Entropy: Example of Wear & Tear with a Broken Door

[avito009]

A few months ago my door broke, so can I say the Entropy of the door is increased? This is because I read that Entropy is wear and tear. So the door broke due to wear and tear.

 

[txdw16]

Formally, entropy is the irreversibly of a process or the lost ability to do useful work, and is often described as "disorder". A common example is a car engine. During the process the joints, pistons, air, fuel, etc. all lose useful energy due to friction, timing, and other "irreversibilities", and so the work output will always be lower than the work input. In this case entropy increases and can help get a sense of the loss of efficiency.

Informally however, I guess your door did break due to entropy in a sense (or atleast your door breaking increased entropy). Over time the hinges wear, and the door becomes harder to open, maybe even becomes a really tight fit in the doorframe or you have to turn the knob a certain way. This causes you to put more work into it, but receive the same output (door opening and closing daily). Now it's broke, and if you choose to fix it this will cost you energy, for the same output of a useful door. These things increase entropy and lower the "efficiency" of the door.

 

[Khashishi]

Casually, you could say that, but if you want to be physically and quantitatively accurate, you need to make careful measurements of the door. In particular, the entropy will be normally be higher when the temperature of the door is higher.

 

[mfb]

Casually, you could say that, but if you want to be physically and quantitatively accurate, you need to make careful measurements of the door. In particular, the entropy will be normally be higher when the temperature of the door is higher.

Indeed, and temperature will be the most significant part of the entropy. Your door broke to some number of pieces which now have independent positions and motios - this increased entropy a bit, but the positions and (thermal) motion of the 10^27 atoms in the door completely dominate the total entropy.

 

[jfizzix]

A few months ago my door broke, so can I say the Entropy of the door is increased? This is because I read that Entropy is wear and tear. So the door broke due to wear and tear.

Most generally, entropy is a measure of how dispersed (tending toward maximum uniformity) the probability distribution of all the possible arrangements of the "system" in question.

For the door, the "arrangements" would be all the possible configurations of the atoms making up the door and the distribution of the total energy distributed among those atoms.

Simply put, if there are more ways for a door to be broken than there is for a door to be in good working order (and there is), then the entropy of a door definitely increases when it breaks.

This is also why there is an entropy-based arrow of time (the second law). The entropy of the Universe inexorably increases because there are a lot (a LOT!) more ways for the universe to be in a state of higher entropy than lower entropy by its definition.

 

[Andrew Mason]

A few months ago my door broke, so can I say the Entropy of the door is increased? This is because I read that Entropy is wear and tear. So the door broke due to wear and tear.

Thermodynamic entropy is a statistical concept applicable to large systems of particles in thermodynamic equilibrium. The number of possible microstates (ie. the described by positions and momenta of each particle at a particular time) that result in the same macrostate - ie. the thermodynamic equilibrium state that we observe (eg. P, V, T) - determines the entropy of the system. It has really no application to a single object.

Even if you were to look at the door as a system of molecules that make up the door and hinge, it doesn't help. The thermodynamic state of the door has not changed just because the hinge breaks: ie. the number of possible positions and momenta of the particles that are contained in the door has not materially changed just because the hinge broke. What has changed is the functionality of the door. That is not a thermodynamic property of the door.

AM