A Carnot engine has an efficiency of 22.0 % . It operates...

A Carnot engine has an efficiency of $22.0 \% .$ It operates between constant-temperature reservoirs differing in temperature by $75.0 \mathrm{C}^{\circ} .$ What is the temperature of the (a) lower-temperature and (b) higher-temperature reservoir?

Key Concepts

Temperature Difference in Thermodynamic Processes

The difference in temperature between the hot and cold reservoirs directly influences the work output and efficiency of a heat engine. In calculations, even if the temperature difference is given in a relative unit like degrees Celsius, it can be directly used when converting to an absolute difference in Kelvin, because the size of one degree Celsius is identical to one Kelvin.

Absolute Temperature Scale

In thermodynamics, temperatures must be measured on an absolute scale, typically in Kelvin, to ensure proper comparison and calculation in processes such as those involving heat engines. This is because the laws governing thermal efficiency rely on ratios of absolute temperatures, making it crucial to convert any temperature differences from degrees Celsius to Kelvin.

Heat Engine Efficiency

Heat engine efficiency, particularly in the context of the Carnot engine, is defined as the ratio of work output to heat input. For a Carnot engine, this efficiency is determined by the absolute temperatures of the high- and low-temperature reservoirs, using the formula ? = 1 - (T_low/T_high). This relation provides a benchmark for evaluating the performance of real engines.

Carnot Engine

A Carnot engine is an idealized heat engine that operates on the Carnot cycle, which is a reversible process consisting of two isothermal processes and two adiabatic processes. Its significance lies in establishing the maximum possible efficiency that any heat engine operating between two thermal reservoirs can achieve, depending solely on the temperatures of these reservoirs.

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