Carnot cycle efficiency and what it depends on: In classical thermodynamics, the thermal efficiency of an ideal Carnot heat engine depends on which fundamental parameter(s) of the two heat reservoirs?

Introduction / Context:
The Carnot cycle is the theoretical benchmark for heat engines operating between two thermal reservoirs. Its efficiency sets the upper limit that no real engine can surpass. Knowing exactly which variables the Carnot efficiency depends on is essential to avoid common confusions with other cycles (Otto, Diesel, Brayton) that involve pressures, volumes, and cut-off ratios.

Given Data / Assumptions:

• Heat addition from a high-temperature reservoir at T_h (absolute scale).
• Heat rejection to a low-temperature reservoir at T_c (absolute scale).
• Internally reversible processes (idealization).
• No assumptions on specific working fluid beyond reversibility.

Concept / Approach:
The thermal efficiency of a Carnot engine is governed solely by the two temperature limits. The well-known relation is η_Carnot = 1 − (T_c / T_h). Variables like pressure ratio or volume compression ratio may change along the cycle, but they do not enter the efficiency expression; they are consequences of the temperatures and the working fluid state, not independent determinants of η.

Step-by-Step Solution:

Verification / Alternative check:
Changing compression ratio or pressure ratio without altering T_h and T_c does not change η_Carnot. Conversely, lowering T_c or raising T_h increases η according to the formula, consistent with second-law limits and real-engine trends (within material constraints).

Why Other Options Are Wrong:

• Pressure ratio: Relevant for Brayton/Gas-turbine ideal cycles, not Carnot efficiency.
• Volume compression ratio: Central to Otto/Diesel efficiency formulas, not Carnot.
• Cut-off ratio and compression ratio: Diesel/dual-cycle parameters, not applicable here.

Common Pitfalls:
Assuming that higher compression ratio always raises efficiency even for Carnot; conflating practical engine parameters with the purely temperature-based Carnot limit.

Final Answer:
temperature limits