Temperature–entropy diagram

For other uses, see Tanabe–Sugano diagram.

In thermodynamics, a temperature–entropy (T–s) diagram is a thermodynamic diagram used to visualize changes to temperature (T ) and specific entropy (s) during a thermodynamic process or cycle as the graph of a curve. It is a useful and common tool, particularly because it helps to visualize the heat transfer during a process. For reversible (ideal) processes, the area under the T–s curve of a process is the heat transferred to the system during that process.^[1]

Working fluids are often categorized on the basis of the shape of their T–s diagram.

An isentropic process is depicted as a vertical line on a T–s diagram, whereas an isothermal process is a horizontal line.^[2]

Example T–s diagram for a thermodynamic cycle taking place between a hot reservoir (T_H) and a cold reservoir (T_C).
For reversible processes, such as those found in the Carnot cycle:

  Q_C = the amount of energy exchanged between the system and the cold reservoir

  W = work exchanged by the system with its surroundings

Q_H = W + Q_C = heat exchanged with the hot reservoir. η = W / (Q_C + Q_H) = thermal efficiency of the cycle
If the cycle moves in a clockwise sense, then it is a heat engine that outputs work; if the cycle moves in a counterclockwise sense, it is a heat pump that takes in work and moves heat Q_H from the cold reservoir to the hot reservoir.

T–s diagram for steam, US units

See also

• Carnot cycle
• Pressure–volume diagram
• Rankine cycle
• Saturation vapor curve
• Working fluid
• Working fluid selection