What must be true about the temperatures when discussing the Carnot cycle?

In the context of the Carnot cycle, the requirement for using absolute temperatures is crucial for accurately determining the efficiency of thermodynamic cycles. The Carnot cycle is fundamentally based on the second law of thermodynamics, which states that no engine operating between two heat reservoirs can be more efficient than a Carnot engine operating between the same reservoirs.

Using absolute temperatures, measured in Kelvin, is essential because the efficiency of the Carnot cycle is given by the formula:

Efficiency = 1 - (T_low / T_high)

where T_low and T_high are the absolute temperatures of the cold and hot reservoirs, respectively. Absolute temperature scales, such as Kelvin, provide a framework where temperatures can be treated uniformly. This prevents issues like negative values that would arise if relative or other temperature scales were used, which could lead to nonsensical or undefined efficiency calculations.

In summary, using absolute temperatures ensures that any calculations regarding the Carnot cycle are valid and reflect the thermodynamic principles involved.