#T-s diagrams

Imagine encountering the diagram below without any accompanying equations.

Figure 1 — An unfamiliar T–s diagram. What can you infer before calculating anything?

What can this picture tell us before we calculate anything?

Quite a lot—but only if we read it in the right order. A temperature–entropy diagram combines several kinds of information: thermodynamic states, the process connecting those states, and sometimes a geometric representation of heat transfer. Those layers are related, but they are not interchangeable.

The safest approach is to treat the diagram like a route on a map. First identify the coordinates. Then locate the stops and follow the direction of travel. Only after that should you ask what the shape of the route means.

1. Read the axes

A temperature–entropy diagram, usually called a T–s diagram, places absolute temperature on the vertical axis and specific entropy on the horizontal axis.

The vertical coordinate is

$$ T = \text{absolute temperature}. $$

Temperature is normally expressed in kelvins. Because thermodynamic equations use absolute temperature, a T–s diagram should not be interpreted using Celsius or Fahrenheit as though their zero points were physically absolute.

The horizontal coordinate is

$$ s = \text{specific entropy}. $$

Lowercase $s$ means entropy per unit mass. Common units include joules per kilogram-kelvin or kilojoules per kilogram-kelvin: