An isochoric ( also called isovolumetric) process is a thermodynamic process that takes place at constant volume.
This means that the system does not experience changes in its volume throughout the transformation.
Relationship between pressure and temperature
In an ideal gas, if the volume remains constant, it is true that:
That is, the pressure is directly proportional to the absolute temperature.
Physical interpretation:
As the temperature increases, the gas particles move faster and collide more frequently and intensely against the walls of the vessel, causing an increase in pressure.
Graphical representation
Isochoric transformations are represented by isochores:
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In a P–V diagram → vertical line (constant volume)
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In a P–T diagram → increasing straight line
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In a V–T diagram → horizontal line
Work in an isochoric process
The work in thermodynamics is given by:
As in this process:
Then:
Conclusion:
An isochoric process does not perform mechanical work.
First Law of Thermodynamics
The first law establishes:
Since there is no work:
Interpretation:
All the energy transferred in the form of heat is converted into variation of the internal energy of the system.
Internal energy in an ideal gas
In an ideal gas:
The internal energy depends solely on the temperature.
Therefore, any change in internal energy implies a change in temperature.
Heat in an isochoric process
If the amount of gas remains constant, the heat exchanged is calculated as:
where:
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n = number of moles
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Cv = molar specific heat at constant volume
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ΔT = temperature variation
Examples of isochoric processes
Ideal example
A gas contained in a rigid, closed, non-deformable container to which heat is supplied.
Example in applied thermodynamics
In the Otto cycle (ideal model of gasoline engines), there are two isochoric transformations:
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Heat input (combustion)
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Heat transfer
Comparison with other processes
| Process | Constant magnitude | Main feature |
|---|---|---|
| Isochoric | Volume | No work (W = 0) |
| Isothermal | Temperature | Constant internal energy |
| Isobaric | Pressure | Non-Zero Work |
| Adiabatic | Heat (Q = 0) | No heat exchange |
Final Key Idea
In an isochoric process:
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Volume does not change
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No work is done
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All the heat exchanged is transformed into internal energy
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Pressure and temperature are directly related