(as well as energy).
The first law of thermodynamics was formulated by the German scientist Yu. L. Maner in 1842 and confirmed experimentally by the English scientist J. Joule in 1843.
Formulated like this:
Change internal energy system during its transition from one state to another is equal to the sum of the work of external forces and the amount of heat transferred to the system:
ΔU = A + Q,
Where ΔU- change in internal energy, A- Job external forces, Q is the amount of heat transferred to the system.
From ( ΔU = A + Q) should law of conservation of internal energy. If the system is isolated from external influences, then A = 0 And Q = 0 , and hence also ΔU = 0 .
For any processes occurring in an isolated system, its internal energy remains constant.
If the work is done by the system, and not by external forces, then the equation ( ∆U = A + Q) is written as:
Where A" is the work done by the system A" = -A).
The amount of heat transferred to the system is used to change its internal energy and to perform work on external bodies by the system.
The first law of thermodynamics can be formulated as the impossibility of the existence of a perpetual motion machine of the first kind, which would do work without drawing energy from any source (i.e., only due to internal energy).
Indeed, if no heat is supplied to the body ( Q - 0 ), then work A", according to the equation , occurs only due to the loss of internal energy A" \u003d -ΔU. After the energy supply is exhausted, the engine stops working.
It should be remembered that both work and the amount of heat are characteristics of the process of changing internal energy, so it cannot be said that the system contains a certain amount of heat or work. The system in any state has only a certain internal energy.
Application of the first law of thermodynamics to various processes.
Consider application of the first law of thermodynamics to various thermodynamic processes.
isochoric process.
Addiction p(T) the thermodynamic diagram shows isohoRoy.
Isochoric (isochoric) process- a thermodynamic process occurring in the system at a constant volume.
The isochoric process can be carried out in gases and liquids enclosed in a constant volume vessel.
In an isochoric process, the volume of the gas does not change ( ∆V=0), and, according to the first law of thermodynamics,
ΔU = Q,
i.e., the change in internal energy is equal to the amount of heat transferred, since work ( A = pΔV=0 ) is not performed by the gas.
If the gas is heated, then Q > 0 And ∆U > 0, its internal energy increases. When gas is cooled Q< 0 And ΔU< 0 , the internal energy decreases.
isothermal process.
Isothermal process is graphically depicted isotherm.
Isothermal process is a thermodynamic process that occurs in a system at a constant temperature.
Since the internal energy of the gas does not change during an isothermal process, see the formula 
, (T = const), then all the amount of heat transferred to the gas is used to perform work:
When the gas receives heat ( Q > 0 ) it does positive work ( A" > 0). If the gas gives off heat to the environment Q < 0 And A"< 0 . In this case, work is done on the gas by external forces. For external forces, the work is positive. Geometrically, work in an isothermal process is determined by the area under the curve p(V).
isobaric process.
The isobaric process on the thermodynamic diagram is depicted isobar.
Isobaric (isobaric) process- thermodynamic process occurring in a system with constant pressure R.
An example of an isobaric process is the expansion of a gas in a cylinder with a freely moving loaded piston.
In an isobaric process, according to the formula, the amount of heat transferred to the gas goes to change its internal energy ΔU and to do their work A" at constant pressure:
Q = ∆U + A".
The work of an ideal gas is determined from the dependence graph p(V) for an isobaric process ( A" = pΔV).
For an ideal gas in an isobaric process, the volume is proportional to the temperature, in real gases, part of the heat is spent on changing the average interaction energy of particles.
adiabatic process.
Adiabatic process (adiabatic process) is a thermodynamic process that occurs in a system without heat exchange with environment (Q= 0) .
Adiabatic isolation of the system is approximately achieved in Dewar vessels, in the so-called adiabatic shells. An adiabatically isolated system is not affected by changes in the temperature of the surrounding bodies. Her inner energy U can change only due to the work done by external bodies on the system, or the system itself.
According to the first law of thermodynamics ( ΔU = A + Q), in the adiabatic system
∆U=A,
Where A is the work of external forces.
With the adiabatic expansion of the gas A< 0 . Hence,
,
which means a decrease in temperature during adiabatic expansion. It leads to the fact that the gas pressure decreases more sharply than in an isothermal process. In the figure below, the adiabat 1-2, passing between two isotherms, clearly illustrates what has been said. The area under the adiabat is numerically equal to the work done by the gas during its adiabatic expansion from volume V 1 , before V 2.
Adiabatic compression leads to an increase in the temperature of the gas, because as a result of elastic collisions of gas molecules with the piston, their average kinetic energy increases, in contrast to expansion, when it decreases (in the first case, the speeds of gas molecules increase, in the second they decrease).
Rapid heating of air during adiabatic compression is used in Diesel engines.
Heat balance equation.
In a closed (isolated from external bodies) thermodynamic system, a change in the internal energy of any body of the system ∆U1 cannot lead to a change in the internal energy of the entire system. Hence,
If no work is done inside the system by any bodies, then, according to the first law of thermodynamics, the change in the internal energy of any body occurs only due to the exchange of heat with other bodies of this system: ΔUi = Qi. Given , we get:
This equation is called heat balance equation. Here Q i- the amount of heat received or given away i-th body. Any of the heat Q i can mean the heat released or absorbed during the melting of a body, the combustion of fuel, the evaporation or condensation of steam, if such processes occur with different bodies of the system, and will be determined by the corresponding ratios.
The heat balance equation is mathematical expression the law of conservation of energy during heat transfer.
Internal energy can change due to mainly two different processes: performing work A on the body and imparting to it the amount of heat Q. The performance of work is accompanied by the movement of external bodies acting on the system. So, for example, when a piston closing a vessel with gas is pushed in, the piston, moving, does work L on the gas. According to the third law. Newton's gas does work on the piston
The communication of heat to the gas is not associated with the movement of external bodies and, therefore, is not associated with the performance of macroscopic work on the gas (that is, related to the entire set of molecules that make up the body) work. In this case, the change in internal energy is due to the fact that individual molecules of a more heated body do work on individual molecules of a body that is less heated. The transfer of energy also takes place via radiation. The totality of microscopic (that is, not capturing the whole body, but its individual molecules) processes leading to the transfer of energy from body to body is called heat transfer.
Just as the amount of energy transferred from one body to another is determined by the work A performed on each other by bodies, the amount of energy transferred from body to body by heat transfer is determined by the amount of heat Q given by one body to another. Thus, the increment in the internal energy of the system must be equal to the sum of the work done on the system A and the amount of heat imparted to the system
Here are the initial and final values of the internal energy of the system. Usually, instead of the work A performed by external bodies on the system, one considers the work A (equal to -A) performed by the system on external bodies. Substituting -A for A and solving equation (83.1) for Q, we get:
Equation (83.2) expresses the law of conservation of energy and is the content of the first law (beginning) of thermodynamics. It can be expressed in words as follows: the amount of heat communicated to the system goes to increase the internal energy of the system and to perform work on external bodies by the system.
The foregoing does not mean at all that the internal energy of the system always increases with the addition of heat. It may happen that, despite the communication of heat to the system, its energy does not increase, but decreases. In this case, according to (83.2), i.e., the system does work both due to the received heat Q and due to the internal energy reserve, the loss of which is equal to . It must also be borne in mind that the quantities Q and A in (83.2) are algebraic, which means that the system does not actually receive heat, but gives it away).
From (83.2) it follows that the amount of heat Q can be measured in the same units as work or energy. The SI unit for heat is the joule.
To measure the amount of heat, a special unit called a calorie is also used. One calorie is equal to the amount of heat required to heat 1 g of water from 19.5 to 20.5 °C. A thousand calories is called a big calorie or kilocalorie.
It has been experimentally established that one calorie is equivalent to 4.18 J. Therefore, one joule is equivalent to 0.24 cal. The value is called the mechanical equivalent of heat.
If the quantities included in (83.2) are expressed in different units, then some of these quantities must be multiplied by the corresponding equivalent. So, for example, expressing Q in calories, and U and A in joules, relation (83.2) should be written as
In what follows, we will always assume that Q, A, and U are expressed in the same units, and write the equation of the first law of thermodynamics in the form (83.2).
When calculating the work done by the system or the heat received by the system, it is usually necessary to break the process under consideration into a number of elementary processes, each of which corresponds to a very small (in the limit, infinitesimal) change in the system parameters. Equation (83.2) for an elementary process has the form
where is the elementary amount of heat, is the elementary work, and is the increase in the internal energy of the system during this elementary process.
It is very important to keep in mind that and cannot be considered as increments of Q and A.
Any value corresponding to the elementary process A can be considered as an increment of this value only if the value corresponding to the transition from one state to another does not depend on the path along which the transition occurs, i.e., if the value f is a function of the state. With regard to the state function, we can talk about its "reserve" in each of the states. For example, we can talk about the stock of internal energy that a system has in various states.
As we will see later, the amount of work done by the system and the amount of heat received by the system depend on the path of the system's transition from one state to another. Therefore, neither Q nor A are state functions, so one cannot talk about the amount of heat or work that the system has in different states.
One of characteristic features The thermodynamic consideration of phenomena consists in isolating one body from a multitude of bodies that are in interaction, which is called the system under study, while the rest of the bodies are called the external environment or external bodies. In this method, all attention is paid to the selected system, its geometric boundaries are often chosen to be conditional and such that they are convenient for solving the problem under consideration. The system is assumed to be at rest, so the energy changes in it are completely reduced to a change in its internal energy. Interaction with external bodies is established in the most general form: energy can be transferred between the system and external bodies in the form of heat and work.
Figure 2.5 schematically shows the system under study and external bodies II and III. The system is placed in a cylinder with a bottom and a movable piston A A. Let the walls and piston of the cylinder be adiabatic, and the bottom of the cylinder be heat-permeable. Then, obviously, the selected system I is in thermal contact with body II (heat exchange is possible with this body), while with body III it is in mechanical contact (energy exchange is possible with this body through the work done when the piston moves). The arrows in the figure show that an elementary amount of heat enters the system from body II, while the system, performing elementary work on body III, transfers energy to it. As a result, there is a change
internal energy of the system According to the diagram shown in Figure 2.5,
The written equation expresses the first law of thermodynamics: the amount of heat received by the system from surrounding bodies goes to change its internal energy and to perform work on external bodies.
It must be borne in mind that the quantities are algebraic, it is generally accepted that if the system receives this heat, and if the system does work on external bodies, transferring energy to them. When interpreting equation (17.1), for simplicity, it was said that this received heat is perfect work. But in the general case, a body can give off heat, then either receive energy through work
In a system enclosed in an adiabatic shell, the processes are not accompanied by heat exchange with the surrounding bodies; such processes are called adiabatic. For adiabatic processes and according to The last expression means the following: work in the adiabatic process occurs due to the loss of internal energy. If (external bodies do work on the system), then (the internal energy of the system increases).
If the shell of the system is rigid (mechanical isolation), then the mechanical work with any changes in the system is equal to zero. Such processes are called isochoric (isochoric), for them Thus, with isochoric changes in the system, its internal energy changes only due to the input or output heat.
One more feature of equation (17.1) should be noted: there is a differential of the internal energy of the body under study, while the quantities are elementary (small) values of heat and work; (see Fig. 2.5) - the elementary amount of heat transferred from body II to body work of body I on body III. In this case, body II can exchange energy with a number of other bodies, which is why, in the general case, it cannot be the energy differential of the second body. For the system under study, there is a part and therefore also cannot be the total differential of any state function of the system under study. The elementary work that determines the exchange of energy between the system and the third body is not a complete differential either.
When determining the final change in the state of the system, due to its transition from state 1 to state 2, the expression
(17.1) integrate over the transition line or, which is the same:
The last equality expresses the first law of thermodynamics for the final changes in the system. According to the above, these are the final values of heat and work (but not an increment of something), while the value is an increment of internal energy.
As mentioned earlier (§ 16, 13), it does not depend, but depends on the type of process (on the path of the system's transition from the initial state to the final state). In this regard, it follows from equation (17.2) that it also depends on the type of process.
If, when the state of the system changes, its temperature changes by then, dividing (17.2) by we get:
Ratio - determines the heat capacity of the system. Transitions between two states can occur in such a way that the temperature change is the same, but the values for different transitions will be different (for different jobs). It follows that the heat capacity of system (17.3) will also depend on the type of process.
There are two forms of energy transfer from one body to another - this is the work of some bodies on others and the transfer of heat. The energy of mechanical motion can be converted into the energy of thermal motion and vice versa. In such energy transitions, the law of conservation of energy is fulfilled. When applied to the processes considered in thermodynamics, the law of conservation of energy is called the first law (or first law) of thermodynamics. This law is a generalization of empirical data.
Statement of the first law of thermodynamics
The first law of thermodynamics is formulated as follows:
The amount of heat that is supplied to the system is spent on the performance of work by this system (against external forces) and the change in its internal energy. In mathematical form, the first law of thermodynamics can be written in integral form:
where is the amount of heat received by the thermodynamic system; - change in the internal energy of the system under consideration; A is the work that the system performs on external bodies (against external forces).
In differential form, the first law of thermodynamics is written as:
where is the element of the amount of heat that the system receives; - infinitesimal work performed by a thermodynamic system; is an elementary change in the internal energy of the system under consideration. It should be noted that in formula (2) - an elementary change in internal energy is a total differential, in contrast to and .
The amount of heat is considered positive if the system receives heat and negative if heat is removed from the thermodynamic system. The work will be greater than zero if it is performed by the system, and the work will be considered negative if it is performed on the system by external forces.
In the event that the system returned to its original state, then the change in its internal energy will be equal to zero:
In this case, in accordance with the first law of thermodynamics, we have:
Expression (4) means that a perpetual motion machine of the first kind is impossible. That is, it is fundamentally impossible to create a periodically operating system (heat engine) that performs work that would be greater than the amount of heat received by the system from the outside. The statement about the impossibility of a perpetual motion machine of the first kind is also one of the options for formulating the first law of thermodynamics.
Examples of problem solving
EXAMPLE 1
| Exercise | How much heat () is transferred to an ideal gas having a volume V in the process of isochoric heating if its pressure changes by ? Consider that the number of degrees of freedom of a gas molecule is equal to i. |
| Solution | The basis for solving the problem is the first law of thermodynamics, which we will use in integral form: Since, according to the condition of the problem, the process with gas is isochoric (), then the work in this process is zero, then the first law of thermodynamics for the isochoric process will take the form: The change in internal energy is determined using the formula:
where i is the number of degrees of freedom of a gas molecule; - amount of substance; R is the universal gas constant. Since we do not know how the gas temperature changes in the process under consideration, we use the Mendeleev-Clapeyron equation to find: Let us express the temperature from (1.4), write the formulas for the two states of the system under consideration: Using expressions (1.5) we find : From expressions (1.3) and (1.6) it follows that for an isochoric process the change in internal energy can be found as: And from the first law of thermodynamics for our process (at ), we have that:
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| Answer |  |
EXAMPLE 2
| Exercise | Find the change in the internal energy of oxygen (), the work done by it (A) and the amount of heat received () in the process (1-2-3), which is indicated on the graph (Fig. 1). Consider that m 3; 100 kPa; m 3; kPa. |
| Solution | The change in internal energy does not depend on the course of the process, since internal energy is a state function. It depends only on the final and initial states of the system. Therefore, we can write that the change in internal energy in the process 1-2-3 is:
where i is the number of degrees of freedom of the oxygen molecule (since the molecule consists of two atoms, we consider ), is the amount of substance, . The temperature difference can be found by using the ideal gas equation of state and looking at the process graph: |
It represents the law of conservation of energy, one of the universal laws of nature (along with the laws of conservation of momentum, charge and symmetry):
Energy is indestructible and uncreated; it can only change from one form to another in equivalent proportions.
The first law of thermodynamics is yourself postulate- it cannot be proven logically or deduced from any more general provisions. The truth of this postulate is confirmed by the fact that none of its consequences is in conflict with experience.
Here are some more formulations of the first law of thermodynamics:
- The total energy of an isolated system is constant;
- A perpetual motion machine of the first kind is impossible (an engine that does work without expending energy).
First law of thermodynamics establishes the relationship between the heat Q, the work A and the change in the internal energy of the system? U:
Change in internal energy system is equal to the amount of heat communicated to the system minus the amount of work done by the system against external forces.
dU = δQ-δA (1.2)
Equation (1.1) is mathematical notation of the 1st law of thermodynamics for the finite, equation (1.2) - for an infinitely small change in the state of the system.
Internal energy is a state function; this means that the change in internal energy? U does not depend on the path of the system transition from state 1 to state 2 and is equal to the difference between the values of internal energy U 2 and U 1 in these states:
U \u003d U 2 -U 1 (1.3)
It should be noted, that it is impossible to determine the absolute value of the internal energy of the system; thermodynamics is only interested in the change in internal energy during a process.
Consider an application the first law of thermodynamics to determine the work done by the system in various thermodynamic processes (we will consider the simplest case - the work of expanding an ideal gas).
Isochoric process (V = const; ?V = 0).
Since the work of expansion is equal to the product of pressure and volume change, for an isochoric process we get:
Isothermal process (T = const).
From the equation of state of one mole of an ideal gas, we obtain:
δA = PdV = RT(I.7)
Integrating expression (I.6) from V 1 to V 2 , we obtain
A=RT= RTln= RTln (1.8)
Isobaric process (P = const).
Qp = ?U + P?V (1.12)
In equation (1.12) we group variables with the same indices. We get:
Q p \u003d U 2 -U 1 + P (V 2 -V 1) \u003d (U 2 + PV 2) - (U 1 + PV 1) (1.13)
Let's introduce a new system state function - enthalpy H, identically equal to the sum of internal energy and the product of pressure and volume: Н = U + PV. Then expression (1.13) is transformed to the following form:
Qp= H 2 -H 1 =?H(1.14)
Thus, the thermal effect of an isobaric process is equal to the change in the enthalpy of the system.
Adiabatic process (Q= 0, δQ= 0).
In an adiabatic process, the expansion work is done by reducing the internal energy of the gas:
A = -dU=C v dT (1.15)
If Cv does not depend on temperature (which is true for many real gases), the work done by the gas during its adiabatic expansion is directly proportional to the temperature difference:
A \u003d -C V ?T (1.16)
Task number 1. Find the change in internal energy during the evaporation of 20 g ethanol at its boiling point. The specific heat of vaporization of ethyl alcohol at this temperature is 858.95 J/g, the specific vapor volume is 607 cm 3 /g (disregard the volume of liquid).
Solution:
1 . Calculate the heat of evaporation 20 g of ethanol: Q=q beat m=858.95J/g 20g = 17179J.
2 .Calculate the work on changing the volume 20 g of alcohol during its transition from a liquid state to a vapor state: A \u003d P? V,
where P- alcohol vapor pressure, equal to atmospheric, 101325 Pa (because any liquid boils when its vapor pressure is equal to atmospheric pressure).
V \u003d V 2 -V 1 \u003d V W -V p, because V<< V п, то объмом жидкости можно пренебречь и тогда V п =V уд ·m. Cледовательно, А=Р·V уд ·m. А=-101325Па·607·10 -6 м 3 /г·20г=-1230 Дж
3. Calculate the change in internal energy:
U \u003d 17179 J - 1230 J \u003d 15949 J.
Since? U> 0, then, consequently, when ethanol evaporates, an increase in the internal energy of alcohol occurs.
