It is convenient to consider a particular physical phenomenon or class of phenomena using models of varying degrees of approximation. For example, when describing the behavior of a gas, a physical model is used - an ideal gas.
Any model has limits of applicability, beyond which it needs to be refined or more complex options applied. Here we consider a simple case of describing the internal energy of a physical system based on the most essential properties of gases within certain limits.
Ideal gas
This physical model, for the convenience of describing some fundamental processes, simplifies a real gas as follows:
- Neglects the size of gas molecules. This means that there are phenomena for which this parameter is not essential for an adequate description.
- Neglects intermolecular interactions, that is, it accepts that in the processes of interest to it, they appear in negligible time intervals and do not affect the state of the system. In this case, the interactions have the character of an absolutely elastic impact, in which there is no energy loss ondeformation.
- Neglects interaction of molecules with tank walls.
- Assume that the "gas-reservoir" system is characterized by thermodynamic equilibrium.
This model is suitable for describing real gases if pressures and temperatures are relatively low.
Energy state of a physical system
Any macroscopic physical system (body, gas or liquid in a vessel) has, in addition to its own kinetic and potential, one more type of energy - internal. This value is obtained by summing up the energies of all the subsystems that make up the physical system - molecules.
Each molecule in a gas also has its own potential and kinetic energy. The latter is due to the continuous chaotic thermal motion of molecules. The various interactions between them (electrical attraction, repulsion) are determined by potential energy.
It must be remembered that if the energy state of any parts of the physical system does not have any effect on the macroscopic state of the system, then it is not taken into account. For example, under normal conditions, nuclear energy does not manifest itself in changes in the state of a physical object, so it does not need to be taken into account. But at high temperatures and pressures, this is already necessary.
Thus, the internal energy of the body reflects the nature of the movement and interaction of its particles. This means that the term is synonymous with the commonly used term "thermal energy".
Monatomic ideal gas
Monatomic gases, that is, those whose atoms are not combined into molecules, exist in nature - these are inert gases. Gases such as oxygen, nitrogen or hydrogen can exist in such a state only under conditions when energy is expended from the outside to constantly renew this state, since their atoms are chemically active and tend to combine into a molecule.
Let's consider the energy state of a monatomic ideal gas placed in a vessel of some volume. This is the simplest case. We remember that the electromagnetic interaction of atoms between themselves and with the walls of the vessel, and, consequently, their potential energy is negligible. So the internal energy of a gas only includes the sum of the kinetic energies of its atoms.
It can be calculated by multiplying the average kinetic energy of atoms in a gas by their number. The average energy is E=3/2 x R / NA x T, where R is the universal gas constant, NA is Avogadro's number, T is absolute gas temperature. The number of atoms is calculated by multiplying the amount of matter by the Avogadro constant. The internal energy of a monatomic gas will be equal to U=NA x m / M x 3/2 x R/NA x T=3/2 x m / M x RT. Here m is the mass and M is the molar mass of the gas.
Assume that the chemical composition of the gas and its mass always remain the same. In this case, as can be seen from the formula we obtained, the internal energy depends only on the temperature of the gas. For real gas, it will be necessary to take into account, in addition totemperature, change in volume as it affects the potential energy of atoms.
Molecular gases
In the above formula, the number 3 characterizes the number of degrees of freedom of motion of a monatomic particle - it is determined by the number of coordinates in space: x, y, z. For the state of a monatomic gas, it does not matter at all whether its atoms rotate.
Molecules are spherically asymmetric, therefore, when determining the energy state of molecular gases, it is necessary to take into account the kinetic energy of their rotation. Diatomic molecules, in addition to the listed degrees of freedom associated with translational motion, have two more associated with rotation around two mutually perpendicular axes; polyatomic molecules have three such independent axes of rotation. Consequently, particles of diatomic gases are characterized by the number of degrees of freedom f=5, while polyatomic molecules have f=6.
Due to the randomness inherent in thermal motion, all directions of both rotational and translational movement are absolutely equally probable. The average kinetic energy contributed by each type of motion is the same. Therefore, we can substitute the value of f into the formula, which allows us to calculate the internal energy of an ideal gas of any molecular composition: U=f / 2 x m / M x RT.
Of course, we see from the formula that this value depends on the amount of substance, that is, on how much and what kind of gas we took, as well as on the structure of the molecules of this gas. However, since we agreed not to change the mass and chemical composition, then take into accountwe only need temperature.
Now let's look at how the value of U is related to other characteristics of the gas - volume, as well as pressure.
Internal energy and thermodynamic state
Temperature, as you know, is one of the parameters of the thermodynamic state of the system (in this case, gas). In an ideal gas, it is related to pressure and volume by the relation PV=m / M x RT (the so-called Clapeyron-Mendeleev equation). Temperature determines heat energy. So the latter can be expressed in terms of a set of other state parameters. It is indifferent to the previous state, as well as to the way it was changed.
Let's see how the internal energy changes when the system passes from one thermodynamic state to another. Its change in any such transition is determined by the difference between the initial and final values. If the system returned to its original state after some intermediate state, then this difference will be equal to zero.
Suppose we have heated the gas in the tank (that is, we have brought additional energy to it). The thermodynamic state of the gas has changed: its temperature and pressure have increased. This process goes without changing the volume. The internal energy of our gas has increased. After that, our gas gave up the supplied energy, cooling down to its original state. Such a factor as, for example, the speed of these processes, will not matter. The resulting change in the internal energy of the gas at any rate of heating and cooling is zero.
The important point is that the same value of thermal energy can correspond to not one, but several thermodynamic states.
The nature of the change in thermal energy
In order to change energy, work must be done. Work can be done by the gas itself or by an external force.
In the first case, the expenditure of energy for doing work is done at the expense of the internal energy of the gas. For example, we had compressed gas in a tank with a piston. If the piston is released, the expanding gas will begin to lift it, doing work (for it to be useful, let the piston lift some kind of load). The internal energy of the gas will decrease by the amount spent on work against gravity and friction forces: U2=U1 – A. In this case, the work of the gas is positive because the direction of the force applied to the piston is the same as the direction of movement of the piston.
Let's start lowering the piston, doing work against the force of gas pressure and again against the forces of friction. Thus, we will inform the gas of a certain amount of energy. Here, the work of external forces is already considered positive.
In addition to mechanical work, there is also such a way to take energy from the gas or give it energy, such as heat transfer (heat transfer). We have already met him in the example of heating a gas. The energy transferred to the gas during heat transfer processes is called the amount of heat. There are three types of heat transfer: conduction, convection, and radiative transfer. Let's take a closer look at them.
Thermal conductivity
The ability of a substance to exchange heat,carried out by its particles by transferring kinetic energy to each other during mutual collisions during thermal motion - this is thermal conductivity. If a certain area of the substance is heated, that is, a certain amount of heat is imparted to it, the internal energy after a while, through collisions of atoms or molecules, will be distributed uniformly among all particles on average.
It is clear that thermal conductivity strongly depends on the frequency of collisions, and that, in turn, on the average distance between particles. Therefore, a gas, especially an ideal gas, is characterized by a very low thermal conductivity, and this property is often used for thermal insulation.
Of real gases, thermal conductivity is higher for those whose molecules are the lightest and at the same time polyatomic. Molecular hydrogen meets this condition to the greatest extent, and radon, as the heaviest monatomic gas, to the least extent. The rarer the gas, the worse heat conductor it is.
In general, the transfer of energy by conduction for an ideal gas is a very inefficient process.
Convection
Much more efficient for a gas is this type of heat transfer, such as convection, in which the internal energy is distributed through the flow of matter circulating in the gravitational field. The upward flow of hot gas is formed due to the Archimedean force, since it is less dense due to thermal expansion. The hot gas moving upwards is constantly replaced by colder gas - the circulation of gas flows is established. Therefore, in order to ensure efficient, that is, the fastest heating through convection, it is necessary to heat the gas tank from below - just like a kettle with water.
If it is necessary to take away some amount of heat from the gas, then it is more efficient to place the refrigerator at the top, since the gas that gave energy to the refrigerator will rush down under the influence of gravity.
An example of convection in gas is the heating of indoor air using heating systems (they are placed in the room as low as possible) or cooling using an air conditioner, and in natural conditions, the phenomenon of thermal convection causes the movement of air masses and affects the weather and climate.
In the absence of gravity (with weightlessness in a spacecraft), convection, that is, the circulation of air flows, is not established. So it makes no sense to light gas burners or matches on board the spacecraft: hot combustion products will not be discharged upwards, and oxygen will be supplied to the fire source, and the flame will die out.
Radiant transfer
A substance can also heat up under the action of thermal radiation, when atoms and molecules acquire energy by absorbing electromagnetic quanta - photons. At low photon frequencies, this process is not very efficient. Recall that when we open a microwave oven, we find hot food inside, but not hot air. With an increase in the frequency of radiation, the effect of radiation heating increases, for example, in the upper atmosphere of the Earth, a highly rarefied gas is intensely heated andionized by solar ultraviolet.
Different gases absorb thermal radiation to varying degrees. So, water, methane, carbon dioxide absorb it quite strongly. The phenomenon of the greenhouse effect is based on this property.
The first law of thermodynamics
Generally speaking, the change in internal energy through gas heating (heat transfer) also comes down to doing work either on gas molecules or on them through an external force (which is denoted in the same way, but with the opposite sign). What work is done in this way of transition from one state to another? The law of conservation of energy will help us answer this question, more precisely, its concretization in relation to the behavior of thermodynamic systems - the first law of thermodynamics.
The law, or the universal principle of conservation of energy, in its most generalized form says that energy is not born from nothing and does not disappear without a trace, but only passes from one form to another. In relation to a thermodynamic system, this should be understood in such a way that the work done by the system is expressed in terms of the difference between the amount of heat imparted to the system (ideal gas) and the change in its internal energy. In other words, the amount of heat communicated to the gas is spent on this change and on the operation of the system.
This is much easier to write in the form of formulas: dA=dQ – dU, and accordingly, dQ=dU + dA.
We already know that these quantities do not depend on the way in which the transition between states is made. The speed of this transition and, as a result, the efficiency depends on the method.
As for the secondthe beginning of thermodynamics, then it sets the direction of change: heat cannot be transferred from a colder (and therefore less energetic) gas to a hotter one without additional energy input from the outside. The second law also indicates that part of the energy expended by the system to perform work inevitably dissipates, is lost (does not disappear, but turns into an unusable form).
Thermodynamic processes
Transitions between the energy states of an ideal gas can have different patterns of change in one or another of its parameters. The internal energy in the processes of transitions of different types will also behave differently. Let us briefly consider several types of such processes.
- The isochoric process proceeds without a change in volume, therefore, the gas does no work. The internal energy of the gas changes as a function of the difference between the final and initial temperatures.
- Isobaric process occurs at constant pressure. The gas does work, and its thermal energy is calculated in the same way as in the previous case.
- Isothermal process is characterized by a constant temperature, and, hence, the thermal energy does not change. The amount of heat received by the gas is entirely spent on doing work.
- Adiabatic, or adiabatic process takes place in a gas without heat transfer, in a thermally insulated tank. Work is done only at the expense of thermal energy: dA=- dU. With adiabatic compression, the thermal energy increases, with expansion, respectivelydecreasing.
Various isoprocesses underlie the functioning of thermal engines. Thus, the isochoric process takes place in a gasoline engine at the extreme positions of the piston in the cylinder, and the second and third strokes of the engine are examples of an adiabatic process. When obtaining liquefied gases, adiabatic expansion plays an important role - thanks to it, gas condensation becomes possible. Isoprocesses in gases, in the study of which one cannot do without the concept of the internal energy of an ideal gas, are characteristic of many natural phenomena and are used in various branches of technology.
