# Is there a way to experimentally measure entropy?

I've been doing thermodynamic chemistry, and recently focusing on Gibbs Free Energy. Whilst doing calculations using, $$\Delta G = \Delta H - T \Delta S$$ I have been given a table of values for $\Delta H$ and $\Delta S$, and a temperature to work with. I was wondering , as the unit for entropy is $\mathrm{J/K}$ or $\mathrm{J\ K^{-1}}$ how exactly one would experimentally measure entropy/change in entropy, or can you?

The most common way of measuring $\Delta S^\circ$ for a chemical reaction is probably by making a van't Hoff plot. You measure the equilibrium constant $K$ at different temperatures and plot $\ln K$ vs $T^{-1}$. The $y$-intercept = $R\Delta S^\circ$ and the slope = $-R\Delta H^\circ$.

Another option is to measure $\Delta H^\circ$ by calorimetry and measure $K$ by some other means. Then compute $\Delta G^\circ$ from $K$ and solve for $\Delta S^\circ$

• Thank you. Very helpful answer, I've done calorimetry before so I know how to go about this method. Dec 12, 2015 at 11:59
• This might be a bit unconventional. M.A.Ramezani found an user with your name on it: Jan Jensen. If you recall creating this unregistered version of yourself, you can find out more about merging these accounts. Dec 17, 2015 at 10:46

The entropy change between two thermodynamic equilibrium states of a system can definitely be directly measured experimentally. To do so, one needs to devise (dream up) a reversible path between the initial and final states. Any convenient reversible path will do, since the integral of dq/T is the same for all reversible paths. So you have to identify a path that is easy to implement, and for which the heat flow can be measured easily (say by phase change in a reservoir). The experiment has to be carried in as close to reversible conditions as possible, since, in the real world, there is no perfectly reversible path. The hard part would be measuring the amount of heat flow. In some specific cases it could be done indirectly, such as in the isothermal quasistatic expansion of a gas (say in contact with a heat bath), where the measured amount of work (determined say by gradually removing small weights from a piston) would be equal to the amount of heat added. Of course, in many cases, it is much easier to calculate the entropy change (based on identifiable reversible paths) than it is to measure. In my judgement, devising a method to cause the heat flow to occur gradually and quantitatively measuring the heat flow directly would be the hard part.

• That's very interesting! Do you have a link that explains how to have a chemical reaction done reversibly and with heat measurement? Aug 26, 2022 at 11:14
• @JuanPerez Are you familiar with the vast Hoff equilibrium box concept? Or, are you familiar with how to carry out an electrolytic reaction by controlling the imposed potential difference so that the reaction occurs reversibly? Aug 26, 2022 at 11:42
• Right! An electrochemical reaction can be controlled, makes sense. Never heard of vant hoff box however. Aug 26, 2022 at 21:49
• A van't Hoff equilibrium box is a clever conceptual device for carrying out a gas phase reaction reversibly, starting with pure reactants and ending with pure products. Google it, or see Smith and Van Ness, Introduction to Chemical Engineering Thermodynamics. Aug 27, 2022 at 11:42

Entropy is a measure of randomness. The definition itself is hard to comprehend at times. And when you go to think, about how one would measure randomness, you get no answer. The term Entropy was introduced as a State Function to check whether the reaction is possible or not. Well there are formulae to determine the change in entropy. However as far as I have read, all books say that calculating the absolute value of entropy is quite difficult. According to me if you know the values of Entropy at Standard States you can calculate the Change in entropy for a process from STP to the temperature at which you want its absolute value and then just subtract to get the absolute value. The Standard State entropies are mentioned in quite a few books. Hope the answer helped.:-)