Reversible Processes in a Closed System

 If the changes in kinetic and potential energies are negligible, the first law of thermodynamics can be expressed in differential form as:

dU = dQ + dW

For a reversible process, in the absence of a shaft work the above equation can be simplified as follows:

dU = dQ – PdV

Constant Volume (Isometric or Isochoric) Process

In the case where dV = 0, the above first law of thermodynamics expression simplifies further into:

dU = dQ

Integrating this expression for a reversible isometric process we obtain the following:

Q = ΔU

For a constant volume process, we know that: 

This equation is developed for a closed system undergoing a reversible isometric process. But since U is a state function, the above equation is applicable to all processes where V₁ = V₂ as shown in the following graph:

Constant Pressure (Isobaric) Process

In the case where Pressure is constant, the first law of thermodynamics expression simplifies into:

dU = dQ – d(PV)

or,

dQ = dH

Integrating the above equation for a reversible isobaric equation we obtain;

Q = ΔH

For a constant pressure process we know that;

This equation is developed for a closed system undergoing a reversible isobaric process. However, since H is a state function the ΔH equation becomes applicable to all processes in which P₁ = P₂.