Isobaric process

An isobaric process is a process which takes place at constant pressure (p = constant). This type of process occurs when the thermodynamic system (in this case an ideal gas) is enclosed in a container with a moving wall so that its pressure remains constant.

In these pages we will use the so-called Clausius convention to state the First Law of Thermodynamics.

Where W is the work done by the system on its surroundings.

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Consider n moles of an ideal gas enclosed in a container with a moving wall (a piston for instance) as shown in the figure below.

Note that in the previous figure there is a weight on the movable wall. In this way, when heat is added to the gas, the process it will undergo will take place at constant pressure.

If a certain amount of heat is added, the temperature of the gas will rise, since the heat it absorbs is proportional to its temperature change. The heat absorbed by the gas is given by:

Where Cp is the molar heat capacity at constant pressure of an ideal gas

We can represent the isobaric process in a PV diagram:

The work done by the gas when it goes from state A to state B is given by:

Which is positive since the gas expands when going from state A to state B.

This work corresponds to the shaded area in blue in the PV diagram. The expression of the work in the previous expression is precisely the area of that rectangle.

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Now that we have calculated the work and the heat exchanged by the ideal gas for the isobaric process, we use the First Law of Thermodynamics to find the change in its internal energy:

And after using the equation of state of an ideal gas as well as Mayer’s relation we get:

Which is the expected result because the internal energy is a state function and its variation is always described by the same expression regardless of the process undergone by the ideal gas.

In the process shown in the figure above, the internal energy of the gas increases.

If the ideal gas was compressed, the heat, the work and the change in the internal energy would be calculated with the same expressions deduced on this page, and the three quantities would be negative.

Follow the links below to see how to calculate the work, heat and the change in the internal energy for the following four reversible processes undergone by an ideal gas:

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