid viscosity decreases with increasing temperature, a highly viscous liquid like glycerol is expected to have weaker intermolecular forces than a low-viscosity liquid like water.
TTrue
FFalse
Answer: False
High viscosity in liquids reflects strong or extensive intermolecular forces, not weak ones. Glycerol has three hydroxyl groups, enabling extensive hydrogen bonding across a large molecule, giving it viscosity roughly 1500 times that of water. The correct relationship is the opposite: stronger intermolecular forces → higher activation energy Eₐ for flow → higher viscosity at a given temperature. Temperature decreases viscosity in all liquids because thermal energy helps overcome these forces, but the starting level is set by the strength of those forces.
Question 5 Short Answer
Explain why Maxwell's prediction that gas viscosity is nearly independent of pressure seems counterintuitive, and provide a molecular-level explanation for why it is correct.
Think about your answer, then reveal below.
Model answer: It seems counterintuitive because higher pressure means more molecules per unit volume, and more molecules should mean more momentum transfer and therefore greater viscous drag. The error is forgetting that higher pressure also reduces mean free path: molecules collide more frequently and cannot travel as far between layers. In the kinetic theory expression η = ⅓ρ⟨c⟩λ, increasing pressure raises ρ but reduces λ by exactly the same factor, leaving their product — and therefore viscosity — unchanged. The result only breaks down at very high pressures (where molecular volume and interactions matter) or very low pressures (where the mean free path approaches the container size).
Maxwell's prediction was remarkable because it implied a testable consequence that ran against intuition: pumping more gas into a container should not change how hard it is to stir. His prediction was experimentally confirmed, and the result convinced many physicists of the value of kinetic theory. The practical consequence is important: lubricants in pressurized environments (engines, hydraulic systems) that are gas-phase need not be reformulated for pressure effects, whereas liquid lubricant viscosity is more weakly pressure-dependent but more strongly temperature-dependent — a key engineering consideration.