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Chapter 5: Problem 31

What effect does heating the air in a room have on the relative humidity?

Short Answer

Expert verified
Answer: Heating the air in a room will cause the relative humidity to decrease, as the air's capacity to hold water vapor increases with temperature, resulting in a smaller ratio of actual water vapor content to maximum water vapor capacity.

Step by step solution

01

Define the terms

Relative humidity (RH) is the percentage of water vapor present in the air relative to the maximum amount of water vapor the air can hold at a particular temperature. It is given by the formula: \(\text{Relative Humidity (RH)} = \frac{\text{Actual water vapor content}}{\text{Maximum water vapor capacity}} \times 100\)
02

Understand the relationship between temperature and air's capacity to hold water vapor

The maximum amount of water vapor the air can hold, also known as its saturation point, is directly proportional to its temperature. As the temperature of the air increases, the air can hold more water vapor. This means that the saturation point of the air increases with an increase in temperature.
03

Analyze the effect of heating the air on relative humidity

When the air in a room is heated, its temperature increases. Since the saturation point of the air increases with an increase in temperature, the maximum amount of water vapor the heated air can hold increases. Now, let's assume the actual water vapor content in the room remains constant (no additional moisture is added or removed). As the maximum water vapor capacity increases when heated, the ratio of actual water vapor content to maximum water vapor capacity will decrease. Consequently, the relative humidity will decrease as the temperature increases.
04

Conclusion

Heating the air in a room will cause the relative humidity to decrease, assuming that there is no change in the actual water vapor content in the room. This happens because the air's capacity to hold water vapor increases with temperature, resulting in a smaller ratio of actual water vapor content to maximum water vapor capacity.

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