A reversible heat engine operates between thermal reservoirs...

A reversible heat engine operates between thermal reservoirs at $900 \mathrm{K}$ and $200 \mathrm{K}$. If $9000 \mathrm{J}$ are extracted from the hot reservoir, how much work is done by the heat engine?

Key Concepts

Thermal Reservoirs

Thermal reservoirs are large bodies or systems with an effectively infinite capacity to absorb or supply heat without changing their temperature. In thermodynamic cycles, they are used to represent the sources and sinks of heat, thereby establishing the temperature limits which directly influence the efficiency of the engine.

Work Output Calculation

In the context of heat engines, the work output is determined by the product of the heat absorbed from the hot reservoir and the efficiency of the engine. For a reversible engine operating under the Carnot cycle, this calculation uses the Carnot efficiency to determine the maximum theoretical work that can be extracted from a given amount of heat input.

Carnot Cycle Efficiency

This concept refers to the maximum efficiency that any heat engine can achieve when operating between two thermal reservoirs. It is given by the formula 1 - (T_cold/T_hot), where T_cold and T_hot are the absolute temperatures of the cold and hot reservoirs, respectively. This efficiency represents an ideal limit that real engines approach but never reach due to inherent irreversibilities in actual processes.

Reversible Heat Engine

A reversible heat engine is an idealized system that operates in a manner where all processes can be reversed without any net change in entropy. Such engines are theoretical constructs used to model the maximum efficiency limit in thermodynamics. They perform their cyclic processes infinitely slowly and represent the best-case scenario for energy conversion.

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