Physics 105 - How Things Work - Fall, 1999

Problem Set #9 - Thermodynamics - Solutions

Most cars sold in the south are equipped with air conditioners to keep their passengers cool on hot summer days. The air conditioner transfers heat from the air in the passenger compartment to the air outside the car.

1. Where is the evaporator located in a car's air conditioning system?

Answer: The evaporator is located inside the passenger compartment.

Why: The evaporator is where the working fluid becomes very cold; evaporation requires thermal energy. This allows heat to be transferred from the passenger compartment into the working fluid.

2. Where is the condenser located in the car's air conditioning system?

Answer: The condenser is located outside the passenger compartment.

Why: This is where the working fluid is compressed and condensed, which causes it to become very hot. Since the fluid is now hotter than the outside air it can transfer heat to the air.

3. Why do you get worse gas mileage when you drive with the air conditioner on?

Answer: To move heat from a cold region to a hot region requires energy.

Why: Removing a certain amount of heat from the passenger compartment lowers the entropy there. Adding this same amount of thermal energy to the warm outside air raises its entropy, but not by as much. Since the total entropy of the system cannot go down, energy must be used to add extra heat, and thus entropy, to the outside air. This entropy is added by the compressor, which does work on the fluid causing it to heat up.

4. The heat exchanger that transfers heat to the outside air is typically located just behind the front grill of the car. Usually there is a fan that can draw air across the heat exchanger. If there were no fan, the air conditioner would do a better job of cooling the car's passengers when the car was moving at high speed than when it was stopped. Explain why in terms of convection.

Answer: When the car is moving more air is forced across the surface of the heat exchanger causing better convective heat transfer.

Why: The fan forces air across the heat exchanger when you are stopped so that your air conditioner continues to work even in a traffic jam.

5. How does the entropy inside of the passenger compartment change as it cools off?

Answer: The entropy decreases.

Why: Entropy is a measure of the disorder in a system. Cooler air is more ordered than warmer air.

6. If the air conditioner were able to move a given quantity of heat from the air inside the car to the air outside the car without doing any work, how would the increase in entropy of the hot air outside compare to the decrease in entropy of the cool air inside the car?

Answer: The increase in entropy outside would be less than the decrease in entropy inside.

Why: Heating a cold object creates more disorder than heating a hot object.

Although your car is only a year old it already has some scratches and dings.

7. There is a small dent in the top of your car, maybe from where a walnut hit it after falling out of that big tree you were parked under last week. You heard from a friend that there is a simple way to remove the dent. You should park your car in the sun on a hot summer day and let the metal near the dent get nice and hot. Then, you friend tells you, if you place an ice cube in the dent it will pop out. Why might this work?

Answer: The metal will cool quickly near the ice cube causing it to contract, which may pop the dent out.

Why: A friend did tell me this trick, although I have never tried it. In concept it sounds like it might work, but I'm sure it depends on the dent.

8. One morning you wake up and there is a thick layer of frost on your car. Rather than scrape the frost off of your windshield you decide to pour a bucket of hot water on it to melt the frost. If your windshield has a small crack in it this may cause the crack to run (become longer). Why?

Answer: When you pour hot water on the cold windshield it will expand where the hot water is being poured. This will cause stress in the windshield, which may cause the crack to run.

Why: Again, whether or not the crack runs will depend on where you pour the water relative to the location of the crack.