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) Determine the sign of q (heat) for expansion

During expansion, the liquid refrigerant is released into an expansion chamber at low pressure, where it vaporizes. In order to vaporize, the refrigerant must absorb heat from the surroundings. Since the refrigerant gains heat, the sign of q for the expansion is positive, i.e., \(q > 0\).

02

(b) Determine the sign of q (heat) for compression

During compression, the refrigerant vapor undergoes compression at high pressure back to its liquid phase in a compression chamber. The vapor has to release heat and convert back into the liquid phase. Since the refrigerant loses heat during compression, the sign of q for compression is negative, i.e., \(q < 0\).

03

(c) Identifying the location of chambers in a central air-conditioning system

In a central air-conditioning system, the expansion chamber is placed inside the home, while the compression chamber is placed outside. This is because the expansion chamber absorbs heat from the air inside the house, thereby cooling the interior. The compression chamber releases heat to the environment outside the house. This setup ensures efficient indoor cooling and prevents the heat from being released inside.

04

(d) Determine whether the complete cycle is a reversible process

A process is deemed reversible if it can be reversed by an infinitesimal change in the external conditions. In the case of the air conditioning process, it involves expansion followed by compression of the refrigerant. During expansion, the refrigerant gains heat from the surroundings, and during compression, it releases the heat back. However, in practice, there will be energy losses in the form of heat released to the surroundings and inevitable inefficiencies. Therefore, the process of expansion followed by compression in this case is not completely reversible.

05

(e) Determine whether the process is spontaneous or nonspontaneous

A process is spontaneous if it occurs without any external intervention. In this case, the air conditioner's refrigerant cycle requires external energy input to operate (compression of the refrigerant). Moreover, the process of cooling the house cooling from an initial temperature of \(31^{\circ}\mathrm{C}\) to \(24^{\circ}\mathrm{C}\), requires continuous operation of the air conditioning system. Therefore, the process is nonspontaneous.

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