Thermodynamics
Thermodynamics->> MICROSCOPIC BASIS OF THERMODYNAMICS
The recognition that all matter is made up of molecules provided a microscopic foundation for thermodynamics. A thermodynamic system consisting of a pure substance can be described as a collection of like molecules, each with its individual motion describable in terms of such mechanical variables as velocity and momentum. At least in principle, it should therefore be possible to derive the collective properties of the system by solving equations of motion for the molecules. In this sense, thermodynamics could be regarded as a mere application of the laws of mechanics to the microscopic system.
Objects of ordinary size—that is, ordinary on the human scale—contain immense numbers (on the order of 1024) of molecules. Assuming the molecules to be spherical, each would need three variables to describe its position and three more to describe its velocity. Describing a macroscopic system in this way would be a task that even the largest modern computer could not manage. A complete solution of these equations, furthermore, would tell us where each molecule is and what it is doing at every moment. Such a vast quantity of information would be too detailed to be useful and too transient to be important.
Statistical methods were devised therefore to obtain averages of the mechanical variables of the molecules in a system and to provide the gross features of the system. These gross features turn out to be, precisely, the macroscopic thermodynamic variables. The statistical treatment of molecular mechanics is called statistical mechanics, and it anchors thermodynamics to mechanics.
Viewed from the statistical perspective, temperature represents a measure of the average kinetic energy of the molecules of a system. Increases in temperature reflect increases in the vigor of molecular motion. When two systems are in contact, energy is transferred between molecules as a result of collisions. The transfer will continue until uniformity is achieved, in a statistical sense, which corresponds to thermal equilibrium. The kinetic energy of the molecules also corresponds to heat and—together with the potential energy arising from interaction between molecules—makes up the internal energy of a system.
The conservation of energy, a well-known law of mechanics, translates readily to the first law of thermodynamics, and the concept of entropy translates into the extent of disorder on the molecular scale. By assuming that all combinations of molecular motion are equally likely, thermodynamics shows that the more disordered the state of an isolated system, the more combinations can be found that could give rise to that state, and hence the more frequently it will occur. The probability of the more disordered state occurring overwhelms the probability of the occurrence of all other states. This probability provides a statistical basis for definitions of both equilibrium state and entropy.
Finally, temperature can be reduced by taking energy out of a system, that is, by reducing the vigor of molecular motion. Absolute zero corresponds to the state of a system in which all its constituents are at rest. This is, however, a notion from classical physics. In terms of quantum mechanics, residual molecular motion will exist even at absolute zero. An analysis of the statistical basis of the third law goes beyond the scope of the present discussion.
See Gases; Quantum Theory; Uncertainty Principle.
Objects of ordinary size—that is, ordinary on the human scale—contain immense numbers (on the order of 1024) of molecules. Assuming the molecules to be spherical, each would need three variables to describe its position and three more to describe its velocity. Describing a macroscopic system in this way would be a task that even the largest modern computer could not manage. A complete solution of these equations, furthermore, would tell us where each molecule is and what it is doing at every moment. Such a vast quantity of information would be too detailed to be useful and too transient to be important.
Statistical methods were devised therefore to obtain averages of the mechanical variables of the molecules in a system and to provide the gross features of the system. These gross features turn out to be, precisely, the macroscopic thermodynamic variables. The statistical treatment of molecular mechanics is called statistical mechanics, and it anchors thermodynamics to mechanics.
Viewed from the statistical perspective, temperature represents a measure of the average kinetic energy of the molecules of a system. Increases in temperature reflect increases in the vigor of molecular motion. When two systems are in contact, energy is transferred between molecules as a result of collisions. The transfer will continue until uniformity is achieved, in a statistical sense, which corresponds to thermal equilibrium. The kinetic energy of the molecules also corresponds to heat and—together with the potential energy arising from interaction between molecules—makes up the internal energy of a system.
The conservation of energy, a well-known law of mechanics, translates readily to the first law of thermodynamics, and the concept of entropy translates into the extent of disorder on the molecular scale. By assuming that all combinations of molecular motion are equally likely, thermodynamics shows that the more disordered the state of an isolated system, the more combinations can be found that could give rise to that state, and hence the more frequently it will occur. The probability of the more disordered state occurring overwhelms the probability of the occurrence of all other states. This probability provides a statistical basis for definitions of both equilibrium state and entropy.
Finally, temperature can be reduced by taking energy out of a system, that is, by reducing the vigor of molecular motion. Absolute zero corresponds to the state of a system in which all its constituents are at rest. This is, however, a notion from classical physics. In terms of quantum mechanics, residual molecular motion will exist even at absolute zero. An analysis of the statistical basis of the third law goes beyond the scope of the present discussion.
See Gases; Quantum Theory; Uncertainty Principle.
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