Question

liquid x is known to have a lower surface tension and lower viscosity than liquid y. use these facts to predict the result of each experiment in the table below, if you can.

experiment	predicted outcome
40.0 ml of liquid x are poured into a beaker, and 40.0 ml of liquid y are poured into an identical beaker. stirrers in each beaker are connected to motors, and the forces $f_x$ and $f_y$ needed to stir each liquid at a constant rate are measured.	$f_x$ will be greater than $f_y$ <br> $f_x$ will be less than $f_y$ <br> $f_x$ will be equal to $f_y$ <br> it’s impossible to predict whether $f_x$ or $f_y$ will be greater without more information.

Explanation:

First experiment

• Surface tension is the force per unit length that acts at the surface of a liquid. A liquid with higher surface tension will require a greater force to stretch its surface.
• Since Liquid \(X\) has a lower surface tension than Liquid \(Y\), the force \(F_X\) needed to make the loop (which is related to stretching the liquid - film surface) 5% wider will be less than \(F_Y\). Mathematically, if \(T=\frac{F}{L}\) (where \(T\) is surface - tension, \(F\) is the force and \(L\) is the length), for the same \(L\) (identical loops), \(F = T\times L\). Given \(T_X

Second experiment

• Viscosity is a measure of a fluid's resistance to flow. A liquid with lower viscosity offers less resistance to flow (stirring).
• The force required to stir a liquid at a constant rate is related to its viscosity. Using the formula \(F = \eta A\frac{dv}{dy}\) (where \(\eta\) is viscosity, \(A\) is the area, and \(\frac{dv}{dy}\) is the velocity gradient). For the same \(A\) and \(\frac{dv}{dy}\) (identical beakers and stirring rate), since \(\eta_X<\eta_Y\) (Liquid \(X\) has lower viscosity), \(F_X

Answer:

For the first experiment: \(F_X\) will be less than \(F_Y\).
For the second experiment: \(F_X\) will be less than \(F_Y\).