Isochoric Process (Constant Volume Process)

An Isochoric process, also called a constant volume process, an Iso-volumetric process or an isometric process, is a thermodynamic process during which the volume of the closed system undergoing such a process remains constant. The Isochoric process here should be a quasi-static process.

• P,V,T Relationship:

                                    P/T = Constant

• Work done by the gas:

                                    W_1-2 = P (V₂-V₁) = 0

• Change in Internal Energy:

                                    dU  = mC_v (T₂-T₁)
                                    U₂ - U₁ = mC_v (T₂-T₁)

• Heat Supplied or heat transfer:

                                    Q_1-2 = dU + W_1-2
                                    Q_1-2 = U₂ - U₁ = mC_p (T₂-T₁)

• Change in Enthalphy:

                                    H  = mC_p (T₂-T₁)

Important Note:

• The change in internal energy (dU) and the change in enthalphy (dH) have the same expression for each process.
• During expansion or heating process, work is done by the gas (i.e. W_1-2 is +ve); internal energy of the gas decreases (i.e. dU is -ve) and the heat supplied to the gas (i.e. Q_1-2 is +ve).
• During compression or cooling process, work is done on the gas (i.e. W_1-2 is -ve); internal energy of the gas increases (i.e. dU is +ve) and the heat supplied by the gas (i.e. Q_1-2 is -ve).