An isochoric process, also known as a constant volume process, is a thermodynamic process in which the volume of the system remains constant while pressure and temperature may change. Since there is no volume change, the work done by or on the system is zero.
The first law of thermodynamics can be expressed for this process as:
\[ \Delta U = Q - W \]
Where:
- \(\Delta U\) is the change in internal energy of the system,
- \(Q\) is the heat added to the system,
- \(W\) is the work done by the system.
Since the volume is constant, no work is done (\(W = 0\)). Therefore, the equation simplifies to:
\[ \Delta U = Q \]
This means that any heat added to the system increases its internal energy, and any heat removed decreases the internal energy. For an ideal gas, the change in internal energy can also be related to temperature change:
\[ \Delta U = nC_V \Delta T \]
Where:
- \(n\) is the number of moles of gas,
- \(C_V\) is the molar heat capacity at constant volume,
- \(\Delta T\) is the change in temperature.
In summary, during an isochoric process, the system undergoes changes in temperature and pressure, but the volume remains constant.