An introduction to the entropy concept

The macrostate of a system is what we know about the system, for example the temperaturepressureand volume of a gas in a box. For each set of values of temperature, pressure, and volume there are many arrangements of molecules which result in those values. The number of arrangements of molecules which could result in the same values for temperature, pressure and volume is the number of microstates. The concept of entropy has been developed to describe any of several phenomena, depending on the field and the context in which it is being used.

An introduction to the entropy concept

Thermodynamic states The application of thermodynamic principles begins by defining a system that is in some sense distinct from its surroundings. For example, the system could be a sample of gas inside a cylinder with a movable pistonan entire steam enginea marathon runner, the planet Eartha neutron stara black holeor even the entire universe.

In general, systems are free to exchange heatworkand other forms of energy with their surroundings. For a gas in a cylinder with a movable pistonthe state of the system is identified by the temperaturepressureand volume of the gas. These properties are characteristic parameters that have definite values at each state and are independent of the way in which the system arrived at that state.

In other words, any change in value of a property depends only on the initial and final states of the system, not on the path followed by the system from one state to another.

Such properties are called state functions. In contrast, the work done as the piston moves and the gas expands and the heat the gas absorbs from its surroundings depend on the detailed way in which the expansion occurs. By isolating samples of material whose states and properties can be controlled and manipulated, properties and their interrelations can be studied as the system changes from state to state.

Thermodynamic equilibrium A particularly important concept is thermodynamic equilibrium, in which there is no tendency for the state of a system to change spontaneously. For example, the gas in a cylinder with a movable piston will be at equilibrium if the temperature and pressure inside are uniform and if the restraining force on the piston is just sufficient to keep it from moving.

The system can then be made to change to a new state only by an externally imposed change in one of the state functions, such as the temperature by adding heat or the volume by moving the piston.

A sequence of one or more such steps connecting different states of the system is called a process. In general, a system is not in equilibrium as it adjusts to an abrupt change in its environment. For example, when a balloon bursts, the compressed gas inside is suddenly far from equilibrium, and it rapidly expands until it reaches a new equilibrium state.

However, the same final state could be achieved by placing the same compressed gas in a cylinder with a movable piston and applying a sequence of many small increments in volume and temperaturewith the system being given time to come to equilibrium after each small increment.

Such a process is said to be reversible because the system is at or near equilibrium at each step along its path, and the direction of change could be reversed at any point. This example illustrates how two different paths can connect the same initial and final states.

The first is irreversible the balloon burstsand the second is reversible. The concept of reversible processes is something like motion without friction in mechanics.

It represents an idealized limiting case that is very useful in discussing the properties of real systems. Many of the results of thermodynamics are derived from the properties of reversible processes. Temperature The concept of temperature is fundamental to any discussion of thermodynamics, but its precise definition is not a simple matter.

For example, a steel rod feels colder than a wooden rod at room temperature simply because steel is better at conducting heat away from the skin.

It is therefore necessary to have an objective way of measuring temperature. In general, when two objects are brought into thermal contact, heat will flow between them until they come into equilibrium with each other. When the flow of heat stops, they are said to be at the same temperature.

An introduction to the entropy concept

The zeroth law of thermodynamics formalizes this by asserting that if an object A is in simultaneous thermal equilibrium with two other objects B and C, then B and C will be in thermal equilibrium with each other if brought into thermal contact.

Object A can then play the role of a thermometer through some change in its physical properties with temperature, such as its volume or its electrical resistance. With the definition of equality of temperature in hand, it is possible to establish a temperature scale by assigning numerical values to certain easily reproducible fixed points.

There are absolute temperature scales related to the second law of thermodynamics. Zero in both the Kelvin and Rankine scales is at absolute zero.

Fundamental concepts

Work and energy Energy has a precise meaning in physics that does not always correspond to everyday language, and yet a precise definition is somewhat elusive.

The word is derived from the Greek word ergon, meaning work, but the term work itself acquired a technical meaning with the advent of Newtonian mechanics. For example, a man pushing on a car may feel that he is doing a lot of work, but no work is actually done unless the car moves.

The work done is then the product of the force applied by the man multiplied by the distance through which the car moves. If there is no friction and the surface is level, then the car, once set in motion, will continue rolling indefinitely with constant speed. The rolling car has something that a stationary car does not have—it has kinetic energy of motion equal to the work required to achieve that state of motion.

The introduction of the concept of energy in this way is of great value in mechanics because, in the absence of friction, energy is never lost from the system, although it can be converted from one form to another.

For example, if a coasting car comes to a hill, it will roll some distance up the hill before coming to a temporary stop. At that moment its kinetic energy of motion has been converted into its potential energy of position, which is equal to the work required to lift the car through the same vertical distance.

After coming to a stop, the car will then begin rolling back down the hill until it has completely recovered its kinetic energy of motion at the bottom. In the absence of friction, such systems are said to be conservative because at any given moment the total amount of energy kinetic plus potential remains equal to the initial work done to set the system in motion.

As the science of physics expanded to cover an ever-wider range of phenomena, it became necessary to include additional forms of energy in order to keep the total amount of energy constant for all closed systems or to account for changes in total energy for open systems.2 caninariojana.comuction The concept of entropy is not easy to grasp (even for physicists) and frequently entropy is seen as very mysterious quantity.

Thus, r H° = f H°gypsum - f H°anhydrite - f H°water = kJ/mol. ; Exothermic vs. Endothermic If r H° 0 the reaction produces an increase in enthalpy and is endothermic (heat from the surroundings is consumed by the rock). The concept of entropy plays a central role in information theory.

A visual introduction to machine learning

Boltzmann's constant, and therefore entropy, have dimensions of energy divided by temperature, which has a unit of joules per kelvin (J K −1) in the International System of Units (or kg m 2 s −2 K −1 in terms of base units).

The author defends the position that an appropriate introduction to the concept of entropy can only be made from the Information Theory. And indeed, the robust arguments exhibited by Prof.

Ben-Naim through the present work in order to show it, are overwhelming. the principle of increase of entropy, which is a statement of the second law of thermodynamics in the form of an extremal principle—the equilibrium state of an isolated physical system is that in which the entropy takes the maximum possible value.

First, some intuition. Let’s say you had to determine whether a home is in San Francisco or in New machine learning terms, categorizing data points is a classification task.. Since San Francisco is relatively hilly, the elevation of a home may be a good way to distinguish the two cities.

Evolution & Entropy - Second Law of Thermodynamics