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thermodynamics Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws ...
, an isobaric process is a type of
thermodynamic process Classical thermodynamics considers three main kinds of thermodynamic process: (1) changes in a system, (2) cycles in a system, and (3) flow processes. (1)A Thermodynamic process is a process in which the thermodynamic state of a system is change ...
in which the
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country a ...
of the
system A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and express ...
stays constant: Δ''P'' = 0. The
heat In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is ...
transferred to the system does work, but also changes the
internal energy The internal energy of a thermodynamic system is the total energy contained within it. It is the energy necessary to create or prepare the system in its given internal state, and includes the contributions of potential energy and internal kinet ...
(''U'') of the system. This article uses the physics sign convention for work, where positive work is work done by the system. Using this convention, by the
first law of thermodynamics The first law of thermodynamics is a formulation of the law of conservation of energy, adapted for thermodynamic processes. It distinguishes in principle two forms of energy transfer, heat and thermodynamic work for a system of a constant am ...
, : Q = \Delta U + W\, where ''W'' is work, ''U'' is internal energy, and ''Q'' is heat. Pressure-
volume Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). ...
work by the closed system is defined as: :W = \int \! p \,dV \, where Δ means change over the whole process, whereas ''d'' denotes a differential. Since pressure is constant, this means that : W = p \Delta V\, . Applying the
ideal gas law The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations. It was first s ...
, this becomes : W = n\,R\,\Delta T with ''R'' representing the gas constant, and ''n'' representing the
amount of substance In chemistry, the amount of substance ''n'' in a given sample of matter is defined as the quantity or number of discrete atomic-scale particles in it divided by the Avogadro constant ''N''A. The particles or entities may be molecules, atoms, io ...
, which is assumed to remain constant (e.g., there is no
phase transition In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states ...
during a
chemical reaction A chemical reaction is a process that leads to the chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the positions of electrons in the forming and breaking ...
). According to the equipartition theorem, the change in internal energy is related to the temperature of the system by : \Delta U = n\,c_\,\Delta T, where ''cV, m'' is molar
heat capacity Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin (J/K). Heat cap ...
at a constant volume. Substituting the last two equations into the first equation produces: :\begin Q &= n\,c_\,\Delta T + n\,R\,\Delta T \\ Q &= n\Delta T(c_+R) \\ Q &= n\Delta T c_ \end where ''cP'' is molar heat capacity at a constant pressure.


Specific heat capacity

To find the molar specific heat capacity of the gas involved, the following equations apply for any general gas that is calorically perfect. The property ''γ'' is either called the adiabatic index or the heat capacity ratio. Some published sources might use ''k'' instead of ''γ''. Molar isochoric specific heat: :c_V = \frac. Molar isobaric specific heat: :c_p = \frac. The values for ''γ'' are ''γ'' =  for diatomic gases like air and its major components, and ''γ'' =  for monatomic gases like the
noble gas The noble gases (historically also the inert gases; sometimes referred to as aerogens) make up a class of chemical elements with similar properties; under standard conditions, they are all odorless, colorless, monatomic gases with very low ch ...
es. The formulas for specific heats would reduce in these special cases: Monatomic: :c_V = \tfrac32 R and c_P = \tfrac52 R Diatomic: :c_V = \tfrac52 R and c_P = \tfrac72 R An isobaric process is shown on a ''P''–''V'' diagram as a straight horizontal line, connecting the initial and final thermostatic states. If the process moves towards the right, then it is an expansion. If the process moves towards the left, then it is a compression.


Sign convention for work

The motivation for the specific sign conventions of
thermodynamics Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws ...
comes from early development of heat engines. When designing a heat engine, the goal is to have the system produce and deliver work output. The source of energy in a heat engine, is a heat input. * If the volume compresses (Δ''V'' = final volume − initial volume < 0), then ''W'' < 0. That is, during isobaric compression the gas does negative work, or the environment does positive work. Restated, the environment does positive work on the gas. * If the volume expands (Δ''V'' = final volume − initial volume > 0), then ''W'' > 0. That is, during isobaric expansion the gas does positive work, or equivalently, the environment does negative work. Restated, the gas does positive work on the environment. * If heat is added to the system, then ''Q'' > 0. That is, during isobaric expansion/heating, positive heat is added to the gas, or equivalently, the environment receives negative heat. Restated, the gas receives positive heat from the environment. * If the system rejects heat, then ''Q'' < 0. That is, during isobaric compression/cooling, negative heat is added to the gas, or equivalently, the environment receives positive heat. Restated, the environment receives positive heat from the gas.


Defining enthalpy

An isochoric process is described by the equation ''Q'' = Δ''U''. It would be convenient to have a similar equation for isobaric processes. Substituting the second equation into the first yields : Q = \Delta U + \Delta (p\,V) = \Delta (U + p\,V) The quantity ''U'' + ''pV'' is a state function so that it can be given a name. It is called
enthalpy Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant ...
, and is denoted as ''H''. Therefore, an isobaric process can be more succinctly described as : Q = \Delta H \,. Enthalpy and isochoric specific heat capacity are very useful mathematical constructs, since when analyzing a process in an open system, the situation of zero work occurs when the fluid flows at constant pressure. In an open system, enthalpy is the quantity which is useful to use to keep track of energy content of the fluid.


Examples of isobaric processes

The reversible expansion of an ideal gas can be used as an example of an isobaric process. Of particular interest is the way heat is converted to work when expansion is carried out at different working gas/surrounding gas pressures. In the first process example, a cylindrical chamber 1 m2 in area encloses 81.2438 mol of an ideal diatomic gas of molecular mass 29 g mol−1 at 300 K. The surrounding gas is at 1 atm and 300 K, and separated from the cylinder gas by a thin piston. For the limiting case of a massless piston, the cylinder gas is also at 1 atm pressure, with an initial volume of 2 m3. Heat is added slowly until the gas temperature is uniformly 600 K, after which the gas volume is 4 m3 and the piston is 2 m above its initial position. If the piston motion is sufficiently slow, the gas pressure at each instant will have practically the same value (''p''sys = 1 atm) throughout. For a thermally perfect diatomic gas, the molar specific heat capacity at constant pressure (''cp'') is 7/2R or 29.1006 J mol−1 deg−1. The molar heat capacity at constant volume (''cv'') is 5/2R or 20.7862 J mol−1 deg−1. The ratio \gamma of the two heat capacities is 1.4. The heat ''Q'' required to bring the gas from 300 to 600 K is :Q = = n\,c_p\,\Delta\Tau = 81.2438\times 29.1006\times 300 = 709,274\text. The increase in
internal energy The internal energy of a thermodynamic system is the total energy contained within it. It is the energy necessary to create or prepare the system in its given internal state, and includes the contributions of potential energy and internal kinet ...
is :\Delta\ U = n\,c_v\,\Delta\Tau = 81.2438\times 20.7862\times 300 = 506,625\text Therefore, W = Q - \Delta U = 202,649\text = nR\Delta\Tau Also W = = 1~\text \times 2\text \times 101325\text = 202,650\text , which of course is identical to the difference between Δ''H'' and Δ''U''. Here, work is entirely consumed by expansion against the surroundings. Of the total heat applied (709.3 kJ), the work performed (202.7 kJ) is about 28.6% of the supplied heat. The second process example is similar to the first, except that the massless piston is replaced by one having a mass of 10,332.2 kg, which doubles the pressure of the cylinder gas to 2 atm. The cylinder gas volume is then 1 m3 at the initial 300 K temperature. Heat is added slowly until the gas temperature is uniformly 600 K, after which the gas volume is 2 m3 and the piston is 1 m above its initial position. If the piston motion is sufficiently slow, the gas pressure at each instant will have practically the same value (''p''sys = 2 atm) throughout. Since enthalpy and internal energy are independent of pressure, : Q = = 709,274\text and \Delta U = 506,625\text. :W = = 2~\text \times 1~\text\times 101325\text = 202,650\text As in the first example, about 28.6% of the supplied heat is converted to work. But here, work is applied in two different ways: partly by expanding the surrounding atmosphere and partly by lifting 10,332.2 kg a distance ''h'' of 1 m. :W_ = 10\,332.2~\text \times 9.80665~\text\times1\text = 101,324\text : Thus, half the work lifts the piston mass (work of gravity, or “useable” work), while the other half expands the surroundings. The results of these two process examples illustrate the difference between the fraction of heat converted to usable work (''mg''Δ''h)'' vs. the fraction converted to pressure-volume work done against the surrounding atmosphere. The usable work approaches zero as the working gas pressure approaches that of the surroundings, while maximum usable work is obtained when there is no surrounding gas pressure. The ratio of all work performed to the heat input for ideal isobaric gas expansion is :\frac = \frac = \frac


Variable density viewpoint

A given quantity (mass ''m'') of gas in a changing volume produces a change in
density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematicall ...
''ρ''. In this context the ideal gas law is written : R(T\,\rho) = M P where ''T'' is
thermodynamic temperature Thermodynamic temperature is a quantity defined in thermodynamics as distinct from kinetic theory or statistical mechanics. Historically, thermodynamic temperature was defined by Kelvin in terms of a macroscopic relation between thermodynamic ...
and ''M'' is molar mass. When R and M are taken as constant, then pressure ''P'' can stay constant as the density-temperature quadrant undergoes a squeeze mapping.


Etymology

The adjective "isobaric" is derived from the Greek words ἴσος (''isos'') meaning "equal", and βάρος (''baros'') meaning "weight."


See also

*
Adiabatic process In thermodynamics, an adiabatic process (Greek: ''adiábatos'', "impassable") is a type of thermodynamic process that occurs without transferring heat or mass between the thermodynamic system and its environment. Unlike an isothermal process, ...
* Cyclic process * Isochoric process *
Isothermal process In thermodynamics, an isothermal process is a type of thermodynamic process in which the temperature ''T'' of a system remains constant: Δ''T'' = 0. This typically occurs when a system is in contact with an outside thermal reservoir, and a ...
*
Polytropic process A polytropic process is a thermodynamic process that obeys the relation: p V^ = C where ''p'' is the pressure, ''V'' is volume, ''n'' is the polytropic index, and ''C'' is a constant. The polytropic process equation describes expansion and com ...
* Isenthalpic process


References

{{reflist Thermodynamic processes Atmospheric thermodynamics