Question

Which one of the following makes an ideal air-standard Stirling cycle?

• A. Two reversible isobars, and two reversible adiabatics
• B. Two reversible isotherms, and two reversible isobars
• C. Two reversible isotherms, and two reversible isochores
• D. Isentropic compression, constant volume heat addition, isentropic expansion, and constant volume heat rejection

Hint:

The Stirling cycle is the constant temperature counterpart of the Otto cycle. It swaps the two isentropic legs of the Otto cycle for two isothermal legs, while keeping the two constant volume legs.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
An air-standard cycle is an idealized version of a real engine cycle, built from a fixed sequence of simple reversible processes, constant pressure, constant volume, constant temperature, or isentropic legs, using air as the working fluid. Each named cycle, Otto, Diesel, Brayton, Stirling, is defined by its own specific sequence of four such processes, and the question is asking us to recall the Stirling cycle's specific sequence.

Step 2: Key Formula or Approach:
Picture the Stirling cycle traced on a $p$-$V$ diagram: starting at some state, the gas expands at constant temperature $T_H$, an isotherm, while absorbing heat from a hot source, then it is cooled at constant volume, an isochore, giving up heat internally, typically to a regenerator, then it is compressed at constant temperature $T_L$, a second isotherm, while rejecting heat to a cold sink, and finally it is heated back up at constant volume, a second isochore, typically drawing back the heat stored in the regenerator, to return to the starting state. Four legs total: isotherm, isochore, isotherm, isochore.

Step 3: Detailed Explanation:
Compare this sequence against the four listed options. Two isobars and two adiabatics describes the Brayton cycle used in gas turbines and jet engines, which has constant pressure heat addition and rejection, not constant temperature. Two isotherms and two isobars is not a standard named cycle and does not match the isochoric legs of Stirling. Isentropic compression, constant volume heat addition, isentropic expansion, constant volume heat rejection is the Otto cycle, which uses isentropic legs instead of isothermal legs for the compression and expansion strokes. Only two isotherms and two isochores reproduces the exact four leg sequence built in Step 2.

Step 4: Final Answer:
The ideal air-standard Stirling cycle consists of two reversible isotherms and two reversible isochores.
\[ \boxed{\text{two isotherms and two isochores}} \]