Enthalpy

It is the sum of internal energy and product of pressure and volume. It is denoted by H.

Mathematically, H = U + PV

Let us consider a system which undergoes a change of state through any process. Let 1 and 2 gives the values at initial and final position respectively.

According to 1st Law of Thermodynamics

Q₁₋₂ = dU₁₋₂ + W₁₋₂

Q₁₋₂ = ( U₂ – U₁) + ʃ PdV -----(1)

Assuming the process to be at constant pressure

Q₁₋₂ = mCp( T₂ – T₁)

v₂

ʃ PdV = P ʃ dV = P ( V₂ – V₁)

v₁

inserting above values to eq. (1)

Q₁₋₂ = mCp( T₂ – T₁) = ( U₂ – U₁) + P ( V₂ – V₁)

= ( U₂ – U₁) + (P₂V₂ – P₁V₁)

= (U₂ + P₂V₂) – (U₁ + P₁V₁)

Q₁₋₂ = mCp( T₂ – T₁) = H₂ – H₁ { H = U + PV }

dH = Q₁₋₂ = mCpdT -----(2) {dH = H₂ – H₁}

It implies that change in enthalpy is equal to the heat transferred during constant pressure process.