The heat capacity of a gas is the amount of energy that the body absorbs when it is heated by one degree. Let us analyze the main characteristics of this physical quantity.
Definitions
The specific heat of a gas is the unit mass of a particular substance. Its units are J / (kg · K). The amount of heat that is absorbed by the body in the process of changing its state of aggregation is associated not only with the initial and final state, but also with the method of transition.
Subdivision
The heat capacity of gases is divided by the value determined at a constant volume (C v ), constant pressure (C p ).
In the case of heating without changing the pressure, a certain amount of heat is spent on the work of expanding the gas, and part of the energy is expended to increase the internal energy.
The heat capacity of gases at constant pressure is determined by the amount of heat that is spent on increasing internal energy.
Gaseous state: features, description
The heat capacity of an ideal gas is determined taking into account the fact that C p -C v = R. The latter value is called the universal gas constant. Its value corresponds to 8.314 J / (mol · K).
When carrying out theoretical calculations of heat capacity, for example, describing the relationship with temperature, it is not enough to use only thermodynamic methods, it is important to arm yourself with elements of static physics.
The heat capacity of gases involves the calculation of the average energy of the translational motion of some molecules. Such motion is summed up from the rotational and translational motion of the molecule, as well as from the internal vibrations of atoms.
In static physics, there is information that for every degree of freedom of rotational and translational motion, for gas, a value is equal to half the universal gas constant.
Interesting Facts
A particle of a monatomic gas is supposed to have three translational degrees of freedom, therefore, the specific heat of the gas has three translational, two rotational, and one vibrational degrees of freedom. The law of their uniform distribution leads to the equalization of specific heat at constant volume to R.
During the experiments, it was found that the heat capacity of the diatomic gas corresponds to R. Such a discrepancy between theory and practice is explained by the fact that the heat capacity of an ideal gas is associated with quantum effects, so it is important to use statistics based on quantum mechanics in the calculations.
Based on the foundations of quantum mechanics, any system of particles that oscillate or rotate, including gas molecules, has only some discrete energy values.
If the energy of thermal motion in the system is insufficient to excite oscillations of a certain frequency, such movements do not contribute to the total heat capacity of the system.
As a result, a specific degree of freedom becomes “frozen”; it is impossible to apply the law of equal distribution to it.
The heat capacity of gases is an important characteristic of the state on which the functioning of the entire thermodynamic system depends.
The temperature at which the equidistribution law can be applied to the vibrational or rotational degrees of freedom, is characterized by quantum theory, connects the Planck constant with the Boltzmann constant.
Diatomic Gases
The intervals between the rotational energy levels of such gases are a small number of degrees. The exception is hydrogen, in which the temperature value is determined by hundreds of degrees.
That is why the heat capacity of a gas at constant pressure is difficult to describe by the law of uniform distribution. In quantum statistics, when determining the heat capacity, it is taken into account that its vibrational part rapidly decreases in the event of a decrease in temperature and reaches a zero value.
A similar phenomenon is explained by the fact that at room temperatures there is practically no vibrational part of the specific heat; for a diatomic gas, it corresponds to the constant R.
The heat capacity of a gas with a constant volume in the case of low temperature indicators is determined using quantum statistics. There is the Nernst principle, which is called the third law of thermodynamics. Based on its formulation, the molar heat capacity of the gas will decrease with decreasing temperature, tend to zero.
Features of solids
If the heat capacity of the gas mixture can be explained using quantum statistics, then for the solid state of aggregation, the thermal motion is characterized by insignificant particle vibrations near the equilibrium position.
Each atom has three vibrational degrees of freedom, therefore, in accordance with the law of equal distribution, the molar heat capacity of a solid can be calculated as 3nR, and n is the number of atoms in the molecule.
In practice, such a number is the limit to which the heat capacity of a solid tends at high temperature indicators.
The maximum can be obtained at ordinary temperatures for some elements, including metals. For n = 1, the law of Dulong and Petit holds, but for complex substances it is rather difficult to reach such a limit. Since in reality the limit cannot be obtained, decomposition or melting of the solid occurs.
History of quantum theory
Einstein and Debye at the beginning of the twentieth century are considered the founders of quantum theory. It is based on the quantization of vibrational motions of atoms in a particular crystal. In the case of low temperature indicators, the heat capacity of a solid is directly proportional to the absolute value taken in the cube. This dependence was called Debye's law. As a criterion that allows you to distinguish between low and high temperature indicators, we take their comparison with the Debye temperature.
Such a quantity is determined by the vibration spectrum of the atom in the body, therefore, it seriously depends on the features of its crystal structure.
QD is a value that has several hundred K, but, for example, in diamond it is significantly higher.
Conductivity electrons make a significant contribution to the heat capacity of metals. For its calculation, quantum Fermi statistics are used. Electronic conductivity for metal atoms is directly proportional to absolute temperature. Since it is an insignificant quantity, it is taken into account only at temperatures tending to absolute zero.
Methods for determining heat capacity
Calorimetry is the main experimental method. To carry out a theoretical calculation of heat capacity, statistical thermodynamics is used. It is valid for an ideal gas, as well as for crystalline bodies, carried out on the basis of experimental data on the structure of matter.
Empirical methods for calculating the heat capacity of an ideal gas are based on the idea of the chemical structure, the contribution of individual groups of atoms to C p .
For liquids, methods are also used that are based on the use of thermodynamic cycles that allow us to switch from the heat capacity of an ideal gas to a liquid through the derivative of the enthalpy of the evaporation process.
In the case of a solution, the calculation of heat capacity as an additive function is not allowed, since the excess heat capacity of the solution is mainly significant.
To evaluate it, a molecular statistical theory of solutions is required. The most difficult is the identification of the heat capacity of heterogeneous systems in thermodynamic analysis.
Conclusion
The study of heat capacity allows us to calculate the energy balance of processes occurring in chemical reactors, as well as in other devices of chemical production. In addition, this value is necessary for the selection of optimal types of coolants.
At present, experimental determination of the heat capacity of substances for various temperature ranges is carried out - from low values to high values - the main option for determining the thermodynamic characteristics of a substance. When calculating the entropy and enthalpy of a substance, the heat capacity integrals are used. Information on the heat capacity of chemicals in a certain temperature range allows you to calculate the thermal effect of the process. Information on the heat capacity of solutions allows one to calculate their thermodynamic parameters at any temperature values within the analyzed interval.
For example, it is typical for a liquid to spend part of the heat on changing the potential energy of the reacting molecules. This value is called the "configuration" heat capacity, used to describe solutions.
It is difficult to carry out full-fledged mathematical calculations without taking into account the thermodynamic characteristics of a substance and its state of aggregation. That is why for liquids, gases, solids use such a characteristic as specific heat, which allows to characterize the energy parameters of the substance.