# Dimensionless entropy interpretation

Measuring temperature in joules instead in the artificial units of Kelvin would render entropy as a dimensionless quantity. This is quite appealing since entropy has always been quite a misterious quantity: it is used a measure of the disorder in a system but its units are J/K, which makes it really hard to interpret. The reason why entropy and temperature were defined this way is because they were studied before the athomical composition of matter was completeley accepted. You can read more about this in these posts:

Arieh-Ben Naim, a chemistry from Israel, has really good books in this topic such "Entropy demystified". He is one the main defenders that entropy should be a unitless quantity.

I have always like to understand the gist of things, and the first step to understand a magnitud like entropy is understanding how it can be measured. For instance, I think I know what a speed is because I can reason in terms of space and time. But in entropy, as the way is normally defined, this is hard and tricky, and all the explanations I have heard so far seem to me like quite far-fetched. So here it goes my question. Let's accept for the sake of argument that we are considering entropy a dimensionless quantity. Now we heat a gas, and we calculate the entropy associate to this process. The result would be a number, whatever. Let us say that number is going to be 100. How to interpret this number? What would it be measuring? And finally, do you agree with this vision of temperature units?

What it means is that the number of bits required to specify the exact physical state the system is in, increases by 100/log(2) bits after the gas is heated.

I think measuring the temperature in energy units is a step in the right direction, but what is even better is to do without any units. I.e. while units may be introduced for convenience, the formalism we use in physics should not have units hard wired in them, as that's misleading and leads to stupidities as pointed out by Micheal Duff in this article.

• I like this. You're correct in saying that the entropy change of 100 is an increase in the information needed to specify the state of the system. Where do you get $/log(2)$, though? 100 is already the log of the multiplicity of the state of the system, so assuming you're using a base-2 log, isn't it just 100 bits? Am I doing something stupid there? – calavicci Sep 5 '15 at 16:28
• We can't do away with units entirely; we need at least one arbitrary, physically meaningful constant to enable us to make measurements. This can just be a symbol that gets moved around in the math, though, so I'm not totally sure what you mean by units being 'hard wired' into the 'formalism.' – calavicci Sep 5 '15 at 16:28

I would strongly disagree with your statement that entropy has always been quite a mysterious quantity. Quite the contrary.

What makes water (without something else interfering) always flow down the hill? Gravity.

One does not have to know anything further about gravity to make good use of this statement, and people have used this fact for thousands of years without any further elaboration on the microscopic theories of gravity. Now ask yourself a similar question:

What makes heat (without something else interfering) always flow from the warmer to the colder temperature bath? Entropy.

Logically it's the same statement. We OBSERVE a process that has a preferred direction, and we call the cause of this observation by a name. In one case we call it "gravity", in the other we call it "entropy".

There is absolutely nothing "mystical" about entropy, once you know what it does and why one needs it (because there is not one observation of heat flowing from cold to hot without some other process facilitating it).

To use the same units for temperature as for energy is completely nonsensical, since the definition of energy is "the ability to perform work". Temperature, by itself, can not perform work, no matter how you look at it.

• You sure that temperature by itself can not perform work?? How does a steam engine work then? Temperature is a measure of the mean kinetic energy of the particles in a system, so I think it makes perfect sense to measure it in joules – Adrián A.D. Aug 16 '14 at 21:29
• @user36565: Temperature is an intensive property. A metric ton of steam can perform 1000 times the work of a kg of the same steam. So how much work can the temperature (difference) of the steam perform? One times x, a thousand times x or any arbitrary amount you chose by adjusting the total quantity of steam used to perform work? – CuriousOne Aug 16 '14 at 21:37
• One more thing: I really like your comparison with gravity. But meanwhile Gravity can be explained as a force, which is straightforward, entropy is explained as what? As a tendency to disorder? Why tendency to disorder has units of J/K? To me it is intuitive to think of entropy as the number of information you are losing or gaining, in terms of bits for example, as Count Iblis pointed out. I have to think now about what you said regarding temperature as an intensive property – Adrián A.D. Aug 16 '14 at 22:27
• Other detail regarding your analogy with gravity. If entropy was "created" to explain the flow of thermal procceses, would not have been enough equate it with heat? After all, the sign of entropy is going to be uniquely determined by the sign of the heat, since temperature is always positive. – Adrián A.D. Aug 17 '14 at 0:01
• @user36565: gravity is not a force, not even in the Newtonian case, but even after over 300 years of constant teaching, that fact is still not "straight forward" enough to "sink in". Just because something seems simple, doesn't mean, that it is, and that's true both in case of gravity and entropy. Curiously, gravity is a lot more complicated than entropy, and yet, few people take the time to study the structure of thermodynamics well enough to see, how simple entropy is in comparison to gravity. On a final note, gravity may actually be an entropic force, bringing this matter full circle. – CuriousOne Aug 17 '14 at 0:10