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Concept
Isobaric process
Summary
In thermodynamics, an isobaric process is a type of thermodynamic process in which the pressure of the system stays constant: ΔP = 0. The heat transferred to the system does work, but also changes the internal energy (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,
where W is work, U is internal energy, and Q is heat. Pressure-volume work by the closed system is defined as:
where Δ means change over the whole process, whereas d denotes a differential. Since pressure is constant, this means that
Applying the ideal gas law, this becomes
with R representing the gas constant, and n representing the amount of substance, which is assumed to remain constant (e.g., there is no phase transition during a chemical reaction). According to the equipartition theorem, the change in internal energy is related to the temperature of the system by
where cV, m is molar heat capacity at a constant volume.
Substituting the last two equations into the first equation produces:
where cP is molar heat capacity at a constant pressure.
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:
Molar isobaric specific heat:
The values for γ are γ = 7/5 for diatomic gases like air and its major components, and γ = 5/3 for monatomic gases like the noble gases. The formulas for specific heats would reduce in these special cases:
Monatomic:
and
Diatomic:
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.
The motivation for the specific sign conventions of thermodynamics comes from early development of heat engines.
Official source
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