Problem set with air conditioners and thermodynamics

• Matt Poirier
In summary, the conversation discusses a scenario where the speaker is working on a novel in Paris and needs to design a climate control system for a cabaret in exchange for rent. The system aims to remove excess moisture from the cabaret air by creating a cold surface and then reheating the air to the desired temperature. This process requires the consumption of ordered energy, such as electricity, and can raise the temperature of the air. The system is designed to be more energy-efficient by delivering some of the heat back to the cooler cabaret air instead of the hotter outside air. During the fall, the system can also extract moisture from the outside air to create a drier atmosphere in the cabaret. However, this process also produces more entropy, or
Matt Poirier

Homework Statement

You're in Paris, working on your first novel and short on cash. The owner of the cabaret downstairs has offered to take care of your rent if you'll help her design a climate control system for the place. It gets too hot and damp in the summer, and too cold and dry in the winter. You're up to the challenge, so you begin to make plans for the new system. You start by considering the summer, when the cabaret air and the outside air are normally at the same temperature and the air in both places is moist and hot. It's hard to have a good time when you're dripping wet, so your system's first goal is to extract the excess moisture from the cabaret air. It does this by creating a cold surface and passing the cabaret air across that surface. Some of the moisture will then condense and run down a drain as liquid water. Why will producing that cold surface inevitably require electricity (or an equivalent source of ordered energy) and why will something become hotter than the original outside air?
Select one:
a. You will have to pump heat from the cold surface to the hotter surroundings, a process that requires the consumption of ordered energy. The pumped heat, as well as the electrical energy that becomes disordered, must go somewhere and it will raise the temperature of its destination.
b. You will have to extract thermal energy from the cold surface, convert that thermal energy into electrical energy, and convey that electrical energy to the power company. When that electricity arrives at the power company, the power company will convert it into thermal energy again by operating an electric space heater.
c. You will have to extract thermal energy from the cold surface, convert that thermal energy into entropy, and use electricity to get rid of that entropy. The entropy will be converted into heat that will flow into the outside air, increasing the temperature of that air.
d. You will have to extract thermal energy from the cold surface, convert that thermal energy into work, and use electricity to get rid of the work. Friction will eventually convert the work into thermal energy and produce hot surfaces.

2.
Having chilled the air until it contains only the perfect amount of moisture, you want to reheat it to the ideal cabaret temperature. You could use an electric space heater or wood fire, but you already have another source of heat: the same system that chilled the air in the first place. Instead of sending its heat outdoors, you can use some of that heat to warm the chilled air back to room temperature. But you have to be careful: if you use all of the heat that's released by the cooling system, the cabaret air will become hotter than the outdoor air! Why?
Select one:
a. Whenever you change the temperature of an object, you create thermal energy. With more thermal energy in the cabaret air than before you cooled it, the temperature of the cabaret air will rise above that of the outdoor air.
b. Pumping the heat from cold to hot requires that some ordered energy, such as electricity, become disordered. If you return all the pumped heat plus the newly disordered electrical energy to the room air, its temperature will rise above its starting temperature.
c. When the entropy produced by the cooling system becomes thermal energy and is added to the cabaret air, it will increase the temperature of the cabaret air above that of the outdoor air.
d. The heat released by the cooling system is located far from the cabaret. To convey that heat back from its hotter source to the colder cabaret air requires work and this work will become thermal energy in the cabaret air. With the addition of that new thermal energy, the temperature of the cabaret air will rise above that of the outdoor air.
3.
You arrange your climate control system so that as it pumps heat out of the cabaret air and thereby chills and dries that air. Part of the heat your system removes from the cabaret air goes to the outdoor air and part goes back to the cabaret air. It turns out that delivering some of this heat to the cooler, cabaret air (rather than to the hotter, outdoor air) makes the system more energy efficient--it uses less electricity! Why?
Select one:
a. The cabaret air is denser than is the outdoor air, so it can absorb more heat than the outdoor air.
b. When you add heat to the colder cabaret air, most of that heat becomes entropy. Having that additional entropy allows your system to consume less electricity.
c. The smaller the temperature difference between the system's heat-absorbing cold surface and the air to which your system is pumping heat, the less ordered energy the system must consume to transfer each joule of heat.
d. The cabaret air is closer to your system than is the outdoor air, so it takes less electricity to convey the heat to the nearer cabaret air.
4.
During the fall, the outside air's temperature is comfortable but its humidity is too high for direct use inside the cabaret. The air feels clammy and damp. So your climate control system chills the outdoor air to extract some of its moisture and then reheats that air back up to its original temperature for use inside the cabaret. When all this is done, you have drier air in the cabaret and water running down the drain. Which arrangement has more entropy (more disorder): a cabaret full of outside air (moist but at the right temperature) or a cabaret full of dried air (drier and at the right temperature) plus the extracted water in the drain?
Select one:
a. There is more entropy in the cabaret full of dried air plus the extracted water because electrical energy was converted to thermal energy while producing those two separated materials.
b. There is more entropy in the cabaret full of outside air because it contains more total energy than does the cabaret full of dried air plus the extracted water.
c. There is more entropy in the cabaret full of outside air because if you allow the dried air and extracted water to recombine, they will do so spontaneously.
d. There is more entropy in the cabaret full of dried air plus the extracted water because electrical energy was transformed into entropy while separating the moisture from the air.
5.
During the winter, your climate control system must begin warming the cabaret air so that the cabaret air is hotter than outdoor air. Amazingly enough, it can do this relatively efficiently by transferring heat from the outside air into the cabaret. However, your system must use electricity to carry out this heat transfer. Why won't the heat transfer occur naturally?
Select one:
a. Heat doesn't flow naturally from cold to hot because that would produce a decrease in entropy.
b. Although heat tends to flow from hotter to colder, moving that heat from place to place requires the conversion of ordered energy (such as electricity) into thermal energy.
c. As each joule of heat moves from the colder outdoor air to the warmer cabaret air, the entropy of the cabaret air increases by more than the entropy of the outdoor air decreases. To obtain that increase in entropy, some electrical energy must be converted to thermal energy.
d. Heat tends to flow naturally from inside to outside. Transporting heat against its natural direction of flow requires the consumption of ordered energy.
6.
Instead of pumping heat into the cabaret air from the outside air, you could simply put an electric space heater inside the cabaret. A space heater turns electrical energy directly into thermal energy. Why would operating a space heater consume more electric power than operating a heat pump?
Select one:
a. The space heater delivers exactly as much heat as it receives in electrical energy. The heat pump delivers not only all of the electrical energy converted to thermal energy, but also additional heat that it pumps in from outdoors.
b. The heat pumping system converts entropy into thermal energy, thereby providing more heat to the cabaret air than could be provided by the space heater.
c. To achieve the same increase in the temperature of the cabaret air, the space heater would have to deliver more heat to the cabaret air than is delivered to the cabaret air by the heat pump.
d. A space heater is not 100% energy efficient, meaning that only a fraction of the electrical energy entering the space heater becomes thermal energy. The remaining electrical energy vanishes.
7.
When the air outside is very cold and dry, your climate control system must humidify the cabaret air so that the singers don't lose their voices. The climate control let's pure water evaporate into the dry air and raises the moisture content of that air. As this evaporation occurs, the temperature of the air drops somewhat because thermal energy is used to turn the liquid water into water vapor. But lowering the temperature of something usually means lowering its entropy! Why doesn't this process of mixing water and air to create slightly colder, moister air violate the law of entropy?
Select one:
a. As the air cools by evaporation, heat flows naturally from the warmer dry air to the cooler moist air. The presence of natural heat flow ensures that the law of entropy is not violated.
b. Mixing the two chemicals (water and air) produces a large amount of disorder, so that the total entropy of the system does not decrease.
c. Even though the moist air is cooler than the separated water and dry air, the moist air contains more thermal energy.
d. Slight reductions in temperature produce only slight decreases in entropy. They are therefore statistically likely to occur and do not violate the law of entropy.
8.
Keeping the cabaret door closed is important, so you install a sophisticated door control system that keeps the air exchange between inside and outside to a minimum. Why will such air exchanges always require the climate control system to work harder and consume extra electricity (and cost more money)?
Select one:
a. The air that flows out of the cabaret carries more thermal energy with it than the air that enters the cabaret to replace it. Your system will therefore have to add thermal energy to the cabaret air.
b. Leaks always lead to the creation of additional disorder, so your system will have to consume more electricity to make up for the loss.
c. The air that flows out of the cabaret carries less thermal energy with it than the air that enters the cabaret to replace it. Your system will therefore have to remove thermal energy from the cabaret air.
d. Moving air either into or out of the cabaret involves work and therefore requires the consumption of electricity.

The Attempt at a Solution

1. A, The original situation as a thermal equilibrium--the temperature is uniform everywhere. To create a local cold place, you must upset the equilibrium and that alone would reduce entropy. To satisfy the law of entropy, some disorder must be created and, in this case, that additional disorder is produced when electrical energy becomes thermal energy.
2. B, An air conditioner placed in the middle of your room will pump heat from one end to the other, consuming electricity in the process. When the room reestablishes thermal equilibrium, it will be hotter than before because it will now contain additional thermal energy--the thermal energy that was once electrical energy.
3. C, When you remove heat from the cool cabaret air, that air loses a large amount of entropy. If you were to add the same heat to hotter outdoor air, that hot air would gain a small amount of entropy. If you were to instead add the same heat to the cool cabaret air, that cool air would gain a large amount of entropy. In general, the lower the temperature of the air into which you deposit the heat, the more entropy that destination air will gain. Since you cannot actually decrease the total entropy of the world, electricity must be used to ensure that entropy doesn't decrease. Therefore, the cooler the destination air is, the less electricity you must consume to keep entropy from decreasing.
4. Not too sure but I think A, in order to separate the water and the air, you had to add ordered energy, which increased entropy.
5. C, as the house warms, its temperature is greater than the temp. outside. Carrying out this transfer on energy then, requires work which turns to thermal energy and entropy.
6. A, the pump has the advantage in that it heats from transferring heat, on top of the conversion of electrical to thermal energy.
7. B but I am not sure. By having the water evaporate in the air, entropy would increase due to the mixing of these chemicals.
8. B, Your climate control system has been trying to differentiate the cabaret air from the outdoor air. Any leak will undo some of that differentiation and your climate control system will have to consume electricity to restore the differentiation and make up for the leak. If you give nature a chance to scramble something that you've carefully arranged, it will.

Never mind.

Did you get the solutions to these questions?

So far, I've checked over your answers to questions 1 - 3. The multiple choice selections you have made are all correct. But, your additional explanations make no sense to me. The answers given by the correct multiple choice selections, on the other hand, make perfect sense to me. Compare them to your explanations. Don't you find the correct choices much more rational than your explanations? If not, I suggest you go back and review the associated material in your text.

Chestermiller said:
So far, I've checked over your answers to questions 1 - 3. The multiple choice selections you have made are all correct. But, your additional explanations make no sense to me. The answers given by the correct multiple choice selections, on the other hand, make perfect sense to me. Compare them to your explanations. Don't you find the correct choices much more rational than your explanations? If not, I suggest you go back and review the associated material in your text.
The rest of the answers for questions 4-8 seem correct. Would you agree?

@Chestermiller Can you please give confirmation on 4-8? Thank you!

1. How do air conditioners work?

Air conditioners work by using thermodynamics to transfer heat from inside a building to the outside. They use a compressor and refrigerant to absorb heat from the air inside and release it outside, creating a cooler temperature inside.

2. What is the difference between an air conditioner and a heat pump?

While both air conditioners and heat pumps use thermodynamics to transfer heat, the main difference is that an air conditioner only cools the air while a heat pump can both cool and heat the air. This is because heat pumps have a reversing valve that allows them to switch between absorbing and releasing heat.

3. How do I calculate the energy efficiency of an air conditioner?

The energy efficiency of an air conditioner can be calculated by dividing the cooling output (measured in BTUs) by the energy input (measured in watts). This will give you the Energy Efficiency Ratio (EER) of the air conditioner, which indicates how much cooling power you get for each unit of energy used.

4. Can air conditioners be harmful to the environment?

Air conditioners can contribute to environmental harm if they use refrigerants that contain ozone-depleting substances or contribute to greenhouse gas emissions. However, newer air conditioners are designed to use more environmentally friendly refrigerants and have higher energy efficiency, reducing their impact on the environment.

5. How can I improve the efficiency of my air conditioner?

There are several ways to improve the efficiency of your air conditioner, such as regularly cleaning or replacing air filters, keeping the unit shaded from direct sunlight, and sealing any air leaks in your home. Additionally, upgrading to a newer, more energy-efficient model can also greatly improve the efficiency of your air conditioner.

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