FS 231

Supplement: Energy Balances: Steady State or Unsteady State, that is the question...

The issue of whether a system is operating at Steady State (SS) (and thus accumulation = 0) or not remains a mystery to more than a few students. I hope that the following material helps to clear up some of the mystery. If you are still unsure on this please see me.

The issue of SS vs USS is one involving TIME not SPACE. That is, when trying to determine if a process is running at SS we need to examine how it changes over time at a given point in space not how it changes from one point to another at some time. This is a pivotal point and is important to understand. The following example should help.

Image that it is a very very cold day outside and people are lined up outside the back of Schaub Hall waiting to file in one at a time. They come in at a steady flow rate and work their way through the warm building and eventually come out the front door, all following the same path.

1) Assuming that they all have the same style coat and behave in the same manner as they walk through the building, how does the temperature of their coat change?

Their coats will warm up by absorbing the heat of the surrounding air. (How will the rate of warming for each coat differ from other coats?)

2) If we were to stand at the back door with a digital thermometer and measure the temperature of each person's coat as they came in what would it be?

Assuming that they were all outside for the same (long) period of time, the temperature of each person's coat would be the same - cold!

3) If we were to stand at some point between the back and front doors and measure the temperature of each person's coat as they passed by, what would it be? Should it be the same or different, why?

The temperature of each coat as it passes by will be the same. Why not? What would make it different from the previous coat or the following coat? The point is that while the coat changes temperature from one location to the next, the temperature at any one location will always be the same because each coat has had the same "thermal treatment" up to that point.

4) Assuming that the building is very large and doesn't change temperature just because people enter or exit ( a good assumption) is this process SS?

You bet it is! The temperature of the system (and thus the total energy) is not changing over time.