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). 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?

Step by step solution

01

a) Sign of q for expansion

In the expansion stage, the liquid refrigerant is released into an expansion chamber at low pressure, where it vaporizes and absorbs heat. The absorbed heat is used to break the molecular bonds, allowing the liquid to become a vapor. As the refrigerant absorbs heat, q is positive. Therefore, the sign of q for the expansion stage is positive.

02

b) Sign of q for compression

In the compression chamber, the refrigerant vapor is compressed at high pressure, causing the vapor to undergo a phase transition back to its liquid state. During this process, the refrigerant releases heat. Since the refrigerant loses heat in this process, q is negative. Thus, the sign of q for the compression stage is negative.

03

c) Location of the chambers

In a central air-conditioning system, the expansion chamber (the evaporator) is located inside the house, while the compression chamber (the condenser) is located outside the house. This setup allows the system to absorb heat from the indoor air as the refrigerant evaporates producing a cool air, and then release the heat outside as the refrigerant is compressed back into a liquid. This process cools the indoor air while maintaining the high temperature outside.

04

d) Reversibility of the process

In the process of air conditioning, a sample of the refrigerant undergoes an expansion followed by compression as it cycles through the system. However, the process is not reversible because the air conditioner interacts with the environment, such as transfering heat to the indoors and outdoors. Moreover, the refrigerant in the system would need to be cycled infinitely many times to completely restore its initial state, which by nature cannot occur in a real-life scenario.

05

e) Spontaneity of the process

When a house and its exterior are initially at \(31^{\circ} \mathrm{C}\) and the air conditioner is turned on, the house cools down to \(24^{\circ} \mathrm{C}\). The process is nonspontaneous because it requires external energy input in the form of electrical work to drive the air-conditioning system. However, once the air conditioner is turned off, the house would naturally return to the exterior temperature without any external energy input. That process, the warming of the house to the exterior temperature, would be spontaneous.

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