A passive solar house that was losing heat to the outdoors at 5^∘ C at an average rate of 50,000

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A passive solar house that was losing heat to the outdoors...

A passive solar house that was losing heat to the outdoors at $5^{\circ} \mathrm{C}$ at an average rate of $50,000 \mathrm{~kJ} / \mathrm{h}$ was maintained at $22^{\circ} \mathrm{C}$ at all times during a winter night for $10 \mathrm{~h}$. The house was heated by 50 glass containers, each containing $20 \mathrm{~L}$ of water that was heated to $80^{\circ} \mathrm{C}$ during the day by absorbing solar energy. A thermostat-controlled $15-\mathrm{kW}$ backup electric resistance heater turned on whenever necessary to keep the house at $22^{\circ} \mathrm{C}$. Determine $(a)$ how long the electric heating system was on that night, (b) the exergy destruction, and (c) the minimum work input required for that night, in $\mathrm{kJ}$.

Key Concepts

Thermodynamic Irreversibilities

Irreversibilities in a thermodynamic process refer to losses due to non-ideal effects such as friction, unrestrained expansion, mixing, and heat transfer across finite temperature differences. These irreversibilities result in exergy destruction, reducing the overall efficiency with which energy can be converted to useful work.

Minimum Work Requirement

The minimum work input required for a process is determined by the second law of thermodynamics. This concept uses the idealized Carnot efficiency to evaluate the least amount of work needed to achieve a thermal process, taking into account the irreversibility of real processes. It is a benchmark to compare against actual energy consumption in practical systems.

Exergy Analysis

Exergy analysis is the study of the useful work potential of energy flows within a system; it accounts for the quality of energy and its ability to perform work. This analysis highlights the irreversibilities present in actual processes by quantifying the degradation of energy, which is critical for optimizing system performance and minimizing losses.

Heat Transfer Mechanisms

Understanding the mechanisms of heat transfer—conduction, convection, and radiation—is key in analyzing any thermal system. In many applications, heat losses occur via these processes, and designing systems to minimize unwanted losses is essential for maintaining efficiency and effective energy management.

Sensible Heat Storage

Sensible heat storage refers to the method of storing thermal energy by raising the temperature of a material, typically a fluid like water, within a container. The material absorbs and later releases heat without undergoing a phase change, making it an effective medium for accumulating and utilizing thermal energy in various heating applications.

Energy Balance Analysis

This concept involves accounting for all energy entering and leaving a system, ensuring that energy inputs, outputs, and storage are all properly quantified. It is crucial in thermodynamics to understand how energy flows and transforms within a system, particularly when energy must be supplied to compensate for losses or maintain certain conditions.

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