Temperature–entropy diagram

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Graph relating temperature and entropy during a thermodynamic process or cycle

For other uses, see Tanabe–Sugano diagram.

Thermodynamics

The classical Carnot heat engine

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Note: Conjugate variables in italics

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c=

{\displaystyle c=}

T

{\displaystyle T}

\partial S

{\displaystyle \partial S}

N

{\displaystyle N}

\partial T

{\displaystyle \partial T}

Compressibility

\beta =-

{\displaystyle \beta =-}

1

{\displaystyle 1}

\partial V

{\displaystyle \partial V}

V

{\displaystyle V}

\partial p

{\displaystyle \partial p}

Thermal expansion

\alpha =

{\displaystyle \alpha =}

1

{\displaystyle 1}

\partial V

{\displaystyle \partial V}

V

{\displaystyle V}

\partial T

{\displaystyle \partial T}

Equations

Potentials

Internal energy
$U(S,V)$ {\displaystyle U(S,V)}
Enthalpy
$H(S,p)=U+pV$ {\displaystyle H(S,p)=U+pV}
Helmholtz free energy
$A(T,V)=U-TS$ {\displaystyle A(T,V)=U-TS}
Gibbs free energy
$G(T,p)=H-TS$ {\displaystyle G(T,p)=H-TS}

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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

References

[edit ]

^ "Temperature Entropy (T–s) Diagram - Thermodynamics - Thermodynamics". Engineers Edge. Retrieved 2010年09月21日.
^ "P–V and T–S Diagrams". Grc.nasa.gov. 2008年07月11日. Retrieved 2010年09月21日.

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