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

Expert verified
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

01

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.
02

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.
03

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.
04

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.
05

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.

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Most popular questions from this chapter

The standard entropies at \(298 \mathrm{~K}\) for certain group 14 elements are: \(\mathrm{C}(s,\) diamond $)=2.43 \mathrm{~J} / \mathrm{mol}-\mathrm{K}, \mathrm{Si}(s)=18.81 \mathrm{~J} /$ $\mathrm{mol}-\mathrm{K}, \mathrm{Ge}(s)=31.09 \mathrm{~J} / \mathrm{mol}-\mathrm{K}, \quad\( a n d \)\quad \mathrm{Sn}(s)=51.818 \mathrm{~J} /$ mol-K. All but \(S\) n have the same (diamond) structure. How do you account for the trend in the \(S^{\circ}\) values?

Consider the following reaction between oxides of nitrogen: $$ \mathrm{NO}_{2}(g)+\mathrm{N}_{2} \mathrm{O}(g) \longrightarrow 3 \mathrm{NO}(g) $$ (a) Use data in Appendix \(C\) to predict how \(\Delta G\) for the reaction varies with increasing temperature. (b) Calculate \(\Delta G\) at \(800 \mathrm{~K}\), assuming that \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) do not change with temperature. Under standard conditions is the reaction spontaneous at $800 \mathrm{~K} ?\( (c) Calculate \)\Delta G\( at \)1000 \mathrm{~K}$. Is the reaction spontaneous under standard conditions at this temperature?

For each of the following processes, indicate whether the signs of \(\Delta S\) and \(\Delta H\) are expected to be positive, negative, or about zero. (a) A solid sublimes. (b) The temperature of a sample of \(\mathrm{Co}(s)\) is lowered from \(60^{\circ} \mathrm{C}\) to $25^{\circ} \mathrm{C} .$ (c) Ethyl alcohol evaporates from a beaker. (d) A diatomic molecule dissociates into atoms. (e) A piece of charcoal is combusted to form \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(g)\).

Indicate whether each statement is true or false. (a) The entropy of the universe increases for any spontaneous process. (b) The entropy change of the system is equal and opposite that of the surroundings for any irreversible process. (c) The entropy of the system must increase in any spontaneous process. (d) The entropy change for an isothermal process depends on both the absolute temperature and the amount of heat reversibly transferred.

A system goes from state 1 to state 2 and back to state \(1 .\) (a) Is \(\Delta E\) the same in magnitude for both the forward and reverse processes? (b) Without further information, can you conclude that the amount of heat transferred to the system as it goes from state 1 to state 2 is the same or different as compared to that upon going from state 2 back to state $1 ?(\mathbf{c})$ Suppose the changes in state are reversible processes. Is the work done by the system upon going from state 1 to state 2 the same or different as compared to that upon going from state 2 back to state \(1 ?\)

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