A furnace can supply heat steadily at 1300 K at a rate of 500 kJ / s. The maximum amount of po

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A furnace can supply heat steadily at 1300 K at a rate of...

A furnace can supply heat steadily at $1300 \mathrm{~K}$ at a rate of $500 \mathrm{~kJ} / \mathrm{s}$. The maximum amount of power that can be produced by using the heat supplied by this furnace in an environment at $300 \mathrm{~K}$ is (a) $115 \mathrm{~kW}$ (b) $192 \mathrm{~kW}$ (c) $385 \mathrm{~kW}$ (d) $500 \mathrm{~kW}$ (e) $650 \mathrm{~kW}$

A furnace can supply heat steadily at $1300 \mathrm{~K}$ at a rate of $500 \mathrm{~kJ} / \mathrm{s}$. The maximum amount of power that can be produced by using the heat supplied by this furnace in an environment at $300 \mathrm{~K}$ is
(a) $115 \mathrm{~kW}$
(b) $192 \mathrm{~kW}$
(c) $385 \mathrm{~kW}$
(d) $500 \mathrm{~kW}$
(e) $650 \mathrm{~kW}$

Key Concepts

Carnot Efficiency

Carnot efficiency is the maximum theoretical efficiency that a heat engine operating between two temperature reservoirs can achieve. It is determined solely by the temperatures of the hot and cold reservoirs and is given by 1 minus the ratio of the cold reservoir temperature to the hot reservoir temperature. This concept establishes the upper limit on the efficiency of real heat engines as dictated by the second law of thermodynamics.

Thermal Reservoirs

Thermal reservoirs are idealized systems that can supply or absorb finite amounts of heat at constant temperatures. In heat engine analysis, one reservoir typically represents the high-temperature source and the other the low-temperature sink. The use of thermal reservoirs simplifies calculations by assuming that their temperatures remain unchanged during the heat transfer process.

Heat Engine

A heat engine is a device that converts thermal energy into mechanical work by exploiting the temperature difference between a hot and a cold reservoir. The performance of a heat engine is fundamentally limited by the laws of thermodynamics, specifically through constraints like Carnot efficiency, which define the maximum possible work obtainable from a given amount of heat transfer.

Power

Power is the rate at which energy is transferred or converted and is typically measured in watts (or kilowatts). In the context of heat engines, it quantifies how quickly thermal energy can be converted into mechanical work. Understanding power is crucial when evaluating the performance of an engine, as it relates to both energy input rates and the practical limits imposed by thermal efficiency.

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