In regions with dry climates, evaporative coolers are used to cool air. A typical electric air conditioner is rated at \(1.00 \times 10^{4}\) Btu/h (1 Btu, or British thermal unit = amount of energy to raise the temperature of 1 lb water by \(1^{\circ} \mathrm{F}\) ). What quantity of water must be evaporated each hour to dissipate as much heat as a typical electric air conditioner?

• Heat from the air is used to convert water from liquid to vapor in the process called evaporation.
• During evaporation, energy is absorbed by the water molecules, which then 'carry' the heat away as they leave the surface and enter the air as vapor.
• This phase change requires a significant amount of energy, leading to a reduction in the temperature of the remaining air—a natural example of heat dissipation.

Evaporative coolers harness this process to cool air efficiently. They work best in dry climates because the air has a higher capacity to absorb water vapor, which maximizes the cooling effect. The exercise mentions evaporative coolers as a means to dissipate the same amount of heat as an electric air conditioner, highlighting the clever use of a naturally occurring heat dissipation process to cool indoor spaces.

• One pound of water requires approximately 970 Btu of heat energy to fully evaporate.
• This energy is known as the latent heat of vaporization. The word 'latent' suggests the energy is hidden as it does not result in a temperature change; rather, it's used to change the state of water.
• The exercise demonstrates the use of the evaporation energy to calculate how much water must evaporate to absorb heat from the air equivalent to that dissipated by a standard air conditioner.

Understanding the evaporation energy is crucial because it tells us how much water is needed to evaporate to 'mop up' a certain amount of heat. This allows for practical applications such as calculating the efficiency and needs of an evaporative cooling system.

• The thermal energy (heat) from the air is converted to latent heat of vaporization when water evaporates.
• This conversion causes a decrease in the air's temperature as the heat is used up in transforming water into vapor.
• Effectively, the energy in the warmer air is converted into kinetic energy in water molecules, leading to a cooling effect.

Evaporative cooling is an elegant example of energy conversion: it utilizes the natural properties of water to achieve cooling without complex machinery or refrigerants. Our exercise’s focus on the required quantity of water for evaporation is a practical application of understanding this energy conversion, showing how simple physical processes are harnessed to regulate temperature and contribute to our comfort.