Thread by @BucknellThermo

First up Maggie and Sarah tweeting about the first law of thermodynamics and how fans actually work! 1/30

We all know there is nothing like the relief of a cool breeze from a fan on a hot day. But, have you ever thought how a fan makes things feel colder? 2/30

Contrary to popular belief, a fan does not cool a room down. In fact, it will cause the room’s temperature to slightly increase. 3/30

We can prove this using the First Law of Thermodynamics, which states that energy is conserved.

For example, when people eat food as fuel before exercising, they convert the chemical energy in food into the kinetic energy required for exercise. 5/30

So, the big idea is that energy can only be transformed, neither created nor destroyed. There always has been, and always will be, the same amount of energy in the universe. 6/30

In order to apply the first law to how fans work, we need to discuss enthalpy….a made up thermodynamic property! 7/30

When heat energy enters a system, it can do one of two things: increase internal energy (∆U) or expand the system [∆(PV)]. 8/30

When heat energy enters a system, it can do one of two things: increase internal energy (∆U) or expand the system [∆(PV)]. 8/30

Enthalpy (H) is useful in energy calculations because it tracks energy entering and leaving the system. Enthalpy has been defined as the sum of internal energy (U) and flow work (PV), H = P + UV. 9/30

Enthalpy is a made up property, and can’t be directly measured in the same way as temperature or pressure. Reference state is defined where enthalpy equals zero and the enthalpy of other states is found by calculating the difference in enthalpy between the two states. 10/30

Enthalpy at given conditions is energy needed to move from reference point to those conditions. 11/30

Now that we’ve got a grasp on enthalpy, what does the energy balance for a fan look like? 12/30

For an open system a general energy balance is In - Out = 0. For a fan this simplifies change in enthalpy being equal to work. 13/30

Because work is inputted into the fan, Ws can be calculated from the power load of the fan. We know that Ws is positive, so to satisfy the energy balance, ∆H must also be positive. 14/30

If we assume ideal gas, then the change in enthalpy can be described using the equation below. Let’s break that down. 15/30

Generally, it is accurate to assume that air acts as an ideal gas at room temperature and pressure. The shakiest assumption in the ideal gas law is that molecules have no interactions with each other….at low pressure, there are fewer interactions between gas molecules. 16/30

Heat capacity is a physical property of a material (like density!) that is defined as the amount of energy required to heat a mass of material by one temperature unit. 17/30

Because ∆H is positive and heat capacity is constant, ∆T must also be positive. So, the temperature of the air increases slightly!!! But by how much? 18/30

Picture this: It’s move-in day, and you decide to set up your dorm room with the windows closed (I don’t advise this - open those windows!). It’s August, and it’s hot, so you decided to turn on a fan, while you’re moving in. 19/30

The work put into the fan is equal to the wattage of the fan times the amount of time the fan is run. Then, using our equation for enthalpy, we can use algebra to solve for the change in temperature. 20/30

To find the mass of air, we’ll calculate the volume of air contained in an average dorm room at Bucknell. To do that, we’ll assume that the volume of air is equal to the volume of the dorm room. 21/30

The average wattage of a tower fan is 100 W, and it takes you four hours to set up your room. 22/30

30 degrees Celsius!! That’s 54 degrees Fahrenheit!! I know what you’re thinking, there’s no way the temperature increases that much! And you’d be right. 23/30

Some of that heat is taken up by the fan motor - careful it might be hot - and some of that is absorbed by objects in the room. The actual number is around an order of magnitude smaller, but it is definitely an increase in temperature. 24/30

So, fans slightly increase the temperature of the room they’re in. Then, why do we feel cooler next to a fan? 25/30

You’re most likely already familiar with this concept in the application of wind chill. More formally, this concept is known as convective cooling. 26/30

A person feels hot because they are surrounded by a stagnant layer of hot, humid air, which prevents heat loss. 27/30

Fans increase the movement or velocity of the air in the room. The faster moving air from a fan displaces this layer of air and replaces it with cooler, drier air. 28/30

This cooler, drier air evaporates sweat from your skin, which is how the body eliminates heat. The faster a fan rotates, the faster evaporation occurs, and the cooler you feel. 29/30

To conclude:
a. Fans increase temperature of air
b. Fans still cool you down
See you later thermo fans….we’ll see ourselves out. 30/30