At what cold-reservoir temperature (in ℃) would a Carnot engine with a hot-reservoir temperature of 427℃ have an efficiency of 60%?

Key Concepts

Carnot Efficiency

Carnot efficiency is the maximum possible efficiency of a heat engine operating between two thermal reservoirs. It is defined by the formula η = 1 - (T_c / T_h), where η is the efficiency, T_c is the absolute temperature of the cold reservoir, and T_h is the absolute temperature of the hot reservoir. This concept illustrates the theoretical limits of efficiency based on temperature differences.

Absolute Temperature

Absolute temperature is measured in Kelvin (K) and is a scale that starts at absolute zero, the point where molecular motion ceases. To convert Celsius to Kelvin, you add 273.15. In the context of the Carnot engine, both the hot and cold reservoir temperatures must be expressed in Kelvin to accurately calculate efficiency and understand thermodynamic principles.

Thermodynamic Temperature Scale

The thermodynamic temperature scale is a scale that reflects the energy state of a system and is crucial for understanding heat engines. It is based on the laws of thermodynamics and is measured in Kelvin. This scale is essential for calculating efficiencies and understanding the behavior of heat engines, as it provides a consistent framework for comparing temperatures across different systems.