An isochoric process, also known as an isometric or constant volume process, is a thermodynamic process in which the volume of the system remains constant. This implies that no work is done by or on the system during this process because work in thermodynamics is given by the equation \( W = P \Delta V \), where \( P \) is the pressure and \( \Delta V \) is the change in volume. Since \( \Delta V = 0 \) for an isochoric process, we have:
\[ W = P \cdot 0 = 0 \]
In an isochoric process, any heat added to the system increases the internal energy of the system and results in a change in temperature. This can be described by the first law of thermodynamics:
\[ \Delta U = Q - W \]
Since \( W = 0 \) for an isochoric process, the equation simplifies to:
\[ \Delta U = Q \]
Where:
- \( \Delta U \) is the change in internal energy.
- \( Q \) is the heat added to the system.
In summary, during an isochoric process, the volume remains constant, no work is done, and the heat added to the system directly increases the internal energy.
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