# Thermodynamic equilibrium in a room , in a real situation

In my class about 50 students were seated in a room. The room was medium sized and it had 2 AC, one in the front and one at the back.

The teacher was feeling cold so he switched off the front AC while leaving the back one on. I thought it would not matter because ultimately an AC maintains the temperature and thermodynamic Equilibrium would be attained and he would still feel cold.(They were the powerful overhead type)

But that didn't happen. While at the back it was very cold , the front was at a normal temperature.

But why is it so?? Why was thermodynamic equilibrium not attained. Even if there was warm air was present in front , it should rush back and cool air should move to the front and he should still feel cold....

There are no windows and only a single door.

What I think is that thermodynamic equilibrium can only be achieved after a sufficiently long period of time, due to the nature of particulate matter. Another factor I could say is probably the fact that you have modelled how an AC works ideally, but not actually.

Others feel free to comment on my answer.

A thermodynamic equilibrium doesn't imply a constant temperature field throughout the classroom.

This is just like the case where one end of an iron bar in air can be absolutely cold yet the other end, lets say a mile away, can be at room temp. This is because along its length heat flows from the end without cooling to the cool end. At equilibrium, there is a thermal gradient.

The fact that multiple ACs are being used implies that there is enough of a heat inflow in your classroom to heat the cold air leaving the back AC before it reaches the teacher. How does this happen? Do not have the mental picture that a cold pocket of air moves to the teacher and 'dumps its coldness' there. It heats up along the way by convectional mixing(and not just that, there is contact with class walls, radiation from heated (assuming concrete) walls, turbulence, body heat etc.).

The fact that students at back feel a lot cooler is because they are near the cold generator(AC-the heat sink). Here the just cooled air hasn't had time to warm up--at the moment it blows on the students at the rear, its still cold enough to be chilly. For the same reason the teacher turned off the AC nearest to him.

Is there no effect at all where the teacher sits? No. With only the back AC on the temperature of air where the teacher sits does drop a bit but not as much as when the front AC was on too.

When would the teacher start feeling cold? Shut all the doors and windows in the class room so there are no heat transfers via airflow. Wait for nightfall so the walls are cool. Let the classroom be empty of all students. Now the temp. at front would be a lot similar to that at the back at equilibrium.

The atmosphere of a class room is not an isolated system. There are heat exchanges happening via air flows through windows and doors. Lets say there aren't any--a completely walled off classroom. Then there are heat sources--the human bodies. Lets ignore them(they are negligible anyways)

Since more than one AC was used, the room should surely not be big enough for a single AC. The AC at the back throws out cool air , buy you are neglecting the 50 radiatior (humans) sitting in the class. By the time the air reaches till the front it gets warmer. There is a constant gradient of temperature that is present and is maintained by the humans acting as a source and the AC as a potential sink.