So far, we have considered the first law of thermodynamics in relation to gases. A distinctive feature of gas is that its volume can change significantly. Therefore, according to the first law of thermodynamics transmitted by gas, the amount of heat q is equal to the amount of the perfect gas of work and changes in its internal energy:

Q \u003d ΔU + A

In this paragraph, we will consider cases when a certain amount of heat reports fluid or solid. When heated or cooling, they change slightly in volume, therefore, the work performed by them is usually neglected. Consequently, for liquids and solids, the first law of thermodynamics can be written as

The simplicity of this equation, however, is deceptive.

The fact is that the internal energy of the body is only the total kinetic energy of the chaotic movement of the components of its particles only when the body is perfect gas. In this case, as we already know, the internal energy is directly proportional to the absolute temperature (§ 42). In liquids, the potential energy of the interaction of particles plays a large role in liquids and in solid bodies. And she, as experience shows, can change even at a constant temperature!

For example, if we transmit some warmth of the mixture of water with ice, then its temperature will remain constant (equal to 0 ºС), until all the ice is melted. (It is for this reason that the temperature of ice melting and accepted at one time as a reference point when determining the Celsius scale.) In this case, the resulting heat is consumed to increase the potential energy of the interaction of molecules: to turn the crystal into a liquid, it is necessary to spend energy to destroy the crystal lattice.

A similar phenomenon occurs when boiling: if we transmit a certain amount of water with water at a boiling point, its temperature will remain constant (equal to 100 ºС at normal atmospheric pressure) until all the water is popped up. (Therefore, it was chosen as a second reference point for Celsius scale.) In this case, the resulting heat is also spent on an increase in the potential energy of the interaction of molecules.

It may seem strange that the potential energy of the interaction of molecules in a pair is greater than in water. After all, gas molecules almost do not interact with each other, so the potential energy of their interaction is naturally taken for zero level. So come. But then the potential energy of the interaction of molecules in the liquid should be considered negative.

Such a sign of potential interaction energy is characteristic of attractive bodies. In this case, to increase the distance between the bodies, you need to work, that is, increase the potential energy of their interaction. And if after that it becomes equal to zero, it means that it was negative before that.

So, the change in the state of liquids and solids when they communicate with a certain amount of heat should be considered, taking into account the possibility of changing their aggregate state. Changes in the aggregate state are called phase transitions. This is the conversion of a solid body into a liquid (melting), a liquid into a solid body (hardening or crystallization), liquids in pairs (vaporization) and steam into liquid (condensation).

The law of conservation of energy in thermal phenomena taking place with liquids and solid bodies is called the heat balance equation.
Consider the thermal balance equation first for the case when heat exchange occurs between two bodies, and their heat exchange with other bodies can be neglected (calorimeters are used for creating such conditions - vessels that provide thermal insulation of their contents).

We will assume (as we thought earlier for gases) the amount of heat transmitted by the body is positive, if, due to this, the internal energy of the body increases, and negative if the internal energy decreases. In this case, the thermal balance equation has the form

Q 1 + Q 2 \u003d 0, (1)

where Q 1 is the amount of heat transmitted by the first body from the second side, and Q 2 is the amount of heat transmitted by the second body from the first side.

From equation (1) it can be seen that if one body gets warm, then another body gives it. Let's say if Q 1\u003e 0, then Q 2< 0.

If the heat exchange occurs between N bodies, the thermal balance equation has the form

Q 1 + Q 2 + ... + Q n \u003d 0.

2. The thermal balance equation without phase transitions

We will consider a homogeneous body, that is, consisting entirely of a substance (for example, some mass of water, steel or copper bar, etc.). Consider first the case when the aggregate state of the body does not change, that is, the phase transition does not occur.

From the course of the main school physicists, you know that in this case the amount of heat transmitted by the body is directly proportional to the mass of the body M and the change in its temperature ΔT:

In this formula, both q and Δt can be both positive and negative values.

Incoming into this formula, the value of C is called the specific heat capacity of the substance from which the body consists. Usually, the temperature of the Celsius scale is used in the challenges of the heat balance. We will also do that too.

1. Figure 48.1 shows the dependence of the temperature of the two bodies from the amount of heat transferred to them. Q. Mass of each body 100 g.

A) Which body is the specific heat capacity and how many times?
b) What is the specific heat capacity of each body?

2. In a calorimeter containing 150 g of water at a temperature of 20 ºС, a metal cylinder is immersed from boiling water. The specific heat capacity of water is 4.2 kJ / (kg * k). Please accept that thermal losses can be neglected.
a) Explain why the equation is true

c m m m (t - 100º) + C in m in (t to - 20º) \u003d 0,

where C m and C B is the values \u200b\u200bof the heat capacity of this metal and water, respectively, m M and M B - the values \u200b\u200bof the mass of the cylinder and water, respectively, T K is the value of the final temperature of the content of the calorimeter, when thermal equilibrium is established.

b) Which of the two components in the above formula is positive, and what - Negative? Explain your answer.
c) What is equal to the specific heat capacity of this metal, if the mass of the cylinder is 100 g, and the final temperature is 25 ºС?
D) What is the finite temperature, if the cylinder is made of aluminum, and its mass is 100 g? The specific heating capacity of aluminum is 0.92 kJ / (kg * k).
e) What is the cylinder mass, if it is made of copper and its end temperature 27 ºС? Specific heat capacity 0.4 kJ / (kg * k).

Consider the case when the mechanical energy goes into the inner. The English physicist J. Joble tried to measure how much water heats up in a waterfall when hitting the Earth.

3. From what height should the water fall so that when it is hitting the ground, its temperature rose by 1 ºС? Please accept in the internal energy of water, half of its potential energy passes.

The answer you received will explain why the scientist has suffered a failure. Take into account that the experiments the scientist put in his homeland, where the height of the highest waterfall is about 100 m.

If the body is heated using an electric heater or burning fuel, it is necessary to consider the efficiency of the heater. For example, if the coefficient of the heater is 60%, this means that an increase in the internal energy of the heated body is 60% of the heat released during the combustion of the fuel or when the electric heater is operated.

We also remind that when combustion of fuel, M mass is distinguished by the amount of heat q, which is expressed by the formula

where q is the specific heat of combustion.

4. To bring 3 liters of water in the bowler from a temperature of 20 ºС to a boil, tourists had to burn 3 kg of dry twig in the fire. What is the coefficient of the useful effect of the fire as a heating device? The specific heat of the combustion of the twigs. Take an equal to 107 J / kg.

5. With the help of an electric heater, it is trying to boil 10 liters of water, but water does not boil: with the heater turned on, its temperature remains constant, below 100 ºС. The power of the heater is 500 W, the efficiency of 90%.
a) What amount of heat is transmitted for 1 with water from the heater?
b) What amount of heat is transmitted for 1 ° C from water to the surrounding air when the heater is turned on when the water temperature remains constant?
c) How much heat will transmit water for 1 min around the ambient air immediately after turning off the heater? Consider that during this time the water temperature will not change significantly.
d) how much water temperature drops for 1 minute immediately after turning off the heater?

3. The thermal balance equation in the presence of phase transitions

Recall some facts known for you from the course of physics of the main school.

In order to completely melt a crystalline solid at its melting point, it is necessary to inform it the amount of heat Q, proportional mass M of the body:

The proportionality coefficient λ is called the specific heat of melting. It is numerically equal to the amount of heat that must be informant to the crystalline body weighing 1 kg at a melting point to completely turn it into a liquid. The unit of specific heat melting is 1 J / kg (joule per kilogram).

For example, the specific ice melting heat is 330 kJ / kg.

6. What height could be lifted by a person weighing 60 kg, if it increases its potential energy by magnitude, numerically equal to the amount of heat that is needed in order to melt 1 kg of ice at a temperature of 0 ºС?

When solving problems, it is important to take into account that the solid will start melting only after it all heats up to the melting point. On the graph of the temperature of the body temperature from the amount of heat transmitted to it, the melting process is a horizontal segment.

7. Figure 48.2 shows a graph of the body temperature dependence weighing 1 kg from the amount of heat transmitted.


a) What is the specific heat capacity of the body in a solid state?
b) What is the melting point?
c) What is the specific heat of melting?
d) What is the specific heat capacity of the body in a liquid state?
e) What kind of substance can this body consist of?

8. Iron meteorite flies into the atmosphere of the Earth. The specific iron heat capacity is 460 J / (kg * k), the melting point is 1540 ºС, the specific heat of melting 270 kJ / kg. The initial temperature of the meteorite before entering the atmosphere, take equal to -260 ºС. Please accept the 80% of the kinetic energy of the meteorite when moving through the atmosphere proceeds to its internal energy.
a) What should be the minimum starting speed of the meteorite, so that it is heated to the melting point?
b) What part of the meteorite melts if its initial speed is 1.6 km / s?

If, in the presence of phase transitions, it is necessary to find a koyful temperature of bodies, then first of all it is necessary to find out what the final state will be. For example, if in the initial state, the mass of ice and water and their temperatures are given, that is, three possibilities.

In the ultimately, only ice (this may be if the initial ice temperature was low enough or the mass of ice was large enough). In this case, the unknown value is the final ice temperature. If the task is solved correctly, the value obtained does not exceed 0 ºС. When the thermal equilibrium is established, the ice is heated to this finite temperature, and all the water is cooled to 0 ºС, then freezes, and the ice formed from it is cooled to the final temperature (if it is below 0 ºС).

In the ultimately, there are ice and water in thermal equilibrium. This is possible only at a temperature of 0 ºС. An unknown value in this case will be the final mass of the ice (or the final mass of water: the amount of mass of water and ice is given). If the task is solved correctly, then the finite masses of ice and water are positive. In this case, when the thermal equilibrium is determined, the ice is heated to 0 ºС, and the water is cooled to 0 ºС. Then either part of ice melts, or part of the water freezes.

In the ultimately water only. Then the unknown value is its temperature (it should be not lower than 0 ºС), in this case the water is cooled to the final temperature, and the ice has to go through a more complex path: first it is heated to 0 ºС, then the whole melts, and then formed from it Water heats up to the final temperature.

To determine which of these features is implemented in a particular task, it is necessary to carry out a small study.

9. In a calorimeter containing 1.5 liters of water at a temperature of 20 ºС, a piece of ice is placed at a temperature of -10 ºС. Please accept that thermal losses can be neglected. Specific heat capacity 2.1 kJ / (kg * k).
a) What could be the mass of ice, if only ice is in the ultimate condition in the calorimeter? Only water? ice and water in thermal equilibrium?
b) What is the ultimate temperature, if the initial mass of ice is 40 kg?
c) What is the final temperature, if the initial mass of ice 200 g?
d) What is the ultimate mass of water, if the initial mass of the ice is 1 kg?

The fact that for melting the body must be reported by a certain amount of warmth, it seems natural. This phenomenon serves us a good service: it slows down the melting of snow, reducing floods in the spring.

But the fact that when crystallization, the body gives some of the heat, maybe surprise: Does water really give a certain amount of warmth during freezing? Nevertheless, it is: freezing and turning into ice, water gives pretty a large number of Warm cold air or ice, the temperature of which is below 0 ºС. This phenomenon also serves to us a good service, softening the first frosts and the offensive of winter.
We will now take into account the possibility of converting fluid into pairs or steam into a liquid.

As you know from the course of physics of the main school, the amount of heat q required to turn the fluid into steam at a constant temperature is proportional to the mass M of the liquid:

The coefficient of proportionality l is called the specific heat of the vaporization. It is numerically equal to the amount of heat that must be reported to 1 kg of fluid to completely turn it into steam. The unit of specific heat of the vaporization is 1 J / kg.

For example, the specific heat of the water vaporization at boiling point and the normal atmospheric pressure of the air is about 2300 kJ / kg.

10. In the calorimeter in which 1 l of water is located at a temperature of 20 ºС, 100 g of water vapor is introduced at a temperature of 100 ºС. What will be the temperature in the calorimeter after the establishment of thermal equilibrium? Thermal loss can be neglected.

Additional questions and tasks

11. To heat on the plate some mass of water from 20 ºС to the boiling point, it took 6 minutes. How much time will you need all this water to throw out? Please accept that heat loss can be neglected.

12. In the calorimeter containing ice weighing 100 g at a temperature of 0 ºС, steam is admitted at a temperature of 100 ºС. What will be the mass of water in the calorimeter, when all the ice melts and the water temperature will be equal to 0 ºС?

13. Heated aluminum cube was put on a flat layer, the temperature of which is 0 ºС. What temperature was the heated cube, if he completely plunged into the ice? Please accept that heat loss can be neglected. Specific heat capacity of aluminum 0.92 kJ / (kg * k).

14. The lead bullet hits the steel plate and bounces off it. The temperature of the bullet to the blow is 50 ºС, the speed is 400 m / s. The speed of the bullet after the strike is 100 m / s. What part of the bullet melted if 60% of the lost kinetic energy was translated into the internal energy of the bullet? Specific heat capacity 0.13 kJ / (kg * k), melting point 327 ºС, Specific melting heat 25 kJ / kg.

15. In the calorimeter, which contains 1 l of water at a temperature of 20 ºС, is put 100 g of wet snow, the water content in which (by weight) is 60%. What temperature will be installed in the calorimeter after establishing thermal equilibrium? Thermal loss can be neglected.
Prompt. Under wet snow, a mixture of water and ice is meant at a temperature of 0 ºС.

Solving challenges on boiling and condensation is largely similar to solving melting and hardening tasks. This helps the formation of students with the appropriate concepts and practical skills. At the same time, with an insufficiently durable and deep assimilation of the material, when the characteristic and specific features of each of these processes are not emphasized, such as evaporation and boiling, there is also unwanted "interference" of similar skills, mixing or erroneous identification by students of similar concepts.

This teacher should pay serious attention. One of the means to eliminate this disadvantage is the solution when reducing the combined tasks, in which all studied aggregate transformations of the substance are considered (No. 222, 223).

Most tasks are high-quality or uncomplicated calculated, in which it is required to determine, for example,

the amount of heat required to transform into steam when the liquid is boiling.

The most difficult task is to calculate the specific heat of the vaporization. This task should be solved in the class with the help of a teacher. To facilitate the calculations, the condition can not include the calorimeter data.

217. Graphics of heating and boiling water, alcohol and ether (Fig. 32). Determine which graphs are built for each of these liquids.

218. What has larger internal energy: water or steam taken in equal amounts when checking your conclusions on experience.

Decision. In order to turn water into a pair, she needs to report some amount of heat. Consequently, the internal energy of steam is greater. To check, skip into a glass with water from a boiler for a certain amount of steam, we note a new level of water and changing its temperature. In another glass, with the same initial amount of water, Nallem so much boiling water as it was condensed from steam. The water temperature will change in the second case significantly less than in the first one.

219. What amount of energy is required to appeal to steam at boiling point and normal water pressure? alcohol? Ether? How much energy will be required to circulate liquids in pairs, if they are pre-heated to boiling from

Decision. Taking advantage of the table of specific heat of the vaporization, the first part of the task the students first should solve orally, arguing as follows. To appeal to couples

waters at boiling point is required consequely, to appeal to steam water, it is necessary to spend 10 times more energy, similarly find the amount of heat for alcohol and ether. Then use the formula

The second part of the problem is solved as follows. Total amount of energy consumed

Similarly, the total amount of heat required to circulate alcohol and ether.

When solving the problem, you need to pay special attention to the skills of students to use the tables and understanding the physical meaning of the quantities given in them.

220. Pour into the water test tube and measure its temperature. Heat the test tube, noticing the time, first to boil, and then before turning all the water in steam. According to experience, determine approximately the value of the specific heat of the vaporization, compare it with the tabular and specify the reasons that reduce the accuracy of the result.

Decision. In one of the experiments, the following data were obtained. The initial temperature of heating time to a boil - 2.5 min, boiling time - 20 min.

Heat, which went to heat the heat of heat required for the vaporization

Considering the amount of heat given by the heater proportional to the heating time, we obtain:

The accuracy of the result reduced a number of factors: hot water gives more heat to the environment than cold, therefore the amount of warmth obtained heat is not strictly proportional to time. When little water remains in the test tube, a large amount of heat goes to heating air and the test tube itself.

221. Performing laboratory work, in a calorimeter, containing water with a student invested at 100 ° C. As a result, the temperature of the water rose to what the value of the specific heat of the vaporization will result in the data of this experience, if the water mass increased by

The task should be solved on the board with questions, writing formulas:

If the students learned well these formulas, then there is no need to rewrite them in relation to each specific case: it is possible to immediately substitute the numerical values \u200b\u200bof the values \u200b\u200bin the formula. This remark is true for high grades, since the solution of calorimetric equations in general is often too bulky.

1. What amount of warmth gave steam during condensation?

2. What amount of warmth gave the water formed from steam when cooled?

3. What amount of heat got water?

Since the amount of heat, given by steam and obtained during condensation with water, is equal to the amount of heat obtained by water in the calorimeter, then you can write:

222. What amount of heat is necessary to appeal to ice pairs taken to build an approximate process schedule.

223. What amount of heat is allocated during condensation 200 g of steam taken with and then converting water into ice? Build an approximate process graph.

The same substance in the real world, depending on the surrounding conditions, can be in different states. For example, water can be in the form of a liquid, in the idea of \u200b\u200ba solid - ice, in the form of gas - water vapor.

• These states are called the aggregate states of the substance.

Molecules of matter in various aggregate states are no different from each other. A specific aggregate state is determined by the location of molecules, as well as the nature of their movement and interaction between themselves.

Gas - the distance between molecules is significantly larger than the sizes of the molecules themselves. Molecules in the liquid and in the solid body are located close enough to each other. In solids even closer.

To change the aggregate state of the body, He needs to inform some energy. For example, in order to translate water into a pair of it, it is necessary to heat it. The pairs have become water again, it must give energy.

The transition from a solid state into liquid

The transition of a substance from a solid state into liquid is called melting. In order for the body to start melting, it must be heated to a certain temperature. Temperature at which the substance melts, called the melting point of the substance.

Each substance has its melting point. Some bodies are very low, for example, at ice. And in some boding the melting point is very high, for example, iron. In general, melting crystal body is a complex process.

Ice melting schedule

The figure below shows a graph of melting a crystalline body, in this case of ice.

• The graph shows the dependence of the ice temperature from time that heats it. At the vertically axis, the temperature was postponed, horizontal - time.

From the graph that initially the ice temperature was -20 degrees. Then he began to heal. Temperature began to grow. Plot AV is a plot of ice heating. Over time, the temperature has increased to 0 degrees. This temperature is considered to be the melting point of ice. At this temperature, the ice began to melt, but at the same time it ceased to increase its temperature, although the ice also continued to heat up. The melting area corresponds to the Sun section on the chart.

Then, when all the ice was melted and turned into a liquid, the water temperature began to increase again. This is shown on the graph of the beam of C. That is, we conclude that during melting the body temperature does not change, all incoming energy goes to melting.

a decrease in temperature will resume, but only cooling will already be the resulting solid body (section F G).

As experience shows, when crystallization in the EF section, exactly the same amount of heat q \u003d m is distinguished, which was absorbed when melting on the BC plot.

10.5 Various and condensation

Variousness is a liquid transition to a gaseous state (in pairs). There are two ways to vaporization: evaporation and boiling.

The evaporation is called vaporization, which occurs at any temperature from the free surface of the fluid. How do you remember from a sheet of постания couples, the cause of evaporation is the departure of the fluid of the fastest molecules that are able to overcome the forces of the intermolecular attraction. These molecules form steam above the surface of the liquid.

Different fluids evaporate with different speeds: the greater the force of attraction of molecules to each other, the smaller number of molecules per unit of time will be able to overcome them and fly outward, and the less the speed of evaporation. Ether, acetone, alcohol evaporates quickly (they are sometimes called volatile fluids), slower water, much slower water is evaporated and mercury.

The evaporation rate is growing with an increase in temperature (in the heat of linen he dries rather), since the average kinetic energy of the fluid molecules is increasing, and thus the number of fast molecules that can leave its limits increases.

The evaporation rate depends on the surface area of \u200b\u200bthe liquid: the greater the area, the greater the number of molecules get access to the surface, and evaporation is faster (which is why it is carefully straightened by linen).

Simultaneously with evaporation, the reverse process is observed: steam molecules, making a messy movement above the surface of the liquid, partially returned back into the liquid. Transformation of steam into liquid is called condensation.

Condensation slows down the evaporation of the fluid. So, in dry air linen dries faster than in the wet. It will dry faster in the wind: steam is demolished by the wind, and evaporation goes more intensively.

In some situations, the condensation speed may be equal to evaporation rate. Then both processes compensate each other and there is a dynamic balance: from a tightly closed bottle, the liquid does not disappear for years, and the saturated pair is in the surface of the liquid.

Condensation of water vapor in the atmosphere we constantly observe the clouds, rain and falling in the mornings of dew; It is evaporation and condensation that provide a cycle of water in nature, supporting life on Earth.

Since evaporation is a loaf of the fluid of the fastest molecules, in the process of evaporation, the average kinetic energy of the fluid molecules is reduced, i.e. the liquid cools. You are well familiar with the feeling of coolness and sometimes even zyability (especially in the wind), when you leave the water: water, evaporating all over the entire surface of the body, takes heat, the wind accelerates the evaporation process19.

The same coolness can be felt if you spend on hand a piece of cotton wool moistened in a fly solvent (let's say, in acetone or liquid for removing varnish). To the forty-portus heat, thanks to the enhanced evaporation of moisture through the pores of our body, we preserve our temperature at the level of normal; Do not be this thermostatic mechanism, in such a heat

19 Now it is clear why we blow on hot tea. By the way, it is even better to pull the air into my senses, because the dry surrounding air comes to the surface of the tea, and not wet air out of our lungs ;-)

we would simply died.

On the contrary, in the condensation process, the liquid heats up: steam molecules when returning to the liquid, they are accepted by attracting the fluid molecules near the nearby, as a result of which the average kinetic energy of the fluid molecules increases (compare this phenomenon with the release of energy during melt crystallization!).

10.6 boiling

The boiling process of water is well acquainted. Unlike evaporation, which occurs only from the free surface of the fluid, boiling is a vaporization that occurs throughout the volume of the fluid.

Boiling turns out to be possible because the liquid always dissolved some amount of air that has happened there as a result of diffusion. When the fluid is heated, this air expands, air bubbles gradually increase in size and become visible to the naked eye (in a water saucepan, they are precipitated the bottom and walls). Inside air bubbles there is a saturated pair, the pressure of which, as you remember, is growing rapidly with increasing temperature.

The larger the bubbles become, the time the Archimedean's force acts on them, and a certain moment begins a gap and the flood of bubbles. Lifting up, bubbles fall into less heated layers of fluid; Couples are condensed in them, and bubbles are compressed again. The collapse of bubbles causes the noise to us preceding the boiling of the kettle. Finally, over time, the entire liquid is evenly warming up, the bubbles reach the surface and burst, throwing out the air and steam noise is replaced by boulder, fluid boils.

The bubbles, thus, serve as a pair of conductors from inside a liquid onto its surface. When boiling, along with conventional evaporation, there is a conversion of fluid into pairs all over the volume by evaporation inside air bubbles, followed by a pair output. That is why the boiling liquid will fly very quickly: a kettle, from which water would evaporate a lot of days, will pop up for half an hour.

In contrast to evaporation occurring at any temperature, the liquid begins to boil only when the boiling point is reached, precisely the temperature at which air bubbles turn out to be able to pop up and get to the surface. At boiling point, the pressure of the saturated pair becomes equal to the external pressure on the liquid (in particular, atmospheric pressure). Accordingly, the more external pressure, the boiling will begin at a higher temperature.

Under normal atmospheric pressure (1 atm or 105 pa) water boiling point is equal to

100 C. Therefore, the pressure of a saturated water vapor at a temperature of 100 c is 105 Pa. This fact needs to be known to solve problems often it is considered to be known by default.

At the top of Elbrus, the atmospheric pressure is 0.5 atm, and the water is boiled there at a temperature of 82 C. And under the pressure of 15 atm, the water will begin to boil only at 200 C.

The boiling point (at normal atmospheric pressure) is strictly defined for this fluid value 20. So, the alcohol is boiling at 78 C, the ether at 35 c, mercury at 357 C. Please note: the more volatile is fluid, the lower its boiling point. In the boiling point table, we also see that oxygen boils at 183 C. So, at ordinary oxygen temperatures, this gas!

20 boiling points in tables of textbooks and reference books are boiling temperatures of chemical fluids. The presence of impurities in the fluid can change the boiling point. Say, tap water contains dissolved chlorine and some salts, so its boiling point at normal atmospheric pressure may differ slightly from 100 C.

We know that if you remove the kettle from the fire, the boiling process will immediately cease the boiling process requires continuous heat supply. At the same time, the temperature of the water in the kettle after the boil is stopped changing, all the time remains equal to 100 C. Where is the resulting heat?

The situation is similar to the melting process: heat goes to an increase in the potential energy of molecules. In this case, to perform work on the removal of molecules at such distances, that the attraction forces will not be able to hold the molecules near each other, and the liquid will switch to the gaseous state.

10.7 Kipping schedule

Consider a graphical representation of the fluid heating process the so-called boiling schedule (Fig. 24).

Temperature
t kip
Fig. 24. Chart of Boil

Plot AB precedes the start of boiling. In the BC section, fluid boils, its mass decreases. At the point C, the liquid rolls completely.

In order to completely pass the site BC, i.e. so that the liquid has already brought to the boiling point, to completely turn into pairs, to this liquid you need to supply a certain amount of heat of Qar. Experience shows that this amount of heat is directly proportional to the mass of the liquid:

Qar \u003d lm:

The coefficient of proportionality L is called the specific heat of the vaporization of the liquid (at boiling point). The specific heat of the vaporization is numerically equal to the amount of heat that needs to be brought to 1 kg of liquid taken at the boiling point to completely turn it into pairs.

So, at 100 c, the specific heat of water vaporization is 2300 kJ / kg. It is interesting to compare it with the specific warmth of melting ice (340 kJ / kg) the specific heat of the vaporization almost seven times more! This is not surprising: because for melting ice you only need to destroy the ordered location of water molecules in the nodes of the crystal lattice; At the same time, the distances between molecules remain about the same (the order of the sizes of the molecules themselves). But for the conversion of water into steam, it is necessary to accomplish where it is used to work on the rupture of all links between molecules and removing molecules to considerable distances from each other (much large than the dimensions of molecules).

10.8 Condensation schedule

The process of condensation of steam and the subsequent cooling of the fluid looks on the graph symmetrically the process of heating and boiling. Here is the corresponding condensation schedule for the case of the Strategic Water Age, which is most common in tasks (Fig. 25).

Temperature
Fig. 25. Condensation schedule

At point C, we have water steam at 100 C. There is condensation on the CD section; Inside this section, a mixture of steam and water at 100 C. At point D, there is no longer there, there is only water at 100 C. Plot de cooling of this water.

Experience shows that when condensation of a pair of M mass M (i.e., during the passage of the CD section), exactly the same amount of heat q \u003d lm is distinguished, which was spent on the transformation of mass M fluid at this temperature.

Let's compare the following amounts of warmth:

Q1, which is distinguished by condensation 1 g of water vapor;

Q2, which is distinguished when cooled by the resulting gradual water to a temperature, say, 20 C.

Q1 \u003d LM \u003d 2300000 0; 001 \u003d 2300 J;

Q2 \u003d cm t \u003d 4200 0; 001 80 \u003d 336 J:

These numbers clearly show that the burn of the ferry is much worse than burn boiling water. If you get boiling water, it is allocated only to q2 (boiling water cool). But when the burn is a ferry, it will first stand out for an order of magnitude more heat q1 (steam condensed), the graduate water is formed, after which the same value Q2 is added when this water is cooled.

a) heating and cooling

892. What is the mass of mercury has the same heat capacity as 13 kg of alcohol? Specific heat capacity of alcohol 2440 J / (kg × K), the specific heat capacity of mercury 130 J / (kg × k). (244)

893. By friction on each other of two identical bodies, their temperature rose by 30 ° C after one minute. What is the average power developing in both bodies when friction? The heat capacity of each body is 800 j / k. (800)

894. On an electric stove with a capacity of 600 W 3 liters of water heated to a boil in 40 minutes. The initial temperature of water 20 ° C. Specific heat capacity of 4200 J / (kg × K). Determine the efficiency (as a percentage) installation. (70)

895. When the metal drills the hand drill, a weight of 0.05 kg was heated at 20 ° C for 200 from continuous operation. The average power consumed by the drill during drilling is 10 W. How many percent of the energy spent went to heating the drill, if the specific heat capacity of the material of the drill is 460 j / (kg × k)? (23)

896. When operating an electric motor with a capacity of 400 W, it heats up 10 to 50 from continuous operation. What is the efficiency (in percent) of the motor? Motor heat capacity 500 j / k. (75)

897. The transformer immersed in the oil, due to overload begins to warm. What is his efficiency (in percent), if at full capacity 60 kW oil weighing 60 kg heats up 30 ° C for 4 minutes of transformer operation? Specific heat capacity of 2000 J / (kg × k). (75)

898. The generator radiates ultra-high frequency pulses with energy in each pulse of 6 J. The frequency of repetition of the pulses of 700 Hz. CPD generator 60%. How many liters of water per hour should be passed through the cooling system of the generator so that water is not higher than 10 k? Specific heat capacity of 4200 J / (kg · k). (240)

b) phase transformations

899. How many ice, taken at 0 ° C, can we melt, informing it the energy of 0.66 mJ? Specific ice melting ice 330 kJ / kg. (2)

900. Under the hardened 100 kg of steel at the melting point, 21 MJE heat was selected. What is the specific heat of melting (in KJ / kg) steel? (210)

901. What amount of heat (in KJ) should be reported to 2 kg of ice taken at a temperature of -10 ° C to completely melt it? The specific heat capacity of ice is 2100 J / (kg × K), the specific heat of melting ice 330 kJ / kg. (702)

902. In order to transform a certain amount of ice taken at a temperature of -50 ° C into water with a temperature of 50 ° C, 645 kJ energy is required. What is the mass of ice? The specific heat capacity of water is 4200 J / (kg × K), the specific heat capacity of Ice 2100 J / (kg × K), the specific heat of melting ice is 3.3 × 105 J / kg. (one)

903. What amount of heat (in KJ) is necessary to transform 0.1 kg of boiling water to par? The specific heat of water vaporization 2.26 MJ / kg. (226)

904. How much heat (in KJ) is released during condensation of 0.2 kg of water vapor at a temperature of 100 ° C? The specific heat of water vaporization of 2.3 × 106 J / kg. (460)

905. What amount of heat (in KJ) need to notify 1 kg of water taken at 0 ° C to heat it up to 100 ° C and fully evaporate? The specific heat capacity of water is 4200 J / (kg × K), the specific heat of the water vaporization of 2.3 × 106 J / kg. (2720)

906. To heat the water taken at a temperature of 20 ° C, 2596 kJ energy consumed into the pairs. Determine the mass of water. Specific heat capacity of 4200 J / (kg × K), specific heat of water vaporization 2.26 MJ / kg. (one)

907. To melting one ton of steel, a power supply is used with a power of 100 kW. How many minutes will smelting, if the ingot before the start of melting should be heated at 1500 k? The specific heat capacity of the steel is 460 J / (kg × K), the specific heat of melting of steel 210 kJ / kg. (150)

908. For heating some mass of water from 0 ° C to 100 ° C, 8400 J warmth is required. How many heat still need (in KJ) to completely evaporate this water? The specific heat capacity of water is 4200 J / (kg · k), the specific heat of the water vaporization of 2300 kJ / kg. (46)

909. To cool the water in the refrigerator from 33 ° C to 0 ° C, it was required 21 minutes. How long will it take to turn this water into ice? Specific heat capacity of 4200 j / (kg · k), specific ice melting heat 3.3 · 10 5 J / kg. Answer to give in minutes. (fifty)

910. The water vessel is heated on an electric stove from 20 ° C to a boil in 20 minutes. How much time is needed (in minutes) to pay 42% of the water to the pairs? The specific heat capacity of the water is 4200 J / (kg × K), the specific heat of water vaporization 2.2 × 106 J / kg. (55)

911. Calculate the efficiency (as a percentage) of the gas burner if it uses gas with a specific heat of combustion 36 MJ / M 3 , And on the heating of the kettle with 3 liters of water from 10 ° C to the boil, 60 liters of gas were spent. The heat capacity of the kettle is 600 j / k. Specific heat capacity of 4200 J / (kg · k). (55)

912. 210 kg of coal for 1 hour is consumed for the operation of the steam machine in 1 hour. Cooling the machine is carried out by water, which at the inlet has a temperature of 17 ° C, and at the output of 27 ° C. Determine the flow of water (in kg) for 1 s, if 24% of the total heat is on its heating. Specific heat capacity of 4200 j / (kg × K), specific heat combustion of coal 30 MJ / kg. (10)

913. How much kilometers of the road is enough for 10 kg of gasoline for the engine of a car, which develops at a speed of 54 km / h Power of 69 kW and having a 40% efficiency? Specific heat combustion of gasoline 4.6 × 107 J / kg. (40)