Thermodynamics of double-walled carbon nanotubes

<p><strong>Thermodynamics of double-walled carbon nanotubes</strong></p> <p>Junjie Chen</p> <p>Department of Energy and Power Engineering, School of Mechanical and Power Engineering, Henan Polytechnic University, 2000 Century Avenue, Jiaozuo, Henan, 454000, P.R. China</p> <p>Contributor: Junjie Chen, ORCID: 0000-0002-5022-6863, E-mail address: koncjj@gmail.com</p> <p>&nbsp;</p> <p>Thermodynamics deals with the transfer of energy from one place to another and from one form to another. The most important laws of thermodynamics are stated herein. The zeroth law of thermodynamics. When two systems are each in thermal equilibrium with a third system, the first two systems are in thermal equilibrium with each other. This property makes it meaningful to use thermometers as the third system and to define a temperature scale. The first law of thermodynamics. The change in a system&#39;s internal energy is equal to the difference between heat added to the system from its surroundings and work done by the system on its surroundings. The second law of thermodynamics. Heat does not flow spontaneously from a colder region to a hotter region, or, equivalently, heat at a given temperature cannot be converted entirely into work. Consequently, the entropy of a closed system, or heat energy per unit temperature, increases over time toward some maximum value. Thus, all closed systems tend toward an equilibrium state in which entropy is at a maximum and no energy is available to do useful work. The third law of thermodynamics. The entropy of a perfect crystal of an element in its most stable form tends to zero as the temperature approaches absolute zero. This allows an absolute scale for entropy to be established that, from a statistical point of view, determines the degree of randomness or disorder in a system. The laws of thermodynamics are deceptively simple to state, but they are far-reaching in their consequences. The first law is put into action by considering the flow of energy across the boundary separating a system from its surroundings. Consider the classic example of a gas enclosed in a cylinder with a movable piston. The walls of the cylinder act as the boundary separating the gas inside from the world outside, and the movable piston provides a mechanism for the gas to do work by expanding against the force holding the piston in place. If the gas does work as it expands, and absorbs heat from its surroundings through the walls of the cylinder, then this corresponds to a net flow of energy across the boundary to the surroundings. In order to conserve the total energy, there must be a counterbalancing change in the internal energy of the gas. From a formal mathematical point of view, the incremental change in the internal energy is an exact differential, while the corresponding incremental changes in heat and work are not, because the definite integrals of these quantities are path-dependent. These concepts can be used to great advantage in a precise mathematical formulation of thermodynamics. The science of thermodynamics provides a rich variety of formulas and techniques that allow the maximum possible amount of information to be extracted from a limited number of laboratory measurements of the properties of materials. However, as the thermodynamic state of a system depends on several variables, such as temperature, pressure, and volume, in practice it is necessary first to decide how many of these are independent and then to specify what variables are allowed to change while others are held constant. For this reason, the mathematical language of partial differential equations is indispensable to the further elucidation of the subject of thermodynamics. Of especially critical importance in the application of thermodynamics are the amounts of work required to make substances expand or contract and the amounts of heat required to change the temperature of substances. The first is determined by the equation of state of the substance and the second by its heat capacity. Once these physical properties have been fully characterized, they can be used to calculate other thermodynamic properties, such as the free energy of the substance under various conditions of temperature and pressure.</p>