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Isobaric process

Overview

An isobaric process is a thermodynamic process in which the pressure stays constant: The term derives from the Greek isos, meaning "equal," and barus, "heavy." The heat transferred to the system does work but also changes the internal energy of the system:

According to the first law of thermodynamics

First law of thermodynamics

The first law of thermodynamics, an expression of the principle of conservation of energy, states that energy can be transformed , but cannot be created or destroyed. Alternatively:-Description:...

, where W is work done by the system, U is internal energy, and Q is heat.

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Encyclopedia

An isobaric process is a thermodynamic process in which the pressure stays constant: The term derives from the Greek isos, meaning "equal," and barus, "heavy." The heat transferred to the system does work but also changes the internal energy of the system:

According to the first law of thermodynamics

First law of thermodynamics

The first law of thermodynamics, an expression of the principle of conservation of energy, states that energy can be transformed , but cannot be created or destroyed. Alternatively:-Description:...

, where W is work done by the system, U is internal energy, and Q is heat. Pressure-volume work (by the system) is defined as: (Δ means change over the whole process, it doesn't mean differential)
but since pressure is constant, this means that
.

Applying the ideal gas law

Ideal gas law

The Ideal gas law is the equation of state of a hypothetical ideal gas. It is a good approximation to the behaviour of many gases under many conditions, although it has several limitations. It was first stated by Émile Clapeyron in 1834 as a combination of Boyle's law and Charles's law...

, this becomes
assuming that the quantity of gas stays constant (e.g. no phase change during a chemical reaction

Chemical reaction

A chemical reaction is a process that leads to the transformation of one set of chemical substances to another. They are studied by chemists under a field of science called chemistry. Chemical reactions can be either spontaneous, requiring no input of energy, or non-spontaneous, often coming about...

). Since it is generally true that
then substituting the last two equations into the first equation produces:
The quantity in parentheses is equivalent to the molar specific heat for constant pressure

Pressure

Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...

:
and if the gas involved in the isobaric process is monatomic then and .

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 Discussion

If the volume compresses (delta 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 (delta 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.

Defining Enthalpy

An isochoric process

Isochoric process

An isochoric process, also called a constant-volume process, an isovolumetric process, or an isometric process, is a thermodynamic process during which the volume of the closed system undergoing such process remains constant...

is described by the equation . It would be convenient to have a similar equation for isobaric processes. Substituting the second equation into the first yields
The quantity U + p V is a state function so that it can be given a name. It is called enthalpy

Enthalpy

In thermodynamics and molecular chemistry, the enthalpy is a thermodynamic property of a thermodynamic system. It can be used to calculate the heat transfer during a quasistatic process taking place in a closed thermodynamic system under constant pressure...

, and is denoted as H. Therefore an isobaric process can be more succinctly described as
.

Variable density viewpoint

A given quantity (mass M) of gas in a changing volume produces a change in density ρ. In this context the ideal gas law is written

R(T ρ) = M P

where T is thermodynamic temperature

Thermodynamic temperature

Thermodynamic temperature is the absolute measure of temperature and is one of the principal parameters of thermodynamics. Thermodynamic temperature is an “absolute” scale because it is the measure of the fundamental property underlying temperature: its null or zero point, absolute zero, is the...

above absolute zero

Absolute zero

Absolute zero is a temperature marked by a 0 entropy configuration. It is the coldest temperature theoretically possible and cannot be reached by artificial or natural means, because it is impossible to decouple a system fully from the rest of the universe...

.
When R and M are taken as constant, then pressure P can stay constant as the density-tempertature quadrant (ρ,T ) undergoes a squeeze mapping

Squeeze mapping

In linear algebra, a squeeze mapping is a type of linear map that preserves Euclidean area of regions in the Cartesian plane, but is not a Euclidean motion.For a fixed positive real number r, the mapping →...

. It is this context that explains Peter Olver's use of the term isobaric group when referring to the group of squeeze mappings on page 217 of his book Classical Invariant Theory (1999).

Isobaric process

Sign Discussion

Defining Enthalpy

Variable density viewpoint

See also