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:
W1-2 = P (V2-V1) = 0
• Change in Internal Energy:
dU  = mCv (T2-T1)
U2 - U1 =
mCv (T2-T1)
• Heat Supplied or heat transfer:
Q1-2 = dU + W1-2
Q1-2 =
U2 - U1 = mCp (T2-T1)
• Change in Enthalphy:
H  = mCp (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. W1-2 is +ve); internal energy of the gas decreases (i.e. dU is -ve) and the heat supplied to the gas (i.e. Q1-2 is +ve).
• During compression or cooling process, work is done on the gas (i.e. W1-2 is -ve); internal energy of the gas increases (i.e. dU is +ve) and the heat supplied by the gas (i.e. Q1-2 is -ve).