When the addition of the differential amount of component \(i\) \(\mathrm{d}n_{i}^{\sigma }\) or \(\mathrm{d}n_{i}^{\rm{s}}\) is effected at constant pressure \(p\), the differential molar enthalpy of adsorption, \(\Delta _{a}H_{i}^{\sigma}\) or \(\Delta _{a}H_{i}^{\rm{s}}\) also called the isosteric enthalpy of adsorption (\(q^{\rm{st}}\)) is defined as: \[\Delta _{a}H_{i}^{\sigma} = -q^{\rm{st},\sigma} = U_{i}^{\sigma} - H_{i}^{\rm{g}}\] \[\Delta _{a}H_{i}^{\rm{s}} = -q^{\rm{st},\sigma} = H_{i}^{\sigma} - H_{i}^{\rm{g}}\] where \(H_{i}^{\rm{s}}=(\frac{\partial H^{\rm{s}}}{\partial n_{i}^{\rm{s}}})_{T,p,m,n_{j}^{\rm{s}}}\) and \(H_{i}^{\rm{g}}\) is the partial molar enthalpy of component \(i\) in the gas phase, i.e. \((\frac{\partial H^{\rm{g}}}{\partial n_{i}^{\rm{g}}})_{T,p,n_{i}^{\rm{g}}}\)