Question

A standard air conditioner involves a \(r\) frigerant 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). 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 of nonspontaneous?

Short answer

During expansion, q > 0 (endothermic process). During compression, q < 0 (exothermic process). The expansion chamber is inside the home to absorb heat, while the compression chamber is outside the home to release heat. The combined expansion and compression process is not reversible, as there is a net change in the surroundings. The cooling process is spontaneous because the air conditioner uses external work to achieve a reduction in the system's free energy.

Step-by-step solution

a) Sign of q for the expansion

During expansion, the liquid refrigerant vaporizes at low pressure in the expansion chamber. Vaporization is an endothermic process, meaning heat energy is absorbed from the surroundings. Therefore, the sign of q for the expansion is positive, as q > 0 for endothermic processes.

b) Sign of q for the compression

During compression, the refrigerant vapor is compressed back to its liquid phase at high pressure in the compression chamber. This process releases heat energy to the surroundings, making it an exothermic process. Therefore, the sign of q for the compression is negative, as q < 0 for exothermic processes.

c) Location of chambers inside and outside the home

In a central air-conditioning system, the expansion chamber is placed inside the home, and the compression chamber is placed outside the home. The reason for this arrangement is to absorb heat from the air inside the home during the expansion process (endothermic process) and release heat to the air outside the home during the compression process (exothermic process). This setup allows for efficient cooling of the indoor environment.

d) Reversibility of the expansion-compression process

A process is considered reversible when it can be returned to its original state without any net change in the system or surroundings. In this case, the refrigerant undergoes expansion followed by compression and is returned to its initial state. However, there is a net change in the surroundings due to heat transfer during these processes. Therefore, the combined expansion and compression process in an air conditioner is not reversible.

e) Spontaneity of the cooling process

Spontaneous processes occur without any external intervention and proceed in the direction that reduces the overall free energy of the system. When the air conditioner is turned on, the initial temperature of both the interior and exterior is \(31^{\circ}\mathrm{C}\). After running, the temperature of the house is reduced to \(24^{\circ}\mathrm{C}\). Since the air conditioner uses external work (mechanical energy) to drive the cooling process, the overall reduction in the system's free energy is achieved, making this process spontaneous.

Key concepts

Reversible Process

In thermodynamics, a reversible process is an idealized concept where a system can return to its starting state without leaving any net change in the environment or in the system itself. This means that every step of the process can be reversed with no loss of energy as heat or work. However, in reality, reversible processes are theoretical because they require infinite time to execute fully without any energy dissipation.

When considering an air conditioner, the refrigerant passes through expansion and compression cycles. During these cycles, there are unavoidable energy exchanges with the surroundings, primarily as heat. Because of these interactions and changes, the process cannot be fully reversed without an energy cost, making the process irreversible in practice.

• Ideal reversible processes would require perfect insulation and no friction.
• Real processes always involve some form of energy loss, typically as heat due to irreversibility.

Endothermic and Exothermic Processes

Endothermic and exothermic processes are crucial concepts in understanding thermodynamic exchanges of heat energy. An endothermic process is one that absorbs heat from its surroundings. In an air conditioner, this occurs during the vaporization of the refrigerant; the refrigerant absorbs heat from the air inside the house to vaporize.

Conversely, an exothermic process releases heat into the surroundings. During the compression phase in the air conditioner cycle, the refrigerant releases heat as it transitions from a vapor back to a liquid. This release makes the compression process exothermic.

• In endothermic processes, heat energy intake results in a temperature rise of the system.
• In exothermic processes, the system releases heat, often resulting in a temperature decrease in the system itself and a warming of the surroundings.

Spontaneity in Thermodynamics

Spontaneity in thermodynamics refers to the natural direction in which processes occur without the need for an external driving force or intervention. A spontaneous process naturally tends toward a state of reduced free energy.

For the air conditioning example, even though the device uses mechanical energy, the process becomes spontaneous when it is directionally feasible under the given conditions. Cooling a house from a higher temperature to a lower one using an air conditioner uses energy efficiently to achieve a desired state, which aligns with the tendency to minimize free energy in the system.

• Spontaneous processes can be driven by a decrease in enthalpy, or sometimes an increase in entropy, depending on the situation.
• In the practical operation of an air conditioner, work is used to drive spontaneous processes effectively achieving a desired cooling effect within a controlled environment.