Paul Ehrenfest: The Genesis of the Adiabatic Hypothesis, 1911–1914
... target of continuing debate: What is the relationship between classical mechanics and the new quantum mechanics? We also will show in light of EHRENFEST’s correspondence and notebooks that the dates and contents of his publications of 1913 do not provide a fair basis for an account of the evolution ...
... target of continuing debate: What is the relationship between classical mechanics and the new quantum mechanics? We also will show in light of EHRENFEST’s correspondence and notebooks that the dates and contents of his publications of 1913 do not provide a fair basis for an account of the evolution ...
Modern Thermodynamics
... Connecting Models to Reality . . . . . . . . . . . . . . . . . . . . . ...
... Connecting Models to Reality . . . . . . . . . . . . . . . . . . . . . ...
2007 exam 3 with answers
... The factory calibration states that the heat capacity of the calorimeter itself is 50 J/K (Ccal = 50 J/K). You decide to check for yourself what Ccal is; you fill the calorimeter with 2 L of water, and detonate 1 g of sugar which you know releases 4000 calories of heat. You then measure a temperatur ...
... The factory calibration states that the heat capacity of the calorimeter itself is 50 J/K (Ccal = 50 J/K). You decide to check for yourself what Ccal is; you fill the calorimeter with 2 L of water, and detonate 1 g of sugar which you know releases 4000 calories of heat. You then measure a temperatur ...
On the Dipole Approximation
... must be deduced from the time evolution. We will therefore prove that the domain of the quantum harmonic oscillator is left invariant by the time evolution, as this space shows just the desired properties: all of its element display a finite kinetic energy, and moreover their variance and the fourth ...
... must be deduced from the time evolution. We will therefore prove that the domain of the quantum harmonic oscillator is left invariant by the time evolution, as this space shows just the desired properties: all of its element display a finite kinetic energy, and moreover their variance and the fourth ...
Conservation Laws - UFDC Image Array 2
... gains speed, and coming up it slows back down. Having a greater speed is like having more money in your checking account, and being high up is like having more in your savings account. The device is simply shuffling funds back and forth between the two. Having more balls doesn’t change anything fund ...
... gains speed, and coming up it slows back down. Having a greater speed is like having more money in your checking account, and being high up is like having more in your savings account. The device is simply shuffling funds back and forth between the two. Having more balls doesn’t change anything fund ...
Classical Thermodynamics Written by Jussi Eloranta () (Updated: October 31, 2014)
... = “moles of substance” ...
... = “moles of substance” ...
Thermochemistry
... When the units for the expressions for work and energy are collected together, in both cases, the resultant unit is kg m2 s -2. This corresponds to the SI unit of energy called the joule (J). That is, 1 joule (J) = 1 kg m2 s -2. The bouncing ball in Figure 7-2 suggests something about the nature of ...
... When the units for the expressions for work and energy are collected together, in both cases, the resultant unit is kg m2 s -2. This corresponds to the SI unit of energy called the joule (J). That is, 1 joule (J) = 1 kg m2 s -2. The bouncing ball in Figure 7-2 suggests something about the nature of ...
Thermodynamics
... An important concept in thermodynamics is the thermodynamic system, a precisely defined region of the universe under study. Everything in the universe except the system is known as the surroundings. A system is separated from the remainder of the universe by a boundary which may be notional or not, b ...
... An important concept in thermodynamics is the thermodynamic system, a precisely defined region of the universe under study. Everything in the universe except the system is known as the surroundings. A system is separated from the remainder of the universe by a boundary which may be notional or not, b ...
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.