Isochoric process

An isochoric process is a process which takes place at constant volume (V = cte). This type of process occurs when the thermodynamic system (in this case an ideal gas) is enclosed in a container with rigid walls.

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 rigid walls as shown in the figure below.

If a certain amount of heat is supplied, the temperature of the gas will raise, since the heat it receives is proportional to its temperature change. The heat received by the gas is given by:

Where CV is the molar heat capacity at constant volume of an ideal gas

We can represent the isochoric process in a PV diagram:

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As there is no volume change during the isochoric process, the work done by the gas from state A to B is zero:

In the previous pV diagram, states A and B are represented on their respective isotherms. The pressure will increase during this process as the volume is constant and the temperature rises.

We use the First Law of Thermodynamics to find the change in the internal energy that the ideal gas undergoes, which will be equal to the heat it has exchanged:

Note that the expression that gives the change in the internal energy of an ideal gas is the same regardless of the process that it undergoes, since the internal energy is a state function.

If instead of receiving it, the gas dissipated heat to its surroundings, the isochoric process would occur in the opposite direction, therefore, the temperature and the pressure of the gas would decrease.

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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