Q.With an increase in temperature, the viscosity of liquid and gas, respectively will

Imagine a thick, golden stream of honey being poured from a jar. It moves slowly, in a smooth, lazy ribbon. Now picture water from a tap — it rushes out, splashes, and flows freely. The difference you see is viscosity. It is the fluid's internal friction, its reluctance to let one layer slide past another. Honey has high viscosity; water has low viscosity.

At the microscopic level, a fluid is made of molecules that are constantly jostling and colliding. In a more viscous fluid, the molecules are either larger, more tangled, or have stronger attractive forces between them. When you try to make one layer of the fluid move relative to the layer next to it, these molecular interactions resist that motion. That resistance is what you feel as "thickness" or "stickiness."

Now, let's make this precise. Consider a fluid trapped between two large parallel plates, one stationary and one moving at a steady speed. The layer of fluid right next to the moving plate sticks to it and moves with the same speed. The layer next to the stationary plate stays at rest. In between, the speed of the fluid changes gradually from zero to the plate's speed. This is called a velocity gradient.

The force required to keep the top plate moving is the viscous force. Experiments show that this force $F$ is proportional to two things: the area $A$ of the plate in contact with the fluid, and the velocity gradient $\frac{dv}{dx}$ (how quickly the speed changes as you move perpendicular to the flow). The constant of proportionality is called the coefficient of viscosity, denoted by $\eta$ (eta).

Here, $F$ is the viscous force that opposes relative motion between adjacent fluid layers. $A$ is the area of contact between those layers. $\frac{dv}{dx}$ is the velocity gradient — the rate at which velocity changes with distance perpendicular to the flow. And $\eta$ is the viscosity of the fluid, a property that depends on the fluid itself and its temperature (heating a fluid usually lowers its viscosity). …