One of the most efficient heat engines ever built is a...

One of the most efficient heat engines ever built is a coal-fired steam turbine in the Ohio River valley, operating between $1870^{\circ} \mathrm{C}$ and $430^{\circ} \mathrm{C}$. (a) What is its maximum theoretical efficiency? (b) The actual efficiency of the engine is $42.0 \% .$ How much mechanical power does the engine deliver if it absorbs $1.40 \times 10^{5} \mathrm{J}$ of energy each second from its hot reservoir?

Key Concepts

Mechanical Power

Mechanical power is the rate at which work is performed or energy is transferred, typically measured in Watts (Joules per second). In the context of a heat engine, mechanical power is determined by multiplying the actual efficiency (a decimal representing the percentage of energy converted to work) by the rate of energy absorption from the heat source. This concept links the theoretical efficiency to practical performance in real-world applications.

Heat Engine Efficiency

Heat engine efficiency quantifies the fraction of heat energy converted into useful work by a heat engine. It compares the work output to the heat energy input from the hot reservoir. Real engines typically operate at efficiencies lower than the Carnot efficiency due to practical irreversibilities and losses in the system.

Carnot Efficiency

Carnot efficiency is the maximum theoretical efficiency attainable by a heat engine operating between two thermal reservoirs. It is determined by the temperatures of the hot and cold reservoirs expressed in Kelvin, and is given by the formula ? = 1 - (T_c/T_h). This concept is fundamental as it establishes an upper bound on the efficiency of any real heat engine, reflecting the second law of thermodynamics.

Absolute Temperature

Absolute temperature, measured in Kelvin, is crucial in thermodynamics because it provides a scale where zero represents absolute zero, the point of complete thermal inactivity. When working with the Carnot efficiency formula, temperatures must be converted to Kelvin, ensuring that the calculations are thermodynamically valid and consistent.

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