The work of a gas is the first law of thermodynamics. First law of thermodynamics
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 new feature system status - 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. Specific heat of vaporization ethyl alcohol at this temperature is 858.95 J/g, the specific volume of vapor 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 upon its transition from liquid state into vapor: A= 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.
First law of thermodynamics
Plan
Internal energy.
Isoprocesses.
Works at isoprocesses.
adiabatic process.
Heat capacity.
internal energy of the body.
The internal energy of a body is composed of the kinetic energy of the translational and rotational motion of molecules, the kinetic and potential energy of the vibrational motion of atoms in molecules, the potential energy of interaction between molecules and intramolecular energy (intranuclear).
The kinetic and potential energy of the body as a whole is not included in the internal energy.
The internal energy of a thermodynamic system of bodies is composed of the internal energy of interaction between bodies and the internal energy of each body.
The work of a thermodynamic system on external bodies consists in changing the state of these bodies and is determined by the amount of energy that the thermodynamic system transfers to external bodies.
Heat is the amount of energy presented by the system to external bodies during heat exchange. Work and heat are not functions of the state of the system, but a function of the transition from one state to another.
Thermodynamic system - they call such a system, a set of macroscopic bodies that can exchange energy with each other and with external environment(with other bodies) (For example, liquid and vapor above it). The thermodynamic system is characterized by the following parameters:
P, V, T, ρ etc.
The states of the system, when at least one of the parameters changes, are called non-equilibrium.
Thermodynamic systems that do not exchange energy with external bodies are called closed.
Thermodynamic process is the transition of a system from one state (P 1 , V 1 , T 1 ) to another (P 2 , V 2 , T 2 ) is an imbalance in the system.
First law of thermodynamics.
The amount of heat communicated to the system is used to increase the internal energy of the system and to perform work on external bodies by the system.
The first law of thermodynamics is a special case of the law of conservation of energy that takes into account the internal energy of the system:
Q= U 2 - U 1 + A;
U 1, U 2 - the initial and final values of the internal energy of the body.
Ais the work done by the system.
Q- The amount of heat reported to the system.
In differential form:
d Q= dU+ d A;
dU- there is a total differential, and it depends on the difference between the initial and final states of the system.
d Qandd A- incomplete differentials, depend on the process itself, that is, on the path of the process. Work is done when the volume changes:
d A= fdx= pSdx = pdV;
d A= pdV;
The first law of thermodynamics - a perpetual motion machine of the first kind is impossible, that is, an engine that would do work in a larger amount than the energy it receives from outside.
- does not depend on the integration path.
- depends on the integration path of the process function and cannot be written:
A 2 - A 1 ; Q 2 - Q 1 ;
A, Qare not state functions. It is impossible to speak about the law of work and heat.
This is nothing but the law of conservation of energy.
Isoprocesses.
1) Isochoric process:
V=Withonst;
The process of heating a gas in a closed volume.
d Q=dU+pdV,
pdv=0; d U=dU,
The first law of thermodynamics takes on this form.
Heat capacity atV- const:
The heat capacity is determined by the ratio of the increase in heat received by the system to the increase in temperature.
2) Isobaric process:
P= const;
d Q= dU+ d A;
Divide bydT(for 1 mole of gas):
pV=RT,
cp= CV+ R,
3) Isothermal process:
T= const,
P V = A;
Since the internal energy depends onT, then with isothermal expansiondU=0:
d Q= d A,
The heat supplied to the gas during isothermal expansion is entirely converted into the work of expansion.
dQtends to ∞,dTtends to 0.
4) Adiabatic process:
No heat exchange with environment. The first law of thermodynamics takes the form:
d Q=0; dU+d A=0,
dU+d A=0; d A=-dU,
In an adiabatic process, work is done only due to the loss of internal energy of the gas.
Processes in whichd Q=0 - adiabatic. Adiabatic processes are always accompanied by a change in body temperature. Since during adiabatic expansion, work is done due to internal energy (1cal \u003d 4.19 J).
Work with isoprocesses.
1) Isochoric process:
V= const
d A= pdV=0; A v =0,
The work of pressure forces in an equilibrium process is numerically equal to the area under the curve depicting the process onPV- diagram:
d A= pdV.
2) Isobaric process:
p=const;
d A=pdV;
3) Isothermal process:
T= const;
d A= pdV;
dV= RT;
;
Process equilibrium:
4) Adiabatic process:
d Q= dU+ pdV;
dU=-pdV,
d Q=0; dU=C v dT,
,
We integrate:
+ (γ-1) lnV= const,
(TV γ-1 )= const,
(TV γ-1 ) = const -the equationPoisson
;
RV γ = const.
6. Heat capacity.
1) The heat capacity of a body is the amount of heat that must be imparted to the body so that it heats up by 1 0 FROM.
C p = C V + R; C P > C V,
Heat capacity can be attributed to a unit of mass, one mole and a unit of volume. Accordingly: specific, molar, volumetric ([J / kg * deg]; [J / mol * deg]; [J / m 3* deg]).
2) Heat capacity in real gases:
Mole internal energy:
N a k= R,
is the heat capacity of one mole at a constant volume (v= const).
;
– heat capacity of one mole at constant pressure (p= const).
Specific heat.
[ ] ;
State function.
W= U+ PV; C p > C v
When heated while maintaining the P partQgoes for expansion. Only by expanding can R.
Isotherm:PV= const;
Adiabat:PV γ = const;
PV γ
Since γ>1, then the adiabatic curve goes steeper than the isotherm.
;
C v dT + pdV=0;
d A=pdV=-C v dT;
PV γ =P 1 V 1 γ ,
A change in the state of any body or system of bodies, generally speaking, is accompanied by the work produced by this system, or the work performed on it by external forces. This work can be expressed in terms of parameters that determine the state of the system.
If, as we already know, the state of the body is determined by two of the three parameters, then in the general case a change in any of them must be accompanied by external work.
So, for example, a change in the temperature of a gas, i.e., its heating or cooling, can be carried out as a result of the expenditure of mechanical work from the outside (heating) or due to work done against external forces (cooling).
This mechanical work is done when the gas is compressed by an external force, when the gas is heated, or when the gas expands, when it itself performs work, while cooling. A change in the volume of a gas can be made without changing its temperature (see below), in which case less work is required accordingly.
But, as was pointed out, the state of a gas (or other bodies) can be changed by informing it or, conversely, by taking away from it a certain amount of heat, that is, by bringing it into "contact" with a hotter or colder body.
What work will be done in this way of changing the state? The answer to this question is given by the law of conservation of energy. If a certain amount of heat is imparted to a gas (or another body), then, generally speaking, work is done and its internal energy changes by
The law of conservation of energy states that the work done by a system is equal to the difference between the amount of heat supplied to the system and the change in its internal energy:
This equation expresses the most important law of nature, the law of conservation of energy in relation to mechanical and thermal energy. This law is called the first law of thermodynamics.
Work when changing the volume of gas. It is easy to calculate the work associated with the expansion or compression of a gas, i.e., with a change in its volume. Imagine that the gas is in a cylinder, which is closed by a movable piston having an area of 5 (Fig. 31). Let, under the action of an applied external force, the piston descended a distance, while compressing the gas. The gas will be compressed until the force is balanced by the force acting on the piston from the gas and equal to where the gas pressure. The work expended on moving the piston over a distance is, obviously, But there is nothing more than a change in the volume of gas during compression, i.e.
On the contrary, when the gas expands, i.e., when the volume increases by the gas itself, it does work against external forces equal to
A change in the volume of a gas is accompanied by work equal to the product of the pressure under which the gas is located and the change in its volume.
Formula (23.2) is true not only for gas, but also for any bodies. If, when the state of the body changes, the external work is performed only due to a change in volume, then the first law of thermodynamics can be written as:
There are cases when a change in the state of bodies is accompanied by a change in electrical, magnetic or other parameters, then to the right side of the equation should be added
the corresponding terms: electrical, magnetic and other types of energy. We confine ourselves here to considering changing only the parameters and
It is possible to calculate the external work in the case when the change in the state parameters is not infinitesimal.
If the body passes from state to state 2, then the associated work A is determined by integrating equation (23.2):
This dintegral can be determined graphically. Indeed, the state of the body, as was indicated, is characterized by a point on the curve. Therefore, if the dependence is plotted graphically, for example, if this dependence is expressed by the curve in Fig. 32, then
is equal to the shaded area under this curve.
If the transition from state to state 2 occurs in such a way that the change in pressure with volume is represented by a curve, then the work associated with this transition will be different.
The external work done by the body (or on it) when changing its volume depends on the sequence of states that the body goes through from the initial to the final state.
As for the internal energy, it depends only on the state of the body and its change does not depend on the intermediate states in which the body was.
Therefore, equation (23.3) can be rewritten as:
where are the values of the internal energy of the body in states 1 and 2, respectively.
In a particular case, if the body, as a result of all changes in state, returned to its original state, i.e., then in this case they say that the process of changing the state is circular, or cyclic. Graphically, such a process is represented by a closed curve (Fig. 33), and the work done (or expended) is determined by the shaded area.
Obviously if work
for the cycle is positive, i.e. the body itself did work against external forces, then this means that it received an equal amount of heat from the outside. If this work A for the cycle is negative, i.e., work was done on the body by external forces, then at this releases an equal amount of heat
Thus, in a cyclic process
The reader should not be confused by the unusual shape of the curve in Fig. 32 and 33, when in some of its sections the pressure increases with an increase in volume. The "usual" dependence, in which the pressure is inversely proportional to the volume of the gas, is observed only at a constant temperature, i.e., in an isothermal process. The process of changing the volume of gas that we are considering refers to the case when a certain amount of heat is imparted to or removed from it, and work is done on it (or it does it itself), and at different stages of the change in volume, the temperature of the gas is different.
There is nothing surprising in the fact that, simultaneously with expansion (raising the piston), a gas can, due to a heat source, increase its temperature so much that its pressure, despite an increase in volume, will increase (and vice versa, when compressed, a gas can give off heat to a colder body, and his blood pressure will go down).
This also explains the fact that when passing from the same initial state to the same final state but through different intermediate states, the work obtained is different and, therefore, in a circular process it is not equal to zero. It is on this that the work of all heat engines (engines) is based.
It hardly needs to be emphasized that no positive work can be done by the body if the temperature of the body is constant throughout the entire circular process (i.e., if the process is isothermal). In a gas, obviously, such an isothermal circular process is generally impossible, since if the change in pressure with volume occurs along an isotherm, then it is possible to return to the initial state only along the same isotherm; but such a process cannot be called circular in the sense mentioned above.
Quasi-static processes. When deriving equation (23.2) for the work of a gas associated with a change in its volume, it was tacitly assumed that during the entire process of changing the volume, the pressure
at each moment of time is the same at all points of the gas. Otherwise, the value of the pressure would be completely indeterminate. Meanwhile, it is not so easy to ensure such a constancy of pressure in the entire volume of a gas (as, indeed, in any body) in the process of its expansion or contraction.
If the expansion or contraction of the gas occurs rapidly, then the pressures in its different parts do not have time to equalize. Under the influence of the pressure difference, gas flows arise with different velocities at different points, in particular, vortex flows. These movements require some work to create them. In addition, different parts of the gas can have different temperatures and densities.
In short, with a rapid change in volume, the gas is not in a state of equilibrium. In order for the gas to be in equilibrium in the process of changing its volume (or another quantity characterizing the state), it is necessary that this process proceed very slowly, in the limit - infinitely slowly. In this case, all deviations from equilibrium will have time to disappear, the gas will pass through a series of equilibrium states, passing one into another.
Such processes are called quasi-static, because at any given moment the state of the gas differs little from the static state, in which the state parameters are the same throughout the volume. It is clear that only quasi-static processes can be graphically represented in the form of curves similar, for example, to those shown in Fig. 32 or fig. 4 (p. 33). A non-quasi-static process cannot be depicted. Equation (23.2) and its consequences can only be used for quasi-static processes. (See Chapter VI for more on this.)
If the process of changing the volume, i.e., compression or expansion of the gas, occurs non-quasi-statically, then the work done during compression or expansion will be less than during the quasi-static process. This can be understood from the following considerations. Imagine that the gas in a vessel with a piston (see Fig. 31) is first in equilibrium; This means that the pressure of the gas inside the vessel is equal to the external pressure. Let the gas begin to expand (non-quasi-statically) under the influence of one reason or another, i.e., the piston begins to move upward. This means that the external pressure has become less than the equilibrium pressure, therefore, the external work
Accordingly, with non-quasistatic gas compression, the external pressure is greater than the equilibrium one and therefore the work (this time it is negative)
And only in a quasi-static process, the external pressure differs infinitely little from the equilibrium one, and, consequently, the work done in this case is the greatest.
Moreover, the gas can expand without doing any external work at all. Such a case can be realized by connecting two vessels to each other, of which one is filled with gas, and the other is empty. Then the gas will flow from the first vessel to the second and, consequently, will occupy a larger volume. But at the same time, no work (external) will be done (for there are no external forces against which this work could be done). This is the so-called process of expansion into the void (see p. 125). Indeed, during this entire process, the gas is not in equilibrium (no matter how slowly it flows).
Physical processes such as heat and work can be explained by the simple transfer of energy from one body to another. In the case of work we are talking about mechanical energy, while heat presupposes thermal energy. The transfer of energy is carried out according to the laws of thermodynamics. The main provisions of this section of physics are known as "beginnings".
The first law of thermodynamics regulates and limits the process of energy transfer in a particular system.
Types of energy systems
There are two types of energy systems in the physical world. A closed or closed system has a constant mass. In an open or open system, the mass can decrease and increase depending on the processes taking place in this system. Most of the observed systems are open.
Research in such systems is hampered by many random factors that affect the reliability of the results. Therefore, physicists study phenomena in closed systems, extrapolating the results to open ones, taking into account the necessary corrections.
Energy of an isolated system
Any closed system in which there is no exchange of energy with the environment is isolated. The equilibrium state of such a system is determined by the readings of the following quantities:
- P is the pressure in the system;
- V is the volume of the isolated system
- T- temperature;
- n is the number of moles of gas in the system;
as you can see, the amount of heat and the work done are not included in this list. A closed isolated system does not exchange heat and do no work. Its total energy remains unchanged.
Change in system energy
When work is performed or a heat transfer process occurs, the state of the system changes, and it will no longer be considered isolated.
Statement of the first law of thermodynamics
First of all, the first law of thermodynamics was derived for isolated systems. Later it was proved that the law is universal and can be applied to non-closed systems if the change in internal energy due to fluctuations in the amount of matter in the system is correctly taken into account. If the system under consideration passes from state A to state B, then the work done by the system W, and the amount of heat Q will differ. Different processes give different readings of these variables, even if the system eventually returns to its original state. But at the same time, the difference W- Q will always be the same. In other words, if after any impact the system returned to its original state, then regardless of the type of processes involved in the transformation of such a system, the rule is observed W- Q= const.
In some cases, it is more convenient to use the differential formula for the expression of the first law. It looks like this: dU= dw- dQ
here dU- infinitesimal change in internal energy
dW- quantity characterizing the infinitesimal work of the system
dQ- an infinitesimal amount of heat transferred to a given system.
Enthalpy
For a wider application of the first law of thermodynamics, the concept of enthalpy is introduced.
This is the name of the total amount of total energy of a substance and the product of volume and pressure. The physical expression of enthalpy can be represented by the following formula:
The absolute value of enthalpy is the sum of the enthalpies of all the parts that make up the system.
AT quantitative terms this value cannot be determined. Physicists operate only with the difference between the enthalpies of the final and initial states of the system. Indeed, in any calculation of the change in the state of the system, a certain level is chosen at which the potential energy is equal to zero. The same is true for calculating enthalpy. If we apply the concept of enthalpy, then the first law of thermodynamics for isoprocesses will look like this: dU= dw- dH
The enthalpy of any system depends on internal structure substances that make up this system. These indicators, in turn, depend on the structure of the substance, its temperature, quantity and pressure. For complex substances, you can calculate the standard enthalpy of formation, which is equal to the amount of heat that is needed to form a mole of a substance from simple constituents. As a rule, the value of the standard enthalpy is negative, since heat is released in most cases during the synthesis of complex substances.
First law of thermodynamics in adiabatic processes
The application of the first law of thermodynamics for isoprocesses can be viewed graphically. For example, consider an adiabatic process in which the amount of heat remains constant throughout the entire time, that is Q= const. Such an isoprocess takes place in thermally insulated systems, or for such a short time that the system does not have time to exchange heat with the external environment. The slow expansion of a gas in a volume-pressure diagram is described by the following curve:
According to the graph, it is possible to justify the application of the first law of thermodynamics to isoprocesses. Since there is no change in the amount of heat in the adiabatic process, the change in internal energy is equal to the amount of work done. dU= - dW
It follows that the internal energy of the system decreases, and its temperature falls.
Examples of adiabatic processes
The converse statement is also true: a decrease in pressure in the absence of heat transfer sharply increases the temperature of the system. Approximately this is how gas expands in internal combustion engines. In Diesel engines, combustible gas is compressed 15 times. A short-term increase in temperature allows the combustible mixture to self-ignite.
We can consider another example of an adiabatic process - the free expansion of gases. To do this, consider the following installation, consisting of two containers:
In the first container there is gas, in the second it is absent. By turning the tap, we will ensure that the gas fills the entire volume allotted to it. If the system is sufficiently isolated, the gas temperature will remain unchanged. Since the gas did no work, the variable dW= const. It turned out that, other things being equal, the temperature of the gas decreases during expansion. The expansion of the gas occurs unevenly, so this process cannot be represented on the "pressure-volume" diagram.
The first law of thermodynamics is a universal law that applies to all observable processes in the Universe. A deep understanding of the causes of certain energy transformations allows us to understand the existing physical phenomena and discover new laws.
For systems in which creatures, thermal processes (absorption or release of heat) are important. According to the first law of thermodynamics, thermodynamic system (eg, steam in a heat engine) can only do work due to its internal. energy or k.-l. ext. source of energy. The first law of thermodynamics is often formulated as the impossibility of the existence of a perpetual motion machine of the first kind, which would do work without drawing energy from some source.
P The first law of thermodynamics introduces the idea of the internal energy of a system as a function of state. When the system is informed of a certain amount of heat Q, the internal changes. energy of the system DU and the system does work A:
DU = Q + A.
P The first law of thermodynamics states that each state of the system is characterized by a certain value of ext. energy U, regardless of how the system is brought to a given state. Unlike the values of U, the values of A and Q depend on the process that led to the change in the state of the system. If the initial and final states a and b are infinitely close (transitions between such states are called infinitesimal processes), the first law of thermodynamics is written as:
This means that an infinitesimal change in ext. energy dU is the total differential of the state function,those. integral \u003d U b - U a, while infinitesimal quantities of heat and work are not differential. values, i.e. the integrals of these infinitesimal quantities depend on the chosen transition path between the states a and b (sometimes they are called incomplete differentials).
From the total number of work produced by the system of volume Y, one can single out the work of a reversible isothermal. extensions under the action of external pressure p e equal to p e V, and all other types of work, each of which can be represented as the product of a certain generalized force acting on the system from the environment by a generalized coordinate x i changing under the influence of the corresponding generalized force. For an infinitesimal process
P The first law of thermodynamics allows you to calculate the max. work obtained with isothermal expansion of an ideal gas, isothermal. evaporation of liquid at post. pressure, establish the laws of adiabatic. expansion of gases, etc. The first law of thermodynamics is the basis of thermochemistry, which considers systems in which heat is absorbed or released as a result of chemical. p-tions, phase transformations. or dissolution (dilution solutions).
If the system exchanges with the environment not only energy, but also in-tion (see Open system), the change in ext. the energy of the system during the transition from the initial state to the final state includes, in addition to the work A and heat Q, also the so-called. mass energy Z. An infinitesimal amount of mass energy in an infinitesimal process is determined by chem. potentials m k of each of the components of the system:= , where dN k is an infinitesimal change in the number of moles of the k-th component as a result of exchange with the medium.
In the case of a quasi-static process, at which the system at each moment of time is in equilibrium with the environment, the first law of thermodynamics in general view has a trace. mat. expression:
where p and m k are equal to the corresponding values for