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Derive the expression, ΔH = ΔU + PΔV.

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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.

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