Constantvolume

Constant-volume, also called an isochoric process, describes a thermodynamic process in which the volume of the system remains fixed. Because the boundary does not move, the work done by the system on its surroundings is zero (W = ∫ P dV = 0). As a result, any heat added or removed changes the internal energy directly and thus alters the temperature.

For a closed system of an ideal gas, the first law reduces to ΔU = Q, since W = 0. The rise in internal energy is related to temperature by ΔU = n Cv ΔT, where Cv is the molar or specific heat at constant volume. Consequently, the heat transfer is Q = n Cv ΔT. The pressure and temperature are connected through PV = nRT, so a fixed volume will lead to pressure changes as temperature changes.

In contrast to ideal gases, real substances can exhibit U depending on both T and V, so the relation Q = ΔU + W still applies with W = 0, but ΔU may involve volume effects. For an ideal gas, Cp − Cv = R, where Cp is the heat capacity at constant pressure and R is the gas constant.

Applications include constant-volume calorimetry, where a sample is heated in a rigid container (a bomb calorimeter) to determine Cv and reaction enthalpies. Isochoric processes also appear in combustion and thermodynamic cycles; for example, the Otto cycle uses a period of constant-volume heat addition.

See also: isochoric process, calorimetry, ideal gas, thermodynamic cycles.