Question

The coefficient of viscosity for hot air is:
A. greater than the coefficient of viscosity for cold air
B. smaller than the coefficient of viscosity for cold air
C. same as the coefficient of viscosity of cold air
D. increases or decreases depending on the external pressure.

Answer 1

Hint: We know that a viscous force is the force which opposes the movement of a body in the fluid. The property of a fluid to oppose the motion of the body through it is called the viscosity of the body. We can answer this using the definition of coefficient of viscosity.

Formula used: $f=\eta A{\displaystyle \frac{dV}{dx}}$

Complete step by step answer:
We know that viscous force is given as $f=\eta A{\displaystyle \frac{dV}{dx}}$
Where, $\eta$ is the coefficient of viscosity of area $A$ and ${\displaystyle \frac{dV}{dx}}$ is the velocity gradient
Assuming that, some constant number of moles of gases is kept in a container. If the temperature is increased, then we know that the gases move in random motion, then the velocity gradient of the gases increase. Thus the viscous force and the coefficient of viscosity increase.
Similarly, if the temperature is decreased, then we know that the gases move in random motion, then the velocity gradient of the gases decrease. Thus the viscous force and the coefficient of viscosity decrease.
Thus we can say that the coefficient of viscosity for hot air is greater than that of the cold air, due to the random motion of the gases.

So, the correct answer is “Option A”.

Note: Clearly, the viscous force can also be called the fluid friction, as it resists the motion of the body in a fluid. It was observed that more the molecules per unit area, less is the coefficient of viscosity. Which is to say that, if the medium is denser than the movement of the body in that fluid is slower.