### 11.8 In­tro to the Sec­ond Law

Take a look around you. You are sur­rounded by air mol­e­cules. They are all over the place. Isn’t that messy? Sup­pose there would be wa­ter all over the room, wouldn’t you do some­thing about it? Wouldn’t it be much neater to com­press all those air atoms to­gether and put them in a glass? (You may want to wear a space suit while do­ing this.)

The re­al­ity, of course, is that if you put all the air atoms in a glass, the high pres­sure would cause the air to ex­plode out of the glass and it would scat­ter all over the room again. All your ef­forts would be for naught. It is like the clothes of a ten-year old. Na­ture likes messi­ness. In fact, if messi­ness is prop­erly de­fined, and it will be in sec­tion 11.10, na­ture will al­ways in­crease messi­ness as much as cir­cum­stances and the laws of physics al­low. The prop­erly de­fined messi­ness is called “en­tropy.” It is not to be con­fused with en­thalpy, which is a com­pletely dif­fer­ent con­cept al­to­gether.

En­tropy pro­vides an un­re­lent­ing ar­row of time. If you take a movie and run it back­wards, it sim­ply does not look right, since you no­tice messi­ness get­ting smaller, rather than larger. The movie of a glass of wa­ter slip­ping out of your hand and break­ing on the floor be­comes, if run back­wards, a spill of wa­ter and pieces of glass com­bin­ing to­gether and jump­ing into your hand. It does not hap­pen. Messi­ness al­ways in­creases. Even if you mop up the wa­ter and glue the pieces of bro­ken glass back to­gether, it does not work. While you re­duce the messi­ness of the glass of wa­ter, you need to per­form ef­fort, and it turns out that this al­ways in­creases messi­ness else­where more than the messi­ness of the glass of wa­ter is re­duced.

It has big con­se­quences. Would it not be nice if your car could run with­out us­ing gas? Af­ter all, there is lots of ran­dom ki­netic en­ergy in the air mol­e­cules sur­round­ing your car. Why not scope up some of that ki­netic en­ergy out of the air and use it to run your car? It does not work be­cause it would de­crease messi­ness in the uni­verse, that’s why. It would turn messy ran­dom mol­e­c­u­lar mo­tion into or­ga­nized mo­tion of the en­gine of your car, and na­ture re­fuses to do it. And there you have it, the sec­ond law of ther­mo­dy­nam­ics, or at least the ver­sion of it given by Kelvin and Planck:

You can­not just take ran­dom ther­mal en­ergy out of a sub­stance and turn it into use­ful work.
You ex­pected a phys­i­cal law to be a for­mula, in­stead of a ver­bal state­ment like that? Well, you are out of luck for now.

To be sure, if the air around your car is hot­ter than the ground be­low it, then it is pos­si­ble with some in­ge­nu­ity to set up a flow of heat from the air to the ground, and you can then di­vert some of this flow of heat and turn it into use­ful work. But that is not an un­lim­ited free sup­ply of en­ergy; it stops as soon as the tem­per­a­tures of air and ground have be­come equal. The tem­per­a­ture dif­fer­ence is an ex­pend­able en­ergy source, much like oil in the ground is; you are not sim­ply scoop­ing up ran­dom ther­mal en­ergy out of a sub­stance. If that sounds like a fee­ble ex­cuse, con­sider the fol­low­ing: af­ter the tem­per­a­ture dif­fer­ence is gone, the air mol­e­cules still have al­most ex­actly the same ther­mal en­ergy as be­fore, and the ground mol­e­cules have more. But you can­not get any of it out any­more as us­able en­ergy. Zero. (Prac­ti­cally speak­ing, the amount of en­ergy you would get out of the tem­per­a­ture dif­fer­ence is not go­ing to get you to work in time any­way, but that is an­other mat­ter.)

Would it not be nice if your fridge would run with­out elec­tric­ity? It would re­ally save on the elec­tric­ity bill. But it can­not be done; that is the Clau­sius state­ment of the sec­ond law:

You can­not move heat the wrong way, from cold to hot, with­out do­ing work.