• Isochoric process - a process with no change in volume, in which case the system does no work.

• Definition: An isochoric process is a thermodynamic process in which the volume remains constant. Since the volume is constant, the system does no work and W = 0.

• This is perhaps the easiest of the thermodynamic variables to control, since it can be obtained by placing the system in a sealed container which neither expands nor contracts.

• Applying the first law of thermodynamics to this situation, we find that:

• delta-U = Q

• Since delta-U is the change in internal energy and Q is the heat transfer into or out of the system, we see that all of the heat either comes from internal energy or goes into increasing the internal energy.

• Constant Volume, But w is Non-zero

• It is actually possible to do work on a system without changing the volume, as in the case of stirring a liquid. Some sources use "isochoric" in these cases to mean "zero-work" regardless of whether there is a change in volume or not. In most straightforward applications, however, this nuance will not need to be considered ... if the volume remains constant throughout the process, it is an isochoric process.

• Isobaric process - a process with no change in pressure.

Definition: An isobaric process is a thermodynamic process in which the pressure remains constant. This is usually obtained by allowed the volume to expand or contract in such a way to neutralize any pressure changes that would be caused by heat transfer.

In an isobaric process, there are typically internal energy changes, work is done by the system, and heat is transferred, so none of the quantities in the first law of thermodynamics readily reduce to zero. However, the work at a constant pressure can be fairly easily calculated with the equation:

W = p * delta-V

Since W is the work, p is the pressure (always positive) and delta-V is the change in volume, we can see that there are two possible outcomes to an isobaric process:

• If the system expands (delta-V is positive), then the system does positive work (and vice versa)

• If the system contracts (delta-V is negative), then the system does negative work (and vice versa)

• Isothermal process - a process with no change in temperature.

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Definition: An isothermal process is a thermodynamic process in which the temperature of the system remains constant. The heat transfer into or out of the system typically must happen at such a slow rate that the thermal equilibrium is maintained.

Other Factors in an Isothermal Process

In general, during an isothermal process there is a change in internal energy, heat energy, and work.

The internal energy of an ideal gas, however, depends solely on the temperature, so the change in internal energy during an isothermal process for an ideal gas is also 0.

Isothermal Processes & States of Matter

In a phase diagram, an isothermal process is indicated by following a vertical line (or plane, in a 3D phase diagram) along a constant temperature.

Therefore, if the pressure and volume change, it is possible for a substance to change its state of matter even while its temperature remains constant, if you're careful about how you apply or remove heat from the system.