Isochoric or Isometric Process

When a thermodynamic process undergoes a physical change in such a way that its volume remains constant, then the change is known as isochoric process.

In this process P and T changes but V = constant. Hence Gay-lussac’s law is obeyed in this process.

(1) Equation of state

From ideal gas equation PV = mRT

If volume remains constant  P µ T or P₁/T₁=P₂/T₂=constant

(2) Indicator diagram : Graph I and II represent isometric decrease in pressure at volume V₁ and isometric increase in pressure at volume V₂ respectively and slope of indicator diagram dP/dV=∞

(3) Specific heat : Specific heat of gas during isochoric proces

(4) Bulk modulus of elasticity :

(5) Work done in isobaric process : ΔW=PΔV=P(V_f-V_i)                 [As V = 0]

Therefore                     ΔW = 0

(6) FLTD in isochoric process  :  ΔQ= ΔU+ ΔW= ΔU      [As ΔW = 0]

ΔQ=mC_v ΔT