Question

A standard air conditioner involves a refrigerant that is typically now a fluorinated hydrocarbon, such as \(\mathrm{CH}_{2} \mathrm{~F}_{2}\) An air- conditioner refrigerant has the property that it readily vaporizes at atmospheric pressure and is easily compressed to its liquid phase under increased pressure. The operation of an air conditioner can be thought of as a closed system made up of the refrigerant going through the two stages shown here (the air circulation is not shown in this diagram). Expansion (low pressure) Compression chamber Compression (high pressure) During expansion, the liquid refrigerant is released into an expansion chamber at low pressure, where it vaporizes. The vapor then undergoes compression at high pressure back to its liquid phase in a compression chamber. (a) What is the sign of \(q\) for the expansion? (b) What is the sign of \(q\) for the compression? (c) In a central air-conditioning system, one chamber is inside the home and the other is outside. Which chamber is where, and why? (d) Imagine that a sample of liquid refrigerant undergoes expansion followed by compression, so that it is back to its original state. Would you expect that to be a reversible process? (e) Suppose that a house and its exterior are both initially at \(31{ }^{\circ} \mathrm{C}\). Some time after the air conditioner is turned on, the house is cooled to \(24^{\circ} \mathrm{C}\). Is this process spontaneous or nonspontaneous?

Short answer

(a) The sign of q for the expansion is positive, as the refrigerant absorbs heat from the surroundings during the expansion process. (b) The sign of q for the compression is negative, as the refrigerant loses heat to the surroundings during the compression process. (c) The expansion chamber is located inside the home, while the compression chamber is outside, transferring heat absorbed from inside the house to the outdoor environment. (d) The process is not reversible due to heat exchange inefficiencies and losses in the system. (e) The process is nonspontaneous, as external work, in the form of electricity, is required to cool the house.

Step-by-step solution

(a) Sign of q for expansion

When the refrigerant undergoes expansion at low pressure, it absorbs heat from the surroundings and changes from the liquid phase to the vapor phase. Since the system absorbs heat from the surroundings, the heat flow (q) into the system is positive. Therefore, the sign of q for the expansion is positive.

(b) Sign of q for compression

During the compression process, the refrigerant vapor is compressed back to its liquid phase. In the process, the refrigerant loses heat to the surroundings, and the heat flow (q) out of the system is negative. Thus, the sign of q for the compression is negative.

(c) Location of chambers

In a central air-conditioning system, the expansion chamber is located inside the home, while the compression chamber is outside. The reason for this is that when the refrigerant expands, it absorbs heat from the indoor air, cooling the home. Meanwhile, the compression chamber releases heat to the outdoor environment, ensuring that the heat absorbed from inside the house is transferred and dissipated outside.

(d) Reversibility of the process

In the operation of an air conditioner, the refrigerant undergoes expansion and compression, returning to its original state. However, this process would not be considered reversible because the heat exchange between the air conditioner and its surroundings is not infinitely slow. In a real-life scenario, there will always be some heat losses and inefficiencies in the system, causing the process to be irreversible.

(e) Spontaneity of the process

When the house and its exterior are initially at the same temperature of \(31^{\circ} \mathrm{C}\), and some time after the air conditioner is turned on, the house is cooled to \(24^{\circ} \mathrm{C}\), this process is a nonspontaneous one. The reason is that cooling the house requires the input of external work (in the form of electricity) to drive the air conditioner's compressors, making the process nonspontaneous.

Key concepts

Thermodynamics

Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, radiation, and physical properties of matter. Understanding thermodynamics is essential when studying the function of an air conditioner since it operates on the principles of heat and energy transfer.

In the context of an air conditioner, which uses a refrigerant like fluorinated hydrocarbon \(mathrm{CH}_{2} \mathrm{F}_{2}\), the principles govern how the refrigerant absorbs heat from the indoor air (endothermic process) during expansion and releases it outdoors (exothermic process) during compression. Energy in the form of work (usually from electricity) is required to compress the gas, which aligns with the first law of thermodynamics stating that energy cannot be created or destroyed, but only transferred or transformed.

Phase Change

A phase change is a physical process in which a substance transitions between different states of matter: solid, liquid, and gas. In an air conditioner, the refrigerant undergoes two key phase changes. During the expansion phase, the refrigerant transitions from a liquid to a gas, absorbing heat from the indoor environment and thus cooling it. This is why the expansion chamber is within the home.

In contrast, during the compression phase, the refrigerant reverts from a gas back to a liquid. It releases the absorbed heat, which is typically expelled outside the living spaces. These phase changes are critical for the cooling cycle of an air conditioner, as they harness the refrigerant's properties to regulate temperature.

Heat Transfer

Heat transfer is the movement of thermal energy from one object or substance to another. It can occur through conduction, convection, or radiation. In the case of an air conditioner, heat transfer plays a pivotal role in its cooling function.

The refrigerant absorbs indoor heat through convection during expansion—this happens as the liquid evaporates at low pressure in the expansion chamber. Subsequently, during compression, the refrigerant in gas form releases the heat outside—most commonly into the air via a condenser, which may involve convection and radiation to the surroundings. These processes are repeated cyclically, facilitating the continuous removal of heat from the indoor space.

Spontaneous and Nonspontaneous Processes

Spontaneous processes occur without outside intervention, driven by internal energy changes tending towards equilibrium. For example, a ball rolling downhill does so spontaneously due to gravitational pull. However, in the case of an air conditioner, the process of cooling a home is nonspontaneous. It requires external work, such as electrical energy, to operate the compressor, which drives the refrigerant through its phase changes and heat transfer cycle.

Without this external input of energy, the heat would naturally flow from the warmer exterior to the cooler interior, counteracting the desired cooling effect. Thus, the action of the air conditioner actively creates a temperature gradient, which is a deliberate and nonspontaneous process.