A Carnot engine Converts one sixth of the heat input into...

A Carnot engine Converts one sixth of the heat input into work. When the temperature of the sink is reduced by $62^{\circ} \mathrm{C}$ the efficiency of the engine is doubled. The temperature of the source and sink are (A) $80^{\circ} \mathrm{C}, 37^{\circ} \mathrm{C}$ (B) $95^{\circ} \mathrm{C}, 28^{\circ} \mathrm{C}$ (C) $90^{\circ} \mathrm{C}, 37^{\circ} \mathrm{C}$ (D) $99^{\circ} \mathrm{C}, 37^{\circ} \mathrm{C}$

A Carnot engine Converts one sixth of the heat input into work. When the temperature of the sink is reduced by $62^{\circ} \mathrm{C}$ the efficiency of the engine is doubled. The temperature of the source and sink are
(A) $80^{\circ} \mathrm{C}, 37^{\circ} \mathrm{C}$
(B) $95^{\circ} \mathrm{C}, 28^{\circ} \mathrm{C}$
(C) $90^{\circ} \mathrm{C}, 37^{\circ} \mathrm{C}$
(D) $99^{\circ} \mathrm{C}, 37^{\circ} \mathrm{C}$

Key Concepts

Carnot Engine

A Carnot engine is an idealized heat engine that operates on the reversible Carnot cycle and serves as a standard for comparing the efficiency of real heat engines. Its significance lies in the fact that no real engine operating between two heat reservoirs can surpass the efficiency of a Carnot engine, making it fundamental in thermodynamic studies and the understanding of energy conversion processes.

Heat Engine Efficiency

The efficiency of a heat engine indicates the proportion of absorbed heat that is converted into useful work, while the remainder is exhausted to a cold sink. In the context of a Carnot engine, efficiency is expressed through the formula ? = 1 - (T_cold/T_hot), where temperatures are in an absolute scale (Kelvin). This relationship illustrates that efficiency increases as the temperature difference between the hot and cold reservoirs grows.

Thermodynamic Reservoirs

In thermodynamics, heat engines operate between two reservoirs: a hot source that supplies thermal energy and a cold sink that absorbs waste heat. The temperatures of these reservoirs are critical in determining the engine's performance and efficiency, as the maximum possible efficiency is set by the ratio of their absolute temperatures.

Temperature Conversion

Temperature conversion is an essential concept in thermodynamics since calculations involving efficiency must use absolute temperatures (Kelvin) rather than Celsius. Converting from Celsius to Kelvin involves adding 273.15, which ensures that the temperature measurements used in equations are physically meaningful and accurate for theoretical predictions.

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