# In mechanics ($\mathrm dV/\mathrm dx = 0$) in equilibrium, what about thermodynamics?

In mechanics we say that net force acting on a system is zero ($$\mathrm dV/\mathrm dx = 0$$) in equilibrium. In a similar way, which quantity should remain constant in thermodynamics?

• Depends on the case, for chemical systems, we have Gibbs free energy here Commented Aug 29, 2021 at 4:16
• Note, not just net force but also net torque is a requirement for equilibrium in practical mechanics. Commented Aug 29, 2021 at 7:17

Thermodynamics is more likely to use a steady state equilibrium than mechanics is. And that makes the comparison challenging.

This is even more likely if an actual fluid and not just energy or entropy is in flux, which is common as fluid mechanics and thermodynamics are often used together, and have significant areas of overlap, meaning either could legitimately claim certain topics are part of it. (In fact, I’d say a pump running and flows and pressures settling down is a classic example). Fields such as thermalhydraulics cannot rightly be called subfields of either, but are certainly more defined and smaller than both. In this way thermodynamics and fluid mechanics are similar to electrodynamics.

And steady state is different from a mechanical system in equilibrium with constant velocity because thermodynamic steady state equilibria still have a forcing function and a driven, which is not true for $$\sum~F_i=a=0~,~ v=k$$ in dynamics. Therefore, two dynamic systems are matched in their dynamics. For example, temperature differences directly drive heat flow, pressure differences directly drive mass flow, voltage differences directly drive current, so they must match. Nothing drives a constant-velocity object.

SHM is the only thing in mechanics that immediately comes ti my mind as comparable. But a wide variety of steady state equilibria in thermodynamics, without oscillations, are determined.

We could achieve a steady state where:

1. $$\sum q_i = 0 ~,~ \frac{dT}{dt}=0$$ for heat flows and temperatures. For a solid even.

2. $$\frac{dP}{d\vec{s}} = 0$$ for pressure

3. $$\frac{dQ}{d\vec{s}} = 0$$ for flows (and not in any oscillation, at every point in a river for example)

The interconnected nature also means that very often all of the above are balanced with connections between them. Viscosity and density, which determine steady state flow equilibria, are functions of pressure and temperature for example. But heat balance and hence pressure and temperature may change if the fluid dynamics vary.

• Steady state and equilibrium are not neccesarily the same Commented Aug 29, 2021 at 4:59
• physics.stackexchange.com/questions/103921/… Commented Aug 29, 2021 at 5:03
• @Buraian that link was not a rigorous definition and would not apply to many thermalhydraulic equilibria. There are more uses and definitions of each term than that implies. The distinctions are not perfectly cut and dry. Some people believe “has achieved steady state” or even “has settled down to steady state”, is a sensible statement. Other do not. Usually they are thinking of an isolated system and a case where boundaries can or cant be open and think it generalizes. Commented Aug 29, 2021 at 5:12
• If you have boundary conditions that take energy for example. And something else putting energy in. Or if you have a control volume in a pipe with constant flow. Commented Aug 29, 2021 at 5:12
• In fact, according to the definition in the link, a ball moving forever in a line at a constant speed has not reached equilibrium Commented Aug 29, 2021 at 5:19