# Linear decrease in temperature during a redox reaction?

This is physics-related, don't worry. To calculate the enthalpy change of a solution during a redox reaction, what we did in class was measure the temperature of the solution every 30 seconds (before, during, and after the reaction) and waited until it started decreasing. Once the temperature was decreasing, we made sure to get at least around 10 measurements (so 5 minutes of measuring) and then we plotted these. We made a linear fit for the temperature as a function of time but using $\textit{only the data from when the temperature decreased}$. Into this function we plugged in for time the initial time when the reaction began (we call it extrapolating, not sure if that's the correct term) to get the temperature that the solution should have reached right after the reaction.

Now, what I'm not sure about is this: we're using a linear function to model the decrease in temperature of the solution, but doesn't temperature decrease exponentially? (At least according to Newton's law of cooling).

My only guess for why this could be correct is that maybe at short enough time scales, this exponential decrease can be approximated as linear, so it's justified that we're doing this. Is this the reason? Or is there some other justification for doing it this way?

• You are correct, if the heat generation by the reaction is (almost) instantaneous, then one could model the temperature decrease with an exponential (additionally assuming constant heat capacity and heat conduction). If, however, the reaction time constant is similar to the cooling time constant of the solution, then one has to model the system with an inhomogeneous differential equation, with an exponential decrease in heating driving a first order equation for the heat flow. In the latter case it may be possible to get (nearly) linear solutions, which can be fitted with good accuracy. – CuriousOne Aug 28 '14 at 4:28
• Oh cool thanks! One thing I'm unsure about- how does the reaction time affect the way that the material will cool? It seems more intuitive that the solution shouldn't be able to "remember" how the reaction occurred, only the initial temperature it had. – Physics Llama Aug 28 '14 at 22:57
• The reaction time wouldn't affect the cooling but it would change the way the solution is heated, slowly or quickly. Think about the other extreme: if we supply a constant amount of heat per time (e.g. with an electric heater), the temperature will rise, until there is a new equilibrium between supplied heat and heat loss. If both effects, decreased loss of heat because of already sinking solution temperature and decaying heat production in the solution cancel each other out, one may get an almost linear region, but that depends on both time constants. – CuriousOne Aug 28 '14 at 23:36