An isochoric process, sometimes called an isovolumetric or isometric process, is a fundamental concept in thermodynamics where the volume of the working system remains unchanged. This means the boundaries of the system, such as the walls of a container, cannot expand or contract, even as other properties like pressure and temperature shift. This process provides a simplified model for studying the direct relationship between heat, internal energy, and pressure without the complication of movement or expansion.
The Constant Volume Condition
The change in volume (\(\Delta V\)) is zero in an isochoric process. This fixed volume condition means the container walls are rigid and cannot move. Consequently, the system cannot perform mechanical boundary work on its surroundings, nor can the surroundings do work on the system.
For an ideal gas confined within a fixed volume, the relationship between pressure and temperature becomes directly proportional. If heat is introduced, the temperature of the gas must increase, which in turn causes the pressure to rise proportionally. This occurs because the gas particles, with their increased thermal energy, move faster and collide more frequently and forcefully with the rigid container walls.
The fixed volume locks the system into a specific pressure-temperature path. Any increase in the kinetic energy of the gas molecules, which is a measure of temperature, must translate directly into a higher force exerted per unit area, which is pressure. Conversely, if the temperature drops, the molecular collisions become less energetic, causing the internal pressure to fall.
Energy Exchange in Isochoric Processes
The core thermodynamic consequence of a constant volume condition relates to the work done during the process. In thermodynamics, work (\(W\)) performed by or on a system is defined by the product of pressure and the change in volume. Because the volume change (\(\Delta V\)) is zero in an isochoric process, the work done must also be zero (\(W=0\)).
This allows for the application of the First Law of Thermodynamics, which states that the change in the system’s internal energy (\(\Delta U\)) equals the heat added to the system (\(Q\)) minus the work done by the system (\(W\)). Since the work term is zero for an isochoric process, the equation simplifies: any heat added to or removed from the system must go entirely into changing the system’s internal energy (\(\Delta U = Q\)).
Internal energy represents the total energy stored within a system, primarily consisting of the kinetic energy of the molecules and the potential energy stored in their chemical bonds. When heat is added to a system at constant volume, that energy does not go into pushing boundaries outward; instead, it solely increases the average speed of the molecules. This increase in molecular kinetic energy is experienced macroscopically as a rise in temperature.
If you heat a rigid container, every unit of thermal energy supplied directly contributes to a higher internal energy and, consequently, a higher temperature and pressure. This direct conversion highlights the relationship between heat and internal energy.
Real-World Examples and Applications
The isochoric process serves as a model for real-world applications where systems are designed to be rigid or where volume changes are negligible over a short time. A common example is heating a substance inside a sturdy, sealed container, such as a laboratory bomb calorimeter. Since the steel vessel cannot expand, the heat released solely raises the internal energy and temperature of the contents and the surrounding water bath.
Another practical illustration is the combustion phase within a typical gasoline internal combustion engine, which is approximated by the Otto cycle. During the power stroke, the fuel-air mixture ignites, and the combustion happens so rapidly that the piston has not yet had time to move significantly. For a brief moment, the volume of the cylinder is almost constant while the temperature and pressure skyrocket due to the immense heat released by the burning fuel.
A pressurized gas cylinder, such as one containing oxygen or propane, illustrates the principle when exposed to temperature changes. If the cylinder is left in a hot environment, the volume remains fixed, but the gas absorbs heat, leading to a significant increase in internal pressure.