Isobaric Process

The Isobaric Process: Constant Pressure

An isobaric process is a thermodynamic change that takes place at a constant pressure. The word itself comes from the Greek isos (equal) and baros (weight or pressure). In such a process, the system is free to expand or contract, but the external pressure on it remains fixed. A common example is heating a gas in a cylinder fitted with a movable, frictionless piston that is exposed to the atmosphere — as the gas heats up, it pushes the piston outward, but the pressure inside always matches the constant atmospheric pressure outside.

Because pressure $P$ is constant, the $P$–$V$ diagram for an isobaric process is a horizontal straight line. If the volume increases (expansion), the process moves from left to right along this line; if the volume decreases (compression), it moves from right to left.

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Work Done in an Isobaric Process

The work done by a gas during any thermodynamic process is given by the integral

Since $P$ is constant in an isobaric process, it can be taken out of the integral:

Let $V_f$ be the final volume and $V_i$ the initial volume. Then the work done by the gas is

where $\Delta V = V_f - V_i$.

If the gas expands ($\Delta V > 0$), $W$ is positive — the gas does work on its surroundings. If the gas is compressed ($\Delta V < 0$), $W$ is negative — work is done on the gas by the surroundings.

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First Law of Thermodynamics for an Isobaric Process

The first law of thermodynamics states

where $\Delta U$ is the change in internal energy, $Q$ is the heat added to the system, and $W$ is the work done by the system.

For an isobaric process, we substitute $W = P \Delta V$:

This equation tells us that the heat supplied to the system is partly used to do work (expanding against constant pressure) and partly to change the internal energy (and hence the temperature) of the gas.

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Heat Capacity at Constant Pressure ($C_P$)

The molar specific heat capacity at constant pressure, $C_P$, is defined as the amount of heat required to raise the temperature of one mole of a gas by 1 K while keeping the pressure constant. For $n$ moles, the heat added at constant pressure is

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Relation Between $C_P$ and $C_V$ (Mayer's Relation)

Consider one mole of an ideal gas undergoing an isobaric process. The first law gives

For one mole, $Q = C_P \Delta T$ and $\Delta U = C_V \Delta T$ (since internal energy of an ideal gas depends only on temperature). Also, from the ideal gas law $PV = RT$, at constant pressure we have $P \Delta V = R \Delta T$.

Substitute these into the first law: …