I was in the lab, and mentioned to another engineer that the temperature of a device had “come to equilibrium.” He quickly corrected me, and said it had come to steady-state, not equilibrium.
Perhaps he’s correct. I’ve never given much thought to the difference between the two terms. Thoughts on when to use each term?
In general, it depends on whether we’re talking about dynamic or static equilibrium, mechanical or chemical, local or global, … In equilibrium, all processes or forces are balanced on the time scale and in the region of interest. E.g., atoms may be diffusing to the right, but just as many are diffusing to the left or the force trying to push the box up the hill is exactly matched by the gravitational component trying to slide it back down the hill.
In steady state, nothing is changing with time on the time scale and region of interest. The water flowing in from the tap is matched by the water flowing out the drain, so the water in the tub is in steady state. If we back away from the tub, we see that the plumbing in the house or the city water/sewage system can be seen not to be in steady state: the reservoir up i the mountains is draining while sea level is rising (ever so slightly). Back away again, and evaporation from the ocean feeds rainfall in the reservoir, so that global system can again be seen to (perhaps) be in steady state. When casting a jet engine turbine blade, if viewed from a reference frame moving along with the solid-liquid boundary, the crystalline dendrites can be in steady state with no apparent motion of the tips or branches; viewed from the laboratory frame, though, the dendrites tips move from the bottom of the casting to the top.
An ice cube in a glass of 0 °C water is in equilibrium. If the glass sits in a 25 °C room, though, the ice will eventually melt and the water will get warmer, eventually reaching a new equilibrium of just water at 25 °C. If the room is not well insulated against the winter storm outside, the system may eventually reach a new equilibrium of 100% ice. Unless, of course, the furnace is in steady state with the heat losses to the outside.
I would think that if I had a quantity of water at 50 F and an equal amount at 70 F and poured them together and stirred it would be in equilibrium at 60 F.
But if I had two streams of water that merged and the resultant outflow was 60 F they are in steady state.
Maybe ‘equilibrium’ isn’t used because water can be in a steady state that is not in equilibrium. For example, superheated water, or super chilled water. The temp isn’t changing, but add a nucleation site, and…
Usually, that would be called a metastable equilibrium