How do you heat a private office or any room for that matter? If your answer is “by adding energy to the room,” then there’s good news and bad news for you. The good news is that’s what most engineers and scientists would say. The bad news, you’d be wrong.
The challenge lies in the difference between two concepts: energy and temperature. The answer to the question: “How do we heat a room” is in fact, “by increasing the temperature.” But it is not “by increasing the energy of the room.” How is this possible?
The answer can be seen if we look at something called the ideal gas equation, a helpful model for the behavior of air in an enclosed space at room temperature. The ideal gas equation comes up in hundreds of energy optimization problems. It is:
PV = nRT
P is the pressure of the container
V the volume
n the number of gas particles
R is a constant
T is the temperature
Both sides of the equation are in units of energy.
Now let’s consider how this applies to a private office. The volume of an office is fixed: the walls, floor, and ceiling are not moving much. At least we hope not. Additionally, the pressure in the room cannot be very different than it is outside the room, because any increase in pressure in the room will result in air escaping through cracks around the door or elsewhere in order to equalize the pressure.
So both pressure (P) and volume (V) are staying constant. And if you have a pressure throughout a container of fixed volume, then the energy inside that container is the pressure times the volume. Hence, the energy inside our office stays constant.
Let’s look at the other half of the equation, nRT. This is also a measurement of energy. R is just a number so it never changes. But T is going up because we’re heating a room and feeling warmer. So if PV is constant, R is fixed, and T is increasing, then n must be decreasing or else the equation will not hold.
And this means that when we heat a room, the energy of the room stays fixed, but the number of particles in the room goes down. Pretty strange stuff. And what’s left is that the remaining air particles each have more energy than they did before the heater turned on, but there are fewer of them. Air is expelled outside. In fact, the energy used to heat the office actually ends up outside the building, in the form of more particles (a larger n) bouncing around.
What’s happening behind the scenes here is a thermodynamic concept called entropy. The entropy in the office decreases as the temperature goes up. Doesn’t the second law of thermodynamics teach that entropy always increases? That’s only true in closed systems. In the case of heating a room, the entropy of the room decreases, but the overall entropy of the room and the outside of the building goes up.
Thermodynamics may make it impossible to increase the energy of your room, but thankfully we can still increase the temperature, and if we’re smart about how it is we heat that room, we can minimize the energy we waste heating up the great outdoors.