Sterling Cycle

What the Sterling Cycle Is

The Sterling cycle is a closed thermodynamic cycle; the Sterling engine is based on it. The working substance used in a Sterling engine is a gas such as air, helium, hydrogen or nitrogen.

• All the processes in the Sterling cycle are reversible processes.
• When the gas is heated, the Sterling engine produces useful work — it runs as an engine.
• When work is done on the gas, it works as a refrigerator. This is the reverse working of a Sterling cycle.
• The reversed Sterling cycle is extensively used in the field of cryogenics to produce extremely low temperatures and to liquefy air or the gases mentioned above.

The p–V Diagram

Figure 4.28 shows the cycle as a closed loop through four points A, B, C, D. Heat is absorbed at the constant high temperature $T_H$ and rejected at the constant low temperature $T_C$.

The ideal Sterling cycle has two isothermal processes, AB at $T_H$ and CD at $T_C$. These two isothermals are connected by the two processes BC and DA, along which the gas is carried between the two temperatures. AB is the upper curve running to the right (expansion at $T_H$); CD is the lower curve running to the left (compression at $T_C$); BC drops from the high-temperature isotherm to the low-temperature isotherm at the right-hand end of the loop, and DA rises back at the left-hand end.

Note on the textbook: the introductory sentence of section 4.12 describes BC and DA as two isobaric processes, while the step-by-step list that follows calls BC an isochoric process and DA an isobaric heat absorption. Reproduce the four steps as the textbook lists them below; that is the description the board's answers follow.

The Four Processes

• Isothermal expansion (AB): the gas is heated by supplying heat $Q_H$ at constant temperature $T_H$. Useful work is done by the gas in this part of the cycle.
• Isochoric process (BC): part of the heat $Q_H$ absorbed by the gas in the previous part of the cycle is released by the gas to the refrigerator. This heat $Q$ is used in the next part of the cycle. The gas cools down to temperature $T_C$.
• Isothermal compression (CD): the heat generated in this part of the cycle, $Q_C$, is rejected to the coolant (the sink). The temperature of the gas is maintained at $T_C$ during this process.
• Isobaric heat absorption (DA): the compressed gas absorbs the heat $Q$ during this process. Its temperature is increased to $T_H$.

The cycle repeats when the process reaches the point A again.

Standard Results

• Sterling cycle: a closed, fully reversible cycle with two isothermal processes AB (at $T_H$) and CD (at $T_C$) joined by the two processes BC and DA.
• Heat $Q_H$ is absorbed at constant temperature $T_H$ during AB; heat $Q_C$ is rejected at constant temperature $T_C$ during CD; the heat $Q$ released during BC is stored and returned to the gas during DA.
• Working substances: air, helium, hydrogen, nitrogen.
• Heating the gas gives an engine producing useful work; doing work on the gas gives a refrigerator. The reversed Sterling cycle is used in cryogenics to reach extremely low temperatures and to liquefy gases.
• Being a cyclic process, $\Delta U = 0$ over the complete cycle and $Q = W$, the work being the area enclosed by the loop.