Question

Surface tension of liquid is $70 dynes/cm$. Its value in SI units is:
A. $70N/m$
B. $7 \times 10^{-2}N/m$
C. $7 \times 10^{2}N/m$
D. $7\times 10^{3}N/m$

Answer 1

Hint: Surface tension is the tendency of liquids to occupy minimum surface area. This occurs at the liquid- air interface. It can be expressed in different forms like $\gamma=\dfrac{dyn}{cm}=\dfrac{erg}{cm^{2}}=\dfrac{10^{-3}N}{m}=\dfrac{10^{-3}J}{m^{2}}$.Here we should convert the CGS units of surface tension to SI units.

Complete step-by-step solution:
Surface tension is the tendency of liquids to occupy the minimum surface area. It is defined as the force acting per unit length of the liquid. It can also be defined as the energy needed by the liquid to reduce its surface area. This is observed at the liquid-air interface of the liquid, where the force of attraction among the liquid molecules, is greater than that of the liquid-air force. At the surface of the liquid, there are two forces, one is the liquid-liquid interaction which draws the liquid molecule inwards, and the other is the tangential force parallel to the liquid surface. This is responsible for the spherical shape of drops and meniscus formation of liquids when filled in tubes. These are also responsible for the separation of oil and water in the oil-water mixtures.
Surface tension has dimensions of force per unit length or energy per unit area. Surface tension is denoted by $\gamma$ with SI units $N/m$ and CGS units of $dyn/cm$.
We know that $1dyne=10^{-5}N$ and $1cm=10^{-2}m$
Given that $S=70\dfrac{dynes}{cm}=\dfrac{70\times 10^{-5}N}{10^{-2}m}=70\times 10^{-3}N/m =7\times 10^{-2}N/m$

Note: Surface tension is expressed in different forms and units. It is due to unbalanced forces acting on the molecules. Remember that surface tension can be reduced by adding surfactants. It is suggested to remember that, for easy calculations.