The thermal characteristics of a small, dormitory...

The thermal characteristics of a small, dormitory refrigerator are determined by performing two separate experiments, each with the door closed and the refrigerator placed in ambient air at $T_{\infty}=25^{\circ} \mathrm{C}$. In one case, an electric heater is suspended in the refrigerator cavity, while the refrigerator is unplugged. With the heater dissipating $20 \mathrm{~W}$, a steady-state temperature of $90^{\circ} \mathrm{C}$ is recorded within the cavity. With the heater removed and the refrigerator now in operation, the second experiment involves maintaining a steady-state cavity temperature of $5^{\circ} \mathrm{C}$ for a fixed time interval and recording the electrical energy required to operate the refrigerator. In such an experiment for which steady operation is maintained over a 12-hour period, the input electrical energy is $125,000 \mathrm{~J}$. Determine the refrigerator's coefficient of performance (COP).

Key Concepts

Steady-State Thermal Analysis

Steady-state thermal analysis involves evaluating the system when all temperatures and energy flows remain constant over time. In a refrigeration system, achieving a steady state means that the heat entering the refrigerated space (through conduction, convection, etc.) is exactly balanced by the heat removed by the refrigeration cycle. This concept is essential for understanding and predicting the ongoing performance of the system under constant environmental conditions.

Effective Thermal Conductance

Effective thermal conductance is a measure of how easily heat is transferred between two environments, typically characterized by a temperature difference. In the context of refrigeration, it allows for the estimation of the rate of heat leakage from the interior to the exterior environment. By determining the conductance, one can compute the portion of heat load that the refrigeration system must overcome, which is critical for analyzing the energy consumption and overall efficiency of cooling devices.

Coefficient of Performance (COP)

The COP is a key metric in thermodynamics that quantifies the efficiency of a refrigerator. It is defined as the ratio of the amount of heat removed from the cold space to the work input required to remove that heat. A higher COP indicates a more efficient refrigeration process because more cooling is achieved per unit of energy consumed.

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