A Carnot engine is operated between two heat reservoirs at...

A Carnot engine is operated between two heat reservoirs at temperatures of 520 $\mathrm{K}$ and 300 $\mathrm{K}$ . (a) If the engine receives 6.45 $\mathrm{kJ}$ of heat energy from the reservoir at 520 $\mathrm{K}$ in each cycle, how many joules per cycle does it reject to the reservoir at 300 $\mathrm{K} ?$ (b) How much mechanical work is performed by the engine during each cycle? (c) What is the thermal efficiency of the engine?

A Carnot engine is operated between two heat reservoirs at
temperatures of 520 $\mathrm{K}$ and 300 $\mathrm{K}$ . (a) If the engine receives
6.45 $\mathrm{kJ}$ of heat energy from the reservoir at 520 $\mathrm{K}$ in each cycle, how many joules per cycle does it reject to the reservoir
at 300 $\mathrm{K} ?$ (b) How much mechanical work is performed by the
engine during each cycle? (c) What is the thermal efficiency of
the engine?

Key Concepts

Thermal Efficiency

Thermal efficiency is the measure of how well a heat engine converts the heat energy it absorbs into useful work. For a Carnot engine, the efficiency is solely determined by the temperatures of the high and low temperature reservoirs, defined by the relationship ? = 1 - (T_cold/T_hot), which sets the upper limit for the efficiency of any real engine operating between the same temperatures.

Heat Transfer in Thermodynamic Cycles

In any thermodynamic cycle, the engine absorbs energy from a high-temperature reservoir and rejects energy to a low-temperature reservoir. The difference between these two heat quantities represents the net work done by the system. In the Carnot cycle specifically, the ratio of the rejected heat to the absorbed heat is equal to the ratio of the temperature of the cold reservoir to that of the hot reservoir.

Carnot Engine

A Carnot engine is an idealized heat engine that operates on a reversible cycle, known as the Carnot cycle, which allows it to achieve the maximum theoretical efficiency. It serves as a standard for efficiency in thermodynamics because it assumes no entropy production during the cycle, meaning all the processes are reversible.

Work Output

The mechanical work performed by an engine in a cycle is calculated as the difference between the heat input from the hot reservoir and the heat expelled to the cold reservoir. This concept is fundamental because it quantifies the conversion of energy from heat to work, which is a core principle behind heat engine operation.

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