Question

Derive the expression, ΔH = ΔU + PΔV.

Answer 1

Enthalpy (H) of a system is defined as,

H = U + PV 

Where U is internal energy 

P is pressure and V is volume. 

Consider a process in which a state of a system changes from an initial state A to a final state B. 

Let H₁, U₁, P₁, V₁ and H₂, U₂, P₂, V₂ be the state functions of the system in initial and final states.

Then,

H₁ = U₁ + P₂V₂ and H₂ = U₂ + P₂V₂ 

The enthalpy change ΔH is given by,

ΔH = H₂ – H₁

= (U₂ + P₂V₂) – (U₁ + P₁V₁) 

= (U₂ – U₁) + (P₂V₂ – P₁V₁)

= ΔU + ΔPV

Where ΔU = U₂ – U₁ 

At constant pressure, 

P₁ = P₂ = P

∴ P₂V₂ – P₁V₁ = PV₂ – PV₁

= P(V₂ – V₁)

= P × ΔV 

Hence, 

ΔH = ΔU + PΔV 

This is a relation for enthalpy change.