Isobaric process
An isobaric process is a thermodynamic process in which the pressure stays constant: ΔP = 0. The term derives from the Greek iso- (equal) and baros (weight). The heat transferred to the system does work, but also changes the internal energy of the system. This article uses the chemistry sign convention for work, where positive work is work done on 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
assuming that the quantity of gas stays 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 is specific heat at a constant volume.
Substituting the last two equations into the first equation produces:
where cP is specific heat 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:
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