I'm a high school student with basic knowledge about chemical thermodynamics. I have three questions regarding the thermodynamic state functions $H, S, G$. I have searched a lot in textbooks but they don't give the complete information as to whether the properties taken are that of the system or surroundings.

Q1):-Enthalpy is given by the formula

$H = U +PV$ . What I want to know is that whether $P$ mentioned above is the internal pressure of the system or the externally applied pressure?

Q2):- The change in entropy is given by the formula $\Delta S= $$\int_1^2$${\frac{dq_{reversible}}{T}}$. Is the temperature mentioned of the system or the surroundings.

Q3)-On the same lines what temperature is taken to define the Gibbs free energy function:-$G=H-TS$.

Thanks in advance.


The three functions you mentioned are applicable only to thermodynamic equilibrium states of the system, for which the pressures and temperatures of the system and its surroundings match one another to within insignificantly small differences. In the integral to get the entropy change (Q2), the same matching applies; that is, a reversible path consists of a continuous sequence of thermodynamic equilibrium states.

Note that, at the interface between the system and the surroundings, the temperature and pressure of the system always matches the temperature and pressure of the surroundings (irrespective of whether the system is at equilibrium). It's just that, along an irreversible path of the system (for which the system passes through a sequence of non-equilibrium states), the pressure and temperature within the system vary with spatial position, and their average values (averaged over the volume of the system) do not match those of the surroundings at the interface.

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  • $\begingroup$ Thanks for your enlightening answer.. Does it mean that I can apply these equations only during initial and final states for an irreversible process (when the system attains equilibrium after passing through a series of non euilibrium states )and not when the system is undergoing that process? $\endgroup$ – user50247 Sep 8 '17 at 5:08
  • $\begingroup$ I also came across a statement that change in enthalpy when a gas undergoes free expansion process is equal to zero. How would you account for this statement sir? If I assume that the equation mentioned in q1 is applicable only in equilibrium states and the pressure is that of the gas it would give me a non zero change in enthalpy. Am I going wrong somewhere? $\endgroup$ – user50247 Sep 8 '17 at 5:19
  • $\begingroup$ I forgot to mention that the aforementioned process is an adiabatic free expansion. $\endgroup$ – user50247 Sep 8 '17 at 5:25
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    $\begingroup$ The answer to your first question is "yes" for the global system undergoing the irreversible change (because the pressure, temperature, and specific volume are varying with position within the system). But, on a small scale, the answer depends on whether you are willing to approximate the thermodynamic functions locally (per unit mass) using the local conditions of temperature and pressure. We engineers are, but some physicists, chemists, and other purists are not. $\endgroup$ – Chet Miller Sep 8 '17 at 13:05
  • $\begingroup$ Regarding your questions about Joule Thompson and adiabatic free expansion, I feel it would be better to ask these questions in a new thread. $\endgroup$ – Chet Miller Sep 8 '17 at 13:08