Issue 05 of Chalkdust, a magazine for the mathematically curious, is available to read online now.

Read about slide rules (the early calculators), maths and politics, linear algebra with diagrams, among other amazing things. You just have to click here.

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Dear Hugo,

with interest I read your article on absolute Zero. However, your discussion of the 2nd Law is not correct. You write: “every object has a given amount of entropy associated with it, and whatever happens to it …. can never result in a decrease in the amount of entropy.” This is not correct – heat rejection can decrease the entropy of an object. The general form of the 2nd law for a closed system is

dS \ge \delta Q/T

(“Clausius’ inequality”), with that stipulation that for reversible processes

dS = \delta Q/T

So for a reversible process in a closed system, heat rejection is guaranteed to decrease entropy. For an irreversible process, entropy may decrease due to heat rejection provided that entropy generation due to irreversibilities is not too strong.

The form of the 2nd Law given in your blog applies to an adiabatic, closed system (no transfer of heat or mass across the system boundary). In that case indeed

dS \ge 0

Eddington’s famous statement “Entropy always increases ….” refers to the entropy of the universe – which cannot reject heat to an “outside reservoir”. Until cosmologist find one hiding behind a black hole 😉

yours,

Wolfgang

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Good moring Wolfgang. The Chalkdust team appreciate the interest of our readers. And thank you very much for writing me.

Indeed you are absolutely right, maybe I should not have generalised the 2nd law as I did in the blog. As you stated, dS>0 only applies for an isolated system. I would have liked to describe in detail all the laws of thermodynamics (this was one of my favourite subjects when I was an undegraduate student), but we aim to publish articles for a level no higer than 1st year undegraduate in Mathematics, and some of them have never even taken thermodynamics lectures. That was the reason I just made a short review of the laws, and I could not introduce many concepts as I wanted (in fact, this was the hardest part: explaining the laws in a few words for people with no background in thermodynamics ). But I will edit the blog to state that dS>0 is only valid for systems with no exchange of mass and energy with the surroundings.

And again, many thanks for your interest in our magazine, and for dedicating minutes to writing us . The Chalkdust team is always happy to receive comments from our readers.

Have an excellent day

Best regards

Hugo

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