As no heat is added to or removed from the absorber externally, energy balance around the absorber would be
Enthalpy of the absorber feed (solute + air) + Enthalpy of the pure fluid (water,say) which will absorb the solute =Enthalpy of (fluid + solute) + Enthalpy of absorber gas (less amount of solute + air)
As amount of solute is generally very low in absorber we can consider the corresponding inlet and outlet temperature of air and water for calculating the enthalpy at that particular temperature.
As no vapor phase present, enthalpy = mass * specific heat of air or water * { measured temperature - reference temperature (00C, say)}
And if vapor phase present, enthalpy = mass * specific heat of air or water * { measured temperature - reference temperature (00C, say)} + latent heat of vaporisation of fluid at that temperature * mass
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