A house is maintained at 21^∘ C in winter by electric resistance heaters. If the outdoor tempera

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A house is maintained at 21^∘ C in winter by electric...

A house is maintained at $21^{\circ} \mathrm{C}$ in winter by electric resistance heaters. If the outdoor temperature is $3^{\circ} \mathrm{C}$, the second-law efficiency of the resistance heaters is
(a) $0 \%$
(b) $4.1 \%$
(c) $6.1 \%$
(d) $8.6 \%$
(e) $16.3 \%$

Key Concepts

Second-Law Efficiency

Second-law efficiency is a measure of how well a process or device performs relative to the maximum possible (ideal, reversible) performance dictated by the second law of thermodynamics. It takes into account the irreversibilities inherent in real processes, comparing the actual useful effect achieved (such as heating or work output) to the maximum theoretical effect possible under the same conditions.

Carnot Efficiency and Carnot COP

The Carnot cycle represents the idealized behavior of a thermodynamic system operating between two temperature limits, and its efficiency (or coefficient of performance for heating and cooling devices) sets the upper bound for what any real system can achieve. In heating applications, the Carnot coefficient of performance (COP) is defined as the ratio of the hot reservoir temperature (in Kelvin) to the temperature difference between the hot and cold reservoirs, providing a benchmark against which the actual performance of heating devices can be compared.

Coefficient of Performance (COP)

The coefficient of performance (COP) is a metric used to evaluate the efficiency of heating and cooling devices, defined as the ratio of the desired output (e.g., heat provided) to the work input required to produce that output. In an ideal heating system operating reversibly, the COP is maximized and is determined by the working temperatures as per the Carnot COP, serving as a reference point for evaluating real devices.

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