Solving Entropy in Moist Air: No Violation of Law

[Dreebs]

Homework Statement

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. Even though the moist air is cooler than the separated water and dry air, the moist air contains more thermal energy.
c. 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.
d. Mixing the two chemicals (water and air) produces a large amount of disorder, so that the total entropy of the system does not decrease.

Homework Equations

The Attempt at a Solution

C. [/B]Because slight reductions in entropy are still allowed without violating the law of entropy.

 

[haruspex]

Homework Statement

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. Even though the moist air is cooler than the separated water and dry air, the moist air contains more thermal energy.
c. 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.
d. Mixing the two chemicals (water and air) produces a large amount of disorder, so that the total entropy of the system does not decrease.

Homework Equations

The Attempt at a Solution

C. [/B]Because slight reductions in entropy are still allowed without violating the law of entropy.

Such reductions would be random, and if of any magnitude then very rare. That does not cover the process here.

 

[Dreebs]

Such reductions would be random, and if of any magnitude then very rare. That does not cover the process here.

That makes sense. So in D, does mixing the two chemicals cause entropy to increase? I think it does but I'm not entirely sure.