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Chapter 12: Problem 10

Why does your bathroom mirror often fog up when you shower?

Short Answer

Expert verified
The mirror fogs up because warm, humid air from the shower condenses into water droplets when it contacts the cooler mirror surface.

Step by step solution

01

- Understand Water Vapor and Humidity

Hot water from the shower produces steam, which increases the humidity level in the bathroom. This means the air holds more water vapor when it's warm.
02

- Condensation on the Mirror

When the warm, humid air comes in contact with the cooler surface of the mirror, the water vapor condenses. Condensation happens because the cooler temperature of the mirror causes the air to lose heat and the water vapor to turn back into liquid form.
03

- Resulting Fog on the Mirror

The condensed water forms tiny droplets on the surface of the mirror, which scatters light and makes the mirror appear foggy. This is the fog you see on the mirror.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Water Vapor
When you take a hot shower, the water heats up and turns into steam. This steam is actually water molecules in the form of water vapor.
Water vapor is an invisible gas in the air that you can't see but can feel as warmth. As the water temperature rises, more water molecules escape into the air, making it more humid.
  • Water vapor is created when liquid water is heated.
  • It is a key part of the water cycle, moving from liquid to gas and back again.

This high level of water vapor in the air is what causes the air in your bathroom to feel steamy during a hot shower.
Humidity
Humidity is a measure of how much water vapor is in the air. When you take a hot shower, the steam from the water increases the humidity in the bathroom.
Higher humidity means that the air contains a lot of water vapor.
There are two main types of humidity measurements:
  • Absolute Humidity: The total mass of water vapor present in a given volume of air.
  • Relative Humidity: The percentage of water vapor present in the air compared to the maximum amount the air can hold at that temperature.

Warm air can hold more water vapor than cold air, so when you heat your shower, the air becomes humid as it holds more water vapor.
Condensation
Condensation occurs when the water vapor in the air turns back into liquid form. This happens when the warm, humid air comes into contact with a cooler surface like your bathroom mirror.
Here鈥檚 how it works:
  • The warm, moist air from your shower hits the cold mirror surface.
  • The air cools down, and the water vapor loses its heat.
  • The vapor turns into tiny droplets of water on the mirror surface.

These droplets stick to the mirror and scatter light, causing the foggy appearance you see after a shower. It's the same process that forms dew on grass in the early morning.

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Most popular questions from this chapter

Moist air at \(20^{\circ} \mathrm{C}, 1 \mathrm{~atm}, 43 \%\) relative humidity and a volumetric flow rate of \(900 \mathrm{~m}^{3} / \mathrm{h}\) enters a control volume at steady state and flows along a surface maintained at \(65^{\circ} \mathrm{C}\), through which heat transfer occurs. Liquid water at \(20^{\circ} \mathrm{C}\) is injected at a rate of \(5 \mathrm{~kg} / \mathrm{h}\) and evaporates into the flowing stream. For the control volume, \(\dot{W}_{\mathrm{cv}}=0\), and kinetic and potential energy effects are negligible. Moist air exits at \(32^{\circ} \mathrm{C}, 1 \mathrm{~atm}\). Determine (a) the rate of heat transfer, in \(\mathrm{kW}\). (b) the rate of entropy production, in \(\mathrm{kW} / \mathrm{K}\).

Using methods in the most current \(A S H R A E\) Handbook of HVAC Applications, estimate the rate of evaporation from the surface of an Olympic-size swimming pool. The swimming hall is maintained at \(30^{\circ} \mathrm{C}\) with a dew point temperature of \(21^{\circ} \mathrm{C}\). Based on your estimate, determine the load, in \(\mathrm{kW}\), that the added moisture places on the air-conditioning system. Write a memorandum that summarizes your analysis and include at least three references.

An air-handling system is being designed for a \(12 \mathrm{~m} \times\) \(12 \mathrm{~m} \times 2.5 \mathrm{~m}\) biological research facility that houses 3000 laboratory mice. The indoor conditions must be maintained at \(24^{\circ} \mathrm{C}, 60 \%\) relative humidity when the outdoor air conditions are \(32^{\circ} \mathrm{C}, 70 \%\) relative humidity. Develop a preliminary design of an air-conditioning and distribution system that satisfies National Institute of Health (NIH) standards for animal facilities. Assume a biological safety level of one (BSL-1), and that two thirds of the floor space is devoted to animal care. Since an interruption in ventilation or air conditioning could place the laboratory animals under stress and compromise the research under way in the facility, account for redundancy in your design.

Moist air at \(25^{\circ} \mathrm{C}, 1 \mathrm{~atm}\), and \(40 \%\) relative humidity enters an evaporative cooling unit operating at steady state consisting of a heating section followed by a soaked pad evaporative cooler operating adiabatically. The air passing through the heating section is heated to \(43^{\circ} \mathrm{C}\). Next, the air passes through a soaked pad exiting with \(40 \%\) relative humidity. Using data from the psychrometric chart, determine (a) the humidity ratio of the entering moist air mixture. (b) the rate of heat transfer to the moist air passing through the heating section, in \(\mathrm{kJ}\) per kg of mixture. (c) the humidity ratio and temperature, in \({ }^{\circ} \mathrm{C}\), at the exit of the evaporative cooling section.

Write a report explaining the way the human body regulates its temperature, both under cold and hot climate conditions. Based on these thermoregulation mechanisms, discuss designs of personal protective clothing for fire fighters and other first responders. How are such clothing systems designed to provide protection against chemical or biological agents while maintaining sufficient thermal comfort to allow for strenuous physical activity? Include in your report at least three references.
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