In thermodynamics, thermal energy (also called internal energy) is defined as the energy associated with microscopic forms of energy. It is an extensive quantity, and it depends on the size of the system or on the amount of substance it contains. The SI unit of thermal energy is the joule (J). It is the energy contained within the system, excluding the kinetic energy of motion of the system as a whole and the potential energy of the system. Microscopic forms of energy include those due to the rotation, vibration, translation, and interactions among the molecules of a substance. None of these forms of energy can be measured or evaluated directly, but techniques have been developed to evaluate the change in the total sum of all these microscopic forms of energy.
Microscopic Energy
Thermal Energy – Definition
Internal energy involves energy on the microscopic scale. It may be divided into microscopic potential energy, Upot, and microscopic kinetic energy, Ukin, components:
U = Upot + Ukin
where the microscopic kinetic energy, Ukin, involves the motions of all the system’s particles for the center-of-mass frame. For an ideal monatomic gas, this is just the translational kinetic energy of the linear motion of the atoms. Monoatomic particles do not rotate or vibrate. The behavior of the system is well described by kinetic theory of gases. Kinetic theory is based on the fact that during an elastic collision between a molecule with high kinetic energy and one with low kinetic energy, part of energy will transfer to the molecule of lower kinetic energy. However, there is rotational and vibrational kinetic energy as well as for polyatomic gases.
The microscopic potential energy, Upot, involves the chemical bonds between the atoms that make up the molecules, binding forces in the nucleus, and the physical force fields within the system (e.g., electric or magnetic fields).
In liquids and solids there is significant component of potential energy associated with the intermolecular attractive forces.
Thermal Energy and Heat
While thermal energy refers to the total energy of all the molecules within the object, heat is the amount of energy flowing spontaneously from one body to another due to their temperature difference. Heat is a form of energy, but it is energy in transit. Heat is not a property of a system. However, the transfer of energy as heat occurs at the molecular level due to a temperature difference.
Consider a metal block at high temperature that consists of atoms oscillating intensely around their average positions. At low temperatures, the atoms continue to oscillate but with less intensity. If a hotter block of metal is put in contact with a cooler block, the intensely oscillating atoms at the edge of the hotter block give off their kinetic energy to the less oscillating atoms at the edge of the cool block. In this case, there is energy transfer between these two blocks, and heat flows from the hotter to the cooler block by these random vibrations.
Distinguishing Temperature, Heat, and Thermal Energy
A clear distinction between these three properties can be made using the kinetic theory.
- Temperature is related to the kinetic energies of the molecules of material, and it is the average kinetic energy of individual molecules.
- Internal energy refers to the total energy of all the molecules within the object. Therefore, it is an extensive property when two equal-mass hot ingots of steel may have the same temperature, but two of them have twice as much internal energy as one does.
- Finally, heat is the amount of energy flowing spontaneously from one body to another due to their temperature difference.
When a temperature difference exists, it must be added, and heat flows spontaneously from the warmer to the colder system. Thus, if a 5 kg cube of steel at 100°C is placed in contact with a 500 kg cube of steel at 20°C, heat flows from the cube at 300°C to the cube at 20°C even though the internal energy of the 20°C cube is much greater because there is so much more of it.
A particularly important concept is thermodynamic equilibrium. In general, when two objects are brought into thermal contact, heat will flow between them until they come into equilibrium with each other.
Thermal Conductivity
The heat transfer characteristics of solid material are measured by a property called the thermal conductivity, k (or λ), measured in W/m.K. It measures a substance’s ability to transfer heat through a material by conduction. Note that Fourier’s law applies to all matter, regardless of its state (solid, liquid, or gas). Therefore, it is also defined for liquids and gases.
The thermal conductivity of most liquids and solids varies with temperature, and for vapors, it also depends upon pressure. In general:
Most materials are nearly homogeneous. Therefore, we can usually write k = k (T). Similar definitions are associated with thermal conductivities in the y- and z-directions (ky, kz), but for an isotropic material, the thermal conductivity is independent of the direction of transfer, kx = ky = kz = k.
The previous equation follows that the conduction heat flux increases with increasing thermal conductivity and increases with increasing temperature differences. In general, the thermal conductivity of a solid is larger than that of a liquid, which is larger than that of a gas. This trend is due largely to differences in intermolecular spacing for the two states of matter. In particular, diamond has the highest hardness and thermal conductivity of any bulk material.
Internal Energy and the First Law of Thermodynamics
In thermodynamics, the concept of energy is broadened to account for other observed changes. The principle of conservation of energy is extended to include a wide variety of ways systems interact with their surroundings. The only ways the energy of a closed system can be changed are through the transfer of energy by work or by heat. Further, based on the experiments of Joule and others, a fundamental aspect of the energy concept is that energy is conserved. This principle is known as the first law of thermodynamics. The first law of thermodynamics can be written in various forms:
In words:
Equation form:
∆Eint = Q – W
where Eint represents the internal energy of the material, which depends only on the material’s state (temperature, pressure, and volume). Q is the net heat added to the system and W is the net work done by the system. We must be careful and consistent in following the sign conventions for Q and W. Because W in the equation is the work done by the system, then if work is done on the system, W will be negative, and Eint will increase.
Similarly, Q is positive for heat added to the system, so Q is negative if heat leaves the system. This tells us the following: The internal energy of a system tends to increase if heat is absorbed by the system or if positive work is done on the system. Conversely, the internal energy tends to decrease if heat is lost by the system or if negative work is done on the system. It must be added Q and W are path-dependent, while Eint is path-independent.
Differential form:
dEint = dQ – dW
The internal energy Eint of a system tends to increase if energy is added as heat Q and tends to decrease if energy is lost as work W done by the system.