One may suppose that you are talking about vapor sorption of water?  if so, the water activities are those that correspond to the same sorbed amount of water, at both two temperatures. In other words, if you have two water vapor sorption isotherms (determined at two different temperatures) and have selected a certain sorbed water amount, then, for each isotherm, there is a certain water activity corresponding to a given water sorbed concentration. That is what you need. It might be also relative air humidity which is by 100 times greater than pure liquid state-referred activity of water. or, perhaps, the problem arises from the fact that you have mesured the isotherms shown as sorbed water concentrations against equilibrium partial vapor pressures of water. In this case, you can use partial vapor pressures, instead of activity, but keep in mind, that the determined enthalpy change will correspond to the transfer from gas phase reference state but from the liquid water reference state. But you may finally add the vaporization enthalpy of water to the isotheric enthalpy obtained from the sorbed amount vs. partial vapor pressure isotherm, and it will be the same as to use activities, which is the isosteric enthalpy change corresponding to the transfer of water molecules from liquid water to a sorbed state with a given water concentration.....

Hello Mikhail,

Do you mean the equilibrium moisture content of the product at critical water activity.

Hi, R Rajamanickam,

what do you call "critical water activity"? I mean a regular sorption isotherm of water vapor, which is the water content of an adsorbent plotted against pure liquid referred water activity or relative humidity (which water activity X 100) or against partial vapor pressure (which is water activity multiplied by the pressure of a saturated water vapor, at a given temperature)

What I mean as Critical water activity is that above which the product starts spoils.

Dr. Mikhail,

In your answer to Shefali, you have mentioned that

"two water vapor sorption isotherms (determined at two different temperatures) and have selected a certain sorbed water amount, then, for each isotherm, there is a certain water activity corresponding to a given water sorbed concentration. That is what you need."

Can you say with some example. I could not understand the point. 

Wow! it is something behind I could imagine. So, you are talking about complex biochemical processes which are heavily irreversible. If water sorption isotherm is reversible below "critical water activity" (which possible indicates the minimal water activity needed for activity of enzymes and microorganisms?), then, the regular procedures for calculating  isosteric heats are applicable. But the question is whether above this critical water activity value apparent water sorption isotherms are reversible. If not, the thermodynamic procedure will not be unanimously possible. 

Ok. When you determine water sorption isotherm, e.g., for water sorption by meat, you may plot water content of a meat sample equilibrated at a certain relative air humidity (RH); as higher the RH is, the higher water content. Here you have a water sorption isotherm at one temperature; the same may be made at another temperature. Then, just look at the standard procedure of calculating isosteric heats