A windmill uses the convective flow of heat to do useful work; it's a type of heat engine.
1. Wind is the result of convection currents between hot and cold regions on the earth's surface. What is the direction of the wind near the earth's surface in between a hot and cold region?
Answer: The wind blows from the cold region toward the hot region.
Why: The warm region on the earth's surface heats the air above it. This hot air begins to rise due to the buoyant force acting on it. This creates a low pressure region near the hot surface. Cool air flows toward this low pressure region.
2. What is the direction of heat flow in between the hot and cold region on the earth's surface?
Answer: Heat flows from the hot region toward the cold region.
Why: Although the wind is blowing from cold to hot, heat flows from hot to cold. When the air is near the cold region heat flows from the air into the cold surface of the earth. Near the hot region heat flows from the hot earth into the air.
3. The temperature differences on the earth's surface produce ordered energy in the form of wind (the ordered part of the kinetic energies of the air molecules). Describe why this doesn't violate the second law of thermodynamics in terms of heat flow and entropy.
Answer: As heat flows from hot to cold the overall entropy of the system increases so a small amount of this thermal energy can be converted into the organized motion of the wind without violating the second law of thermodynamics.
Why: The natural formation of convection currents is a type of heat engine.
4. The windmill is simply a propeller blade on the end of a tall pole. The wind blowing at this propeller (along the line of the pivot) causes it to spin by producing a torque. Describe how a torque is produced by deflection of the air stream.
Answer: To produce a torque the deflected air must apply a force that is at least partially perpendicular to the long axis of the propeller blades and perpendicular to the original direction of the air stream.
Why: The force associated with a deflection of the air stream perpendicular to its direction of flow is called a lift force. Each of the blades of the propeller must be tilted in such a way that the air stream is deflected to produce a torque in the same direction. The torques from each blade must act together rather than canceling.
5. The wind has translational kinetic energy. When the windmill is spinning, what kind of energy does it have?
Answer: Rotational kinetic energy.
Why: We associate kinetic energy with the energy of a moving object. In the case of rotational motion the kinetic energy depends on the angular speed of the motion and the moment of inertia of the object.
6. The energy of the spinning windmill can be used for many tasks such as generating electricity or pumping water. How does the amount of useful, ordered energy created by the windmill depend on the temperature difference between the hot and cold regions?
Answer: As the temperature difference increases, the amount of ordered energy that can be extracted also increases.
Why: A larger temperature difference allows more ordered energy to be extracted while still not violating the second law of thermodynamics.
To keep cool on a hot day you sweat.
7. Why does the evaporation of sweat keep you cool?
Answer: It takes thermal energy to break the bonds that hold liquid water together.
Why: The energy required to cause a water molecule to break free comes from the motions of neighboring molecules in the liquid water. This leaves the liquid water cooler so heat can flow from you body into the water.
8. Why do you cool off faster when the humidity (the amount of water vapor in the air) is low compared to when the humidity is high?
Answer: When the humidity is low the rate of evaporation is high.
Why: In addition to the water molecules evaporating from the liquid water, some molecules will also be condensing. When the rate of evaporation is equal to the rate of condensation no net heat will be transferred. This happens when the relative humidity is 100%.