# derive the relation between change in internal energy and change in enthalpy for a system in which the reactants and products are gases

Please find the solution to the asked query:

From First law of Thermodynamics we have:

ΔU = q +w

ΔU is the change in internal energy, q is the heat transfered, w is the work done

If a change is brought about at constant pressure , in that case volume changes . Let volume change from V

_{A}to V

_{B}at constant pressure P. The work done by the system is given by:

w = -P (V

_{B}- V

_{A})

Substituting this value in the above equation:

ΔU = q - P (V

_{B}- V

_{A})

or U

_{B}-U

_{A}= q - P (V

_{B}- V

_{A})

(U

_{B}

_{ }+PV

_{B}) - (U

_{ A }+PV

_{A}) =q

The quantity , U +PV is called the enthalpy of the system and is denoted by H

Thus [ H

_{B}-H

_{A}= ΔH = q] and

H = U +PV

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