
Thermal Resistance
... Prevost Theory of Heat Exchange (1792) ............................................................................................... 61 Stefan-Boltzmann Law ................................................................................................................................. 62 Newton's ...
... Prevost Theory of Heat Exchange (1792) ............................................................................................... 61 Stefan-Boltzmann Law ................................................................................................................................. 62 Newton's ...
Chapter 4
... Then in Chap. 3, we learned how to determine the thermodynamics properties of substances. In this chapter, we apply the energy balance relation to systems that do not involve any mass flow across their boundaries; that is, closed systems. We start this chapter with a discussion of the moving boundar ...
... Then in Chap. 3, we learned how to determine the thermodynamics properties of substances. In this chapter, we apply the energy balance relation to systems that do not involve any mass flow across their boundaries; that is, closed systems. We start this chapter with a discussion of the moving boundar ...
Document
... box: for 1 particle the energy of the state is identified by three quantum number, nx , ny , and nz . • One particle would remain in its state indefenitely Now we add more particles- ecah one of these is in a state specified by these quantum numbers (nx , ny , nz) with a total fixed energy • Collisi ...
... box: for 1 particle the energy of the state is identified by three quantum number, nx , ny , and nz . • One particle would remain in its state indefenitely Now we add more particles- ecah one of these is in a state specified by these quantum numbers (nx , ny , nz) with a total fixed energy • Collisi ...
notes on elementary statistical mechanics
... way one also has that U1 = U2 ∝ V · λd . In the thermodynamic limit V → ∞ faster than S and hence Uint can be neglected in Eq. (1.1) (is it true also in an infinite-dimensional space with d = ∞?). This shows that U is an extensive quantity. Notice that the same argument does not apply in system with ...
... way one also has that U1 = U2 ∝ V · λd . In the thermodynamic limit V → ∞ faster than S and hence Uint can be neglected in Eq. (1.1) (is it true also in an infinite-dimensional space with d = ∞?). This shows that U is an extensive quantity. Notice that the same argument does not apply in system with ...
Exercises in Statistical Mechanics ====== [Exercise 0010
... (a) Evaluate the entropy of the system S (n) where n is the number of particles in the upper energy level; assume n >> 1. Draw a rough plot of S (n). (b) Find the most probable value of n and its mean square fluctuation. (c) Relate n to the energy E of the system and find the temperature. Show that ...
... (a) Evaluate the entropy of the system S (n) where n is the number of particles in the upper energy level; assume n >> 1. Draw a rough plot of S (n). (b) Find the most probable value of n and its mean square fluctuation. (c) Relate n to the energy E of the system and find the temperature. Show that ...
Entropy. Temperature. Chemical Potential
... the multiplicity should be proportional to U (3N −1)/2 ≈ U 3N/2 , where N is the number of atoms. It is possible to generalize this result to say that the multiplicity will be proportional to U f N/2 , where f is the number of degrees of freedom a la equipartition. This result should hold for any sy ...
... the multiplicity should be proportional to U (3N −1)/2 ≈ U 3N/2 , where N is the number of atoms. It is possible to generalize this result to say that the multiplicity will be proportional to U f N/2 , where f is the number of degrees of freedom a la equipartition. This result should hold for any sy ...
Exercises in Statistical Mechanics
... (a) Evaluate the entropy of the system S (n) where n is the number of particles in the upper energy level; assume n >> 1. Draw a rough plot of S (n). (b) Find the most probable value of n and its mean square fluctuation. (c) Relate n to the energy E of the system and find the temperature. Show that ...
... (a) Evaluate the entropy of the system S (n) where n is the number of particles in the upper energy level; assume n >> 1. Draw a rough plot of S (n). (b) Find the most probable value of n and its mean square fluctuation. (c) Relate n to the energy E of the system and find the temperature. Show that ...
The Laws of Thermodynamics - FSM-UKSW
... Each degree of freedom contributes 12 R to the molar specific heat. Because an atomic ideal gas can move in three directions, it has a molar specific heat capacity Cv 3( 12 R) 32 R . A diatomic gas like molecular oxygen, O2, can also tumble in two different directions. This adds 2 12 R R to ...
... Each degree of freedom contributes 12 R to the molar specific heat. Because an atomic ideal gas can move in three directions, it has a molar specific heat capacity Cv 3( 12 R) 32 R . A diatomic gas like molecular oxygen, O2, can also tumble in two different directions. This adds 2 12 R R to ...
Equipartition theorem

In classical statistical mechanics, the equipartition theorem is a general formula that relates the temperature of a system with its average energies. The equipartition theorem is also known as the law of equipartition, equipartition of energy, or simply equipartition. The original idea of equipartition was that, in thermal equilibrium, energy is shared equally among all of its various forms; for example, the average kinetic energy per degree of freedom in the translational motion of a molecule should equal that of its rotational motions.The equipartition theorem makes quantitative predictions. Like the virial theorem, it gives the total average kinetic and potential energies for a system at a given temperature, from which the system's heat capacity can be computed. However, equipartition also gives the average values of individual components of the energy, such as the kinetic energy of a particular particle or the potential energy of a single spring. For example, it predicts that every atom in a monatomic ideal gas has an average kinetic energy of (3/2)kBT in thermal equilibrium, where kB is the Boltzmann constant and T is the (thermodynamic) temperature. More generally, it can be applied to any classical system in thermal equilibrium, no matter how complicated. The equipartition theorem can be used to derive the ideal gas law, and the Dulong–Petit law for the specific heat capacities of solids. It can also be used to predict the properties of stars, even white dwarfs and neutron stars, since it holds even when relativistic effects are considered.Although the equipartition theorem makes very accurate predictions in certain conditions, it becomes inaccurate when quantum effects are significant, such as at low temperatures. When the thermal energy kBT is smaller than the quantum energy spacing in a particular degree of freedom, the average energy and heat capacity of this degree of freedom are less than the values predicted by equipartition. Such a degree of freedom is said to be ""frozen out"" when the thermal energy is much smaller than this spacing. For example, the heat capacity of a solid decreases at low temperatures as various types of motion become frozen out, rather than remaining constant as predicted by equipartition. Such decreases in heat capacity were among the first signs to physicists of the 19th century that classical physics was incorrect and that a new, more subtle, scientific model was required. Along with other evidence, equipartition's failure to model black-body radiation—also known as the ultraviolet catastrophe—led Max Planck to suggest that energy in the oscillators in an object, which emit light, were quantized, a revolutionary hypothesis that spurred the development of quantum mechanics and quantum field theory.