Problem 14 - College Physics

Question

\(\cdot\) In one cycle, a freezer uses 785 \(\mathrm{J}\) of electrical energy in order to remove 1750 \(\mathrm{J}\) of heat from its freezer compartment at \(10^{\circ} \mathrm{F}\) . (a) What is the coefficient of performance of this freezer? (b) How much heat does it expel into the room during this cycle?

Step-by-Step Solution

Answer

(a) COP is approximately 2.23. (b) Heat expelled is 2535 J.

Step 1: Understand the Problem

The problem asks us to find the coefficient of performance (COP) of the freezer and the amount of heat expelled into the room. We are given that the freezer uses 785 J of electrical energy to remove 1750 J of heat from the freezer compartment.

Step 2: Calculating Coefficient of Performance (COP)

The coefficient of performance (COP) for a refrigerator or freezer is calculated using the formula: \( \text{COP} = \frac{Q_c}{W} \), where \( Q_c \) is the heat removed from the cold reservoir (1750 J), and \( W \) is the work done by the freezer (785 J). Substituting the values, we have: \[ \text{COP} = \frac{1750 \, \mathrm{J}}{785 \, \mathrm{J}} \approx 2.23 \].

Step 3: Calculating Heat Expelled (Q_h)

The heat expelled into the room, \( Q_h \), can be found using the relation \( Q_h = Q_c + W \). Thus, substituting the values, we get: \[ Q_h = 1750 \, \mathrm{J} + 785 \, \mathrm{J} = 2535 \, \mathrm{J} \].

Step 4: Summarize Results

The coefficient of performance of the freezer is approximately 2.23, and the heat expelled into the room during this cycle is 2535 J.

Key Concepts

Thermodynamics in Refrigeration

Thermodynamics lies at the heart of understanding refrigeration systems, like freezers. The principles of thermodynamics help explain how energy is transferred and transformed. In a refrigeration cycle, heat energy is moved from a cold place (inside the freezer) to a hot place (the surrounding room). Thermodynamics provides the rules for these energy transformations.

During the cycle, work is applied to the system, using electrical energy. This energy helps transfer heat from a cooler to a warmer area, defying the natural flow direction (normally, heat flows from warm to cold). Such processes highlight the beauty of thermodynamics in practical applications, maintaining essential factors like temperature and energy efficiency.

Understanding the Refrigeration Cycle

The refrigeration cycle is the backbone of devices like freezers. It operates through various components and processes to remove heat from the inside of the freezer and expel it outside. Let's break it down simply:

• **Evaporation:** Refrigerant absorbs heat, evaporating into a gas, cooling the internal compartment.
• **Compression:** This gas is compressed, raising its pressure and temperature.
• **Condensation:** The hot, high-pressure gas releases heat to the external environment, turning back into a liquid.
• **Expansion:** The liquid refrigerant goes through an expansion valve, dropping its pressure and temperature, ready for another cycle.

This cycle is repeated over and over to maintain cooling. Understanding the cycle aids in grasping how efficiencies, like the coefficient of performance, come into play.

The Role of Heat Transfer in Refrigeration

Heat transfer is crucial in the operation of freezers. It is the method through which heat moves from inside the freezer compartment to the surroundings. There are three primary modes of heat transfer: conduction, convection, and radiation.

• **Conduction:** Heat moves through solid parts of the freezer.
• **Convection:** Fluid movement inside and outside the freezer helps redistribute heat.
• **Radiation:** The least impactful here, as it involves heat transfer through electromagnetic waves.

In a freezer, we see conduction through the walls, convection through air movement, and a minimal impact from radiation. The aim is to maximize heat removal efficiently, often indicated by the coefficient of performance, which helps us understand how well the freezer performs heat transfer using the least energy possible.

Enhancing Energy Efficiency in Refrigeration

Energy efficiency in freezers is all about doing more with less energy. This is crucial for both environmental and economic reasons. A higher coefficient of performance (COP) indicates a more energy-efficient system.

Some strategies to enhance energy efficiency include:

• **Insulation:** Better insulation reduces heat gain, improving efficiency.
• **Component Quality:** High-efficiency compressors and heat exchangers ensure optimal performance.
• **Regular Maintenance:** Clean coils and components reduce energy wastage.
• **Design Innovations:** New technologies focus on minimizing energy use while maximizing refrigeration capacity.

Understanding and implementing these strategies helps in achieving a higher COP, allowing freezers to operate economically and sustainably.