NationMaster - Encyclopedia: Isothermal process

An isothermal process is a thermodynamic process in which the temperature of the system stays constant: ΔT = 0. This typically occurs when a system is in contact with an outside thermal reservoir (heat bath), and processes occur slowly enough to allow the system to continually adjust to the temperature of the reservoir through heat exchange. An alternative special case in which a system exchanges no heat with its surroundings (Q = 0) is called an adiabatic process. Thermodynamics (from the Greek thermos meaning heat and dynamics meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. ... In thermodynamics, temperature is the physical property of a system that underlies the common notions of hot and cold â€”something that is hotter has the greater temperature. ... System (from the Latin (systÄ“ma), and this from the Greek (sustÄ“ma)) is an assemblage of entity/objects, real or abstract, comprising a whole with each and every component/element interacting or related to another one. ... In mathematics and the mathematical sciences, a constant is a fixed, but possibly unspecified, value. ... A heat bath is a large system that is in thermal contact with some other system of interest. ... Process (lat. ... In physics, heat, symbolized by Q, is defined as energy in transit. ... In a thermodynamics problem, the surroundings, or environment, are anything not part of the system. ... In thermodynamics, an adiabatic process is a process in which no heat is transferred to or from working fluid. ...

Consider an ideal gas, in which the temperature depends only on the internal energy, which is a function of the mean translational kinetic energy of the molecules, as given by a Boltzmann distribution; if the internal energy is constant, so is the temperature. Take the number of moles n as a constant. An ideal gas or perfect gas is a hypothetical gas consisting of identical particles of negligible volume, with no intermolecular forces. ... In thermodynamics, the internal energy of a thermodynamic system, or a body with well-defined boundaries, denoted by U, or sometimes E, is the total of the kinetic energy due to the motion of molecules (translational, rotational, vibrational) and the potential energy associated with the vibrational and electric energy of... In mathematics, an average or central tendency of a set (list) of data refers to a measure of the middle of the data set. ... Kinetic energy is the energy that a body possesses as a result of its motion. ... In chemistry, a molecule is an aggregate of at least two atoms in a definite arrangement held together by special forces. ... The Maxwell-Boltzmann distribution is a probability distribution with applications in physics and chemistry. ... The mole and its simple conversions into different units of measurements. ...

but this means, according to the ideal gas law, that Isotherms of an ideal gas The ideal gas law is the equation of state of an ideal gas. ...

where

P i

and

V i

are the pressure and volume of the initial state,

P f

and

V f

are the pressure and volume of the final state, and the variables P and V stand for the pressure and volume of any intermediate state during an isothermal process. In computer science and mathematics, a variable (sometimes called a pronumeral) is a symbol denoting a quantity or symbolic representation. ...

Curves called isotherms appear as a hyperbolas on a P-V (pressure-volume) diagram (T = constant). Each one asymptotically approaches both the V (abcissa) and P (ordinate) axes. This corresponds to a one-parameter family of curves, a function of T, whose equation is Image File history File links Download high resolution version (1504x1386, 66 KB)Isotherms of an ideal gas in pressure (p) vs. ... Image File history File links Download high resolution version (1504x1386, 66 KB)Isotherms of an ideal gas in pressure (p) vs. ... An isotherm is a line of equal or constant temperature on a graph, plot, or map; an isopleth of temperature. ... A graph of a hyperbola. ... An asymptote is a straight line or curve which a curve approaches as one moves along the curve. ... The factual accuracy of this article is disputed. ... Partial plot of a function f. ...

By the first law of thermodynamics, the isotherms of an ideal gas are also determined by the condition that The first law of thermodynamics, a generalized expression of the law of the conservation of energy, states: // Description Essentially, the First Law of Thermodynamics declares that energy is conserved for a closed system, with heat and work being the forms of energy transfer. ...

where W is work done on the system. (While Q and W are incremental quantities, they do not represent differentials of state functions.) This means that, during an isothermal process, all heat accepted by the system from its surroundings must have its energy entirely converted to work which it performs on the surroundings. That is, all the energy which comes into the system comes back out; the internal energy and thus the temperature of the system remain constant. Quantity is a kind of property which exists as magnitude or multitude. ... In mathematics, the word differential has various meanings: In calculus, a differential is an infinitesimal change in the value of a function. ... In thermodynamics, a state function (or state quantity) is a property of a system that depends only on the current state of the system, not on the way in which the system got to that state. ... Mechanical work is a force applied through a distance, defined mathematically as the line integral of a scalar product of force and displacement vectors. ...

In a minute process of this process, the minute work dW can be shown as follow. Image File history File links Isothermal_process. ... Image File history File links Isothermal_process. ...

Therefore the entire work of the process from A to B is shown with the integration of the previous equation.

Isothermal processes can occur in any kind of system, including highly structured machines, and even living cells. Various parts of the cycle of some heat engines are carried out isothermally and may be approximated by a Carnot cycle. Image File history File links Download high-resolution version (1300x975, 39 KB) Illustration of a Carnot cycle (simplified, with directions) on a temperature-entropy diagram between temperatures of TH and TC, entropies SA and SB. File links The following pages on the English Wikipedia link to this file (pages on... Image File history File links Download high-resolution version (1300x975, 39 KB) Illustration of a Carnot cycle (simplified, with directions) on a temperature-entropy diagram between temperatures of TH and TC, entropies SA and SB. File links The following pages on the English Wikipedia link to this file (pages on... In thermodynamics, temperature is the physical property of a system that underlies the common notions of hot and cold â€”something that is hotter has the greater temperature. ... In thermodynamics, entropy, symbolized by S, is a state function of a thermodynamic system defined by the differential quantity , where dQ is the amount of heat absorbed in a reversible process in which the system goes from the one state to another, and T is the absolute temperature. ... A machine is any mechanical or electrical device that transmits or modifies energy to perform or assist in the performance of tasks. ... For other uses, see Life (disambiguation), Lives (disambiguation) or Living (disambiguation), Living Things (disambiguation) Look up life, living in Wiktionary, the free dictionary. ... In engineering and thermodynamics, a heat engine performs the conversion of heat energy to mechanical work by exploiting the temperature gradient between a hot source and a cold sink. Heat is transferred from the source, through the working body of the engine, to the sink, and in this process some... It has been suggested that this article or section be merged with estimation. ... A heat engine is an engine that uses heat to produce mechanical work by carrying a working substance through a cyclic process. ...

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