When water from an overturned glass spills on the floor, or when we blow a soap bubble, the surface of the liquid increases. In this case, new areas of the rarefied surface layer appear. The average distance between molecules increases as they move from the depth of the liquid to its surface. The forces of attraction between the molecules of the liquid do negative work. In accordance with the laws of mechanics, this means an increase in the potential energy of molecules that have passed from the depth of the liquid to the surface.
The molecules of the surface layer of a liquid have an excess of potential energy compared to the energy that these molecules would have if they were inside the liquid.
The excess potential energy possessed by molecules on the surface of a liquid is called surface energy.
From a macroscopic (thermodynamic) point of view, surface energy is one of the types internal energy, absent in gases, but present in liquids *.
* Surface energy is also possessed by solid bodies. After all, the special conditions in which molecules are located on the surface of a liquid are also characteristic of the surface of solids.
When water spreads from an overturned glass over the floor, an increase in the energy of the molecules of the surface layer occurs due to the work of gravity. And when a soap bubble is blown out, an increase in the potential energy of the molecules of the surface layer occurs due to the work of the air pressure forces in the bubble. After all, in order for the bubble to inflate, the air pressure in it must be greater than atmospheric pressure.
Surface tension
Molecules in all areas of the surface layer of the liquid are in the same conditions, and two areas of the same area have the same surface energy. It means that surface energy is directly proportional to the surface area of the liquid. Therefore, the ratio of surface energy U n section of the surface of the liquid to the area S of this section is a constant value, independent of the area S. This value is called the surface tension coefficient or simply surface tension and is denoted by the letter σ:
The surface tension is specific surface energy, i.e., the energy per unit surface area.
In SI, surface tension is expressed in joules per square meter(J / m 2). Since 1 J = 1 N m, surface tension can be expressed in newtons per meter (N/m).
The surface tension a depends on the nature of the adjacent media and on the temperature. As the temperature rises, the distinction between the liquid and its saturated vapor gradually disappears and disappears altogether at the critical temperature. Accordingly, the surface tension for the liquid-saturated vapor interface decreases with increasing temperature and becomes zero at the critical temperature.
From formula (7.3.1) it follows that
(7.3.2)
Therefore, as the surface area decreases, the surface energy decreases. In this case, molecular forces perform positive work, since the distances between molecules decrease as they pass from the surface layer into the depth of the liquid. In the equilibrium state of a liquid, the surface energy has minimum value. This corresponds to the minimum surface area for a given volume. Therefore, as discussed in § 7.1, a fluid assumes the shape of a sphere if there are no other forces that distort its natural spherical shape.
IN surface layer The energy stored in the liquid is directly proportional to the surface area. surface energy- one of the forms of internal energy.
Features of the liquid state of matter
Properties of liquids
As you know, a substance in a liquid state retains its volume, but takes the shape of the vessel in which it is located. The conservation of the volume of a liquid is explained by the presence of attractive forces between the molecules. These intermolecular forces hold the liquid molecule around its temporary equilibrium position for approximately s, after which it jumps to a new temporary equilibrium position approximately at a distance of its diameter. The time between two jumps of a molecule from one equilibrium position to another is called time of settled life. This time depends on the type of liquid and temperature. When heated, the average time of settled life decreases. Due to the possibility of fairly free movement of molecules relative to each other, liquids are fluid, so they do not have a constant shape, but take the form of a vessel.
If a very small volume is singled out in a liquid, then during the time of settled life, an ordered arrangement of molecules exists in it, as if the nucleus of a crystal lattice. Then this arrangement breaks up, but arises in another place. Therefore, it is customary to say that in a liquid there is short-range order in the arrangement of molecules, but missing distant order.
Liquids exhibit a range mechanical properties, bringing them closer to solids than to gases. These include elasticity (with short-term exposure), fragility (i.e., the ability to break), low compressibility. Another significant difference from gases: in gases, the kinetic energy of molecules is much greater than their potential energy, while in liquids, potential and kinetic energies are approximately equal.
On the surface of a liquid, near the boundary separating the liquid and its vapor, the interaction between liquid molecules differs from the interaction of molecules inside the volume of the liquid. To illustrate this statement, consider Fig. 20 . Molecule 1, surrounded on all sides by other molecules of the same liquid, experiences, on average, the same attraction to all its neighbors. The resultant of these forces is close to zero. Molecule 2 experiences less upward attraction from the vapor molecules and more downward attraction from the liquid molecules. As a result, the molecules located in the surface layer are affected by the downwardly directed resultant R forces, which is usually attributed to the unit area of the surface layer.
To transfer molecules from the depth of a liquid to its surface layer, it is necessary to do work to overcome the force R. This work is on the rise surface energy, i.e. excess potential energy possessed by molecules in the surface layer compared to their potential energy inside the rest of the liquid volume.
Let us denote the potential energy of one molecule in the surface layer, - the potential energy of the molecule in the liquid volume, – the number of molecules in the surface layer of the liquid. Then the surface energy is
Surface tension coefficient(or simply surface tension) of a liquid is called the change in surface energy with an isothermal increase in surface area by one unit:
where is the number of molecules per unit area of the liquid surface.
If the liquid surface is limited by the wetting perimeter, then the surface tension coefficient is numerically equal to strength, acting per unit length of the wetting perimeter and directed perpendicular to this perimeter:
where is the wetting perimeter length, – surface tension force acting on the length of the wetting perimeter. The surface tension force lies in a plane tangential to the surface of the liquid.
Reducing the surface area of a liquid reduces the surface energy. The condition for stable equilibrium of a liquid, like any body, is the minimum potential surface energy. This means that in the absence of external forces, the liquid should have the smallest surface area for a given volume. Such a surface is a spherical surface.
With an increase in the temperature of the liquid and its approach to the critical surface tension coefficient tends to zero. Far from the coefficient s decreases linearly with increasing temperature. To reduce the surface tension of a liquid, special impurities (surfactants) are added to it, which are located on the surface and reduce the surface energy. These include soap and other detergents, fatty acid and so on.
Topic: "Characteristics of the liquid state of matter"
Characteristics of the liquid state of matter
Liquid is a state of aggregation of a substance, intermediate between gaseous and liquid. The conservation of volume in a liquid proves that attractive forces act between its molecules, i.e. the distance between liquid molecules is less than the radius of molecular action.
If a sphere of molecular action is described around any liquid molecule, then inside this sphere there will be centers of many other molecules that will interact with this molecule. These interaction forces keep the liquid molecule near its temporary equilibrium position of approximately 10 -12 - 10 -10 , after which it jumps to a new temporary equilibrium position approximately the distance of its diameter.
Between the transitions, the liquid molecules oscillate about the temporary equilibrium position. The time between two transitions of a molecule from one equilibrium position to another is called settled life time(≈ 10 -11 s). This time depends on the type of liquid and temperature.
The higher the temperature of the liquid, the less time settled life. During the time of settled life, most molecules are held in their equilibrium positions, and only a few have time to move to a new equilibrium position during this time. For more long time already most of the liquid molecules have time to change their location.
If a small volume is isolated in a liquid, then during the time of settled life in it there is an ordered arrangement of molecules, similar to their arrangement in crystal lattice solid body. Then it breaks up and arises elsewhere.
Thus, the entire space occupied by the liquid, as it were, consists of many nuclei of crystals, which disintegrate in some places, but arise in others. This means that in a small volume of liquid, an ordered arrangement of molecules is observed, and in a large volume it turns out to be chaotic.
Those. in a liquid there is a short-range order in the arrangement of molecules and there is no long-range order. This type of fluid is called quasicrystalline(crystal-like).
Liquid properties:
1. elasticity(if the time of action of the force on the liquid is short). If the stick is hit sharply against the surface of the water, the stick may break or fly out of the hand, or the stone may bounce off the surface of the water.
2. fluidity(if the exposure time to the liquid is long) For example, the hand easily penetrates into the water.
3. fragility when a force is applied to a jet of water for a short time.
4. strength(slightly smaller than solids). The tensile strength of water is 2.5∙10 7 Pa.
5. compressibility very small. With an increase in pressure by 1 atm. the volume of water is reduced by 50 ppm.
6. cavitation- a sharp collapse of voids inside the liquid under intense impact on it, for example, during rotation propellers or the propagation of ultrasonic waves in a liquid. Cavitation causes rapid wear of propellers.
When a substance passes from solid state in liquid occurs less abrupt change properties than during the transition from liquid to gaseous.
Means, the properties of the liquid state of matter are closer to the properties of the solid state than to the properties of the gaseous state.
Surface liquid layer
Let us find out how the actions of molecular forces inside a liquid and on its surface differ. Average value of the resultant of molecular forces applied to a molecule M 1, which is inside the liquid, is close to zero.
The situation is different with molecules. M 2 And M 3 located in the surface layer of the liquid. Let us describe spheres of molecular action around the molecules with a radius r m(≈ 10 -9 m). Then for the molecule M 2 there will be a lot of molecules in the lower hemisphere (since there is a liquid below), and much less in the upper hemisphere (because there are vapor and air on top).
So for a molecule M 2 resultant of molecular forces of attraction in the lower hemisphere R F much more than the resultant of molecular forces in the upper hemisphere R P.
Force R P is small and can be neglected. The resultant of the molecular forces of attraction applied to the molecule M 3 less than for a molecule M 2, since it is determined only by the action of molecules in the shaded area. It is important that the resultants for the molecules M 2 And M 3 directed into the liquid perpendicular to its surface.
rice. 20
Thus, all molecules located in the surface layer with a thickness equal to the radius of molecular action (Fig. 20) are drawn into the liquid.
But the space inside the liquid is occupied by other molecules, so the surface layer creates pressure on the liquid, which is called molecular pressure . It is impossible to determine the molecular pressure empirically, because it acts not on a body immersed in a liquid, but on the liquid itself.
Theoretical calculations showed that the molecular pressure is high (for water it is equal to 11∙10 6 Pa, and for ether it is 1.4∙10 8 Pa). Now it is clear why it is difficult to compress a liquid. Indeed, for this it is necessary to create a pressure of the same order as the molecular pressure of the liquid itself. And this is very difficult.
DEFINITION
Surface tension- the desire of the liquid to reduce its free surface, i.e. reduce the excess of its potential energy at the interface with the gaseous phase.
Let's describe surface tension mechanism in liquids. Liquid, unlike gases, does not fill the entire volume of the vessel into which it is poured. An interface is formed between the liquid and the gas (or vapor), which is in special conditions compared to the rest of the mass of the liquid. Consider two molecules A and B. Molecule A is inside the liquid, molecule B is on its surface (Fig. 1). Molecule A is surrounded by other liquid molecules evenly, so the forces acting on molecule A from molecules falling into the sphere of intermolecular interaction are compensated, or, in other words, their resultant is zero. Molecule B is surrounded on one side by liquid molecules, and on the other side by gas molecules, the concentration of which is much lower than the concentration of liquid molecules. Since much more molecules act on the molecule B from the side of the liquid than from the side of the gas, the resultant of all intermolecular forces will no longer be zero and will be directed inside the volume of the liquid. Thus, in order for a molecule to get from the depth of the liquid to the surface layer, it is necessary to perform work against uncompensated intermolecular forces. And this means that the molecules of the near-surface layer, in comparison with the molecules inside the liquid, have an excess potential energy, which is called surface energy.
Obviously than more area surface of the liquid, the more such molecules that have excess potential energy, and hence the greater the surface energy. This fact can be written as the following relationship:
where is the surface energy of the liquid, the area of the free surface of the liquid and the coefficient of proportionality, which is called surface tension coefficient.
Surface tension coefficient
DEFINITION
Surface tension coefficient- This physical quantity, which characterizes the given liquid and is numerically equal to the ratio of the surface energy to the free surface area of the liquid:
The SI unit for the surface tension coefficient is .
The surface tension coefficient of a liquid depends: 1) on the nature of the liquid (for “volatile liquids such as ether, alcohol, gasoline, the surface tension coefficient is less than for “non-volatile liquids - water, mercury); 2) on the temperature of the liquid (the higher the temperature, the lower the surface tension); 3) on the properties of the gas that borders on the given liquid; 4) from the presence of surfactants such as soap or washing powder, which reduce surface tension. It should also be noted that the surface tension coefficient does not depend on the area of the free surface of the liquid.
It is known from mechanics that the equilibrium states of a system correspond to the minimum value of its potential energy. Due to surface tension, a liquid always assumes a shape with a minimum surface area. If no other forces act on the liquid or their action is small, the liquid will tend to take the form of a sphere, such as a drop of water, soap bubble. Water will also behave in zero gravity. The fluid behaves as if forces are acting tangentially to its surface, reducing (contracting) this surface. These forces are called surface tension forces.
That's why surface tension coefficient can also be defined as the modulus of the surface tension force acting per unit length of the contour that bounds the free surface of the liquid:
The presence of surface tension forces makes the liquid surface look like an elastic stretched film, with the only difference that the elastic forces in the film depend on its surface area (i.e., on how the film is deformed), and the surface tension forces do not depend on the surface area of the liquid. If you put a sewing needle on the surface of the water, the surface will bend and prevent it from sinking. The action of surface tension forces can explain the sliding of light insects, such as water striders, on the surface of water bodies (Fig. 2). The foot of the water strider deforms the water surface, thereby increasing its area. As a result, a surface tension force arises, which tends to reduce such a change in area. The resultant force of surface tension will be directed upwards, compensating for the force of gravity.
The principle of operation of a pipette is based on the action of surface tension forces (Fig. 3). The droplet, on which the force of gravity acts, is pulled down, thereby increasing its surface area. Naturally, surface tension forces arise, the resultant of which is opposite to the direction of gravity, and which do not allow the droplet to stretch. When the rubber cap of the pipette is pressed, additional pressure is created, which assists the force of gravity, causing the drop to fall down.
Examples of problem solving
EXAMPLE 1
| Exercise | A thin aluminum ring with a radius of 7.8 cm is in contact with the soap solution. With what force can the ring be torn off the solution? Consider the temperature of the solution as room temperature. Ring weight 7 g. |
| Solution | Let's do the drawing. The following forces act on the ring: gravity, surface tension and external force. Since the ring is in contact with the solution and the outer and inner sides, then the surface tension force is: The length of the contour that bounds the surface of the liquid in this case equal to the circumference of the ring: Taking into account last strength surface tension: The condition for detachment of the ring from the surface of the solution has the form: From the tables, the surface tension coefficient of the soap solution at room temperature. Acceleration of gravity Let's convert the units to the SI system: the radius of the ring is the mass of the ring kg. Let's calculate: |
| Answer | In order to tear the ring from the solution. it is necessary to apply a force of 0.11 N. |
EXAMPLE 2
| Exercise | How much energy is released when small water droplets with a radius of mm merge into one drop with a radius of 2 mm? |
| Solution | The change in the potential energy of the surface layer of drops, due to a decrease in the surface area of the drops when they merge into one drop, is equal to: Where the surface area of all small droplets, the surface area of a large droplet, the coefficient of surface tension of water. It's obvious that: where r is the radius of a small drop, R is the radius of a large drop, and n is the number of small drops. Mass of a small drop:
mass of a large drop:
Since small drops merge into one large drop, we can write:
whence the number of small drops: and the surface area of all small droplets:
Now let's find the amount of energy that is released when the drops merge: From the tables, the coefficient of surface tension of water. Let's convert the units to the SI system: the radius of a small drop is the radius of a large drop. Let's calculate: |
| Answer | When the drops merge, energy J is released. |
EXAMPLE 3
| Exercise | Determine the coefficient of surface tension of the oil, the density of which is equal to, if 304 drops are obtained by passing the oil through a pipette. Pipette neck diameter 1.2 mm. |
| Solution | A drop of oil comes off the pipette when the force of gravity is equal to the force of surface tension: |
Since the molecules of a liquid that are in its surface layer are drawn into the liquid, their potential energy is greater than that of the molecules inside the liquid. This conclusion can also be reached if we recall that the potential energy of the interaction of molecules is negative (§ 2.4), and take into account that the molecules in the surface layer of the liquid in Fig. 10.1) interact with fewer molecules than the molecules inside the liquid
This additional potential energy of the molecules of the surface layer of the liquid is called free energy; due to it, the work associated with a decrease in the free surface of the liquid can be performed. On the contrary, in order to bring the molecules inside the liquid to its surface, it is necessary to overcome the opposition of molecular forces, i.e., to perform the work that is needed to increase the free energy of the surface layer of the liquid. It is easy to see that in this case the change in free energy is directly proportional to the change in the area of the free surface of the liquid
Since we have
So, the work of molecular forces A with a decrease in the area of the free surface of the liquid is straight. proportional But this work must also depend on the type of fluid and external conditions e.g. on temperature. This dependence is expressed by the coefficient .
The value a, which characterizes the dependence of the work of molecular forces when the area of the free surface of the liquid changes on the type of liquid and external conditions, is called the coefficient of surface tension of the liquid (or simply surface tension), and is measured by the work of molecular forces with a decrease in the area of the free surface of the liquid by unit:
Let's derive the unit of surface tension in SI:
In SI, the unit a is taken to be such a surface tension at which molecular forces do work of 1 J, reducing the area of the free surface of the liquid by .
Since any system spontaneously passes into a state in which its potential energy is minimal, the liquid must spontaneously pass into a state in which its free surface area has the smallest value. This can be shown using the following experiment.
On a wire bent in the form of the letter P, a movable cross member I is strengthened (Fig. 10.2). The frame obtained in this way is tightened with a soap film, lowering the frame into a soapy solution. After removing the frame from the solution, the crossbar I moves upward, i.e., molecular forces actually reduce the area of the free surface of the liquid. (Think about where the released energy goes.)
Since a ball has the smallest surface area for the same volume, the liquid in a state of weightlessness takes the form of a ball. For the same reason, small drops of liquid are spherical in shape. The shape of the soap films on different frames always corresponds smallest area free surface of the liquid.
