There were still a few bugs to work out in this novel form of flight. The inventors themselves didn’t quite grasp the physics that made the balloon rise, believing that they had discovered a new kind of gas that was lighter than air. In fact, the gas was air, just hotter and therefore lighter than the air surrounding it. At this point, you might be wondering what this has to do with entropy. Well, entropy is just a fancy word for ‘number of possible arrangements’. Entropy is a count of how many ways you can rearrange the ‘insides’ of a thing (its microscopic internals), while keeping its ‘outwardly’ (macroscopic) state unchanged. (Technically it’s the log of the number of these arrangements, but that’s just a mathematical convenience and doesn’t affect our discussion.)

The Chimney Balloon was started up by an engineer in the 1980s, although many other companies have since set up offering similar products. In 2017, The Chimney Balloon Co. was bought by Chimney Sheep Ltd and although the products they offer are different they now work together. So there’s a deep mystery lurking behind our seemingly simple ice-melting puzzle. At the level of microscopic particles, nature doesn’t have a preference for doing things in one direction versus doing them in reverse. The atomic world is a two-way street. The first free ascent of a hot-air balloon with human passengers, on Nov. 21, 1783. — Jean-François Pilâtre de Rozier and the Marquis d´Arlandes (Image credit: 2001 National Air and Space Museum, Smithsonian Institution (SI Neg. No. 93-2342)) First crewed flightThere’s something curious here. Although the equal energy state is the most likely, it’s still very possible to find all the energy in one solid (the left or right extremes of the graph). In fact, there's about a 1 in 8 chance of this happening. So the entropy in this system can fluctuate, sometimes going up, other times going down. You should see that as you make things bigger, the graph of arrangements becomes more sharply peaked, centered around the most likely (i.e. the highest entropy) state.

Joseph-MichelandJacques-Étienne Montgolfier, prosperous paper manufacturers (a high-tech industry at the time), experimented with lighter-than-air devices after observing that heated air directed into a paper or fabric bag made the bag rise. After several successful tests, the brothers decided to publicly demonstrate their invention. On the left hand side of the sheep simulation above, you can watch the sheep shuffling between the farms at random. There doesn’t seem to be any pattern to their motion.

In sheep land, we’ve removed the fence between two neighboring farms, each with 3 plots of land, and 6 sheep are roaming freely between them. The eight-minute flight, which ended in the woods a few miles from the palace, didn’t seem to do the barnyard trio any harm, Schama writes: “‘It was judged that they had not suffered,’ ran one press comment, ‘but they were, to say the least, much astonished.’” But, when we scale up these solids to having 50 atoms each, and sharing 50 units of energy, the odds of finding all the energy in one solid is about 1 in 133 billion. Now that's starting to look like a much safer bet! As you add more pieces to your system, its entropy graph becomes steeper and steeper. So you're increasingly likely to find it at a state near the peak. The Montgolfiers' next step was to test a balloon with a person as the passenger. On Oct. 15, 1783, the brothers launched a balloon on a tether withJean-François Pilâtre de Rozier, a chemistry and physics teacher, aboard. He stayed aloft for almost 4 minutes, according to Encyclopedia Britannica.

About a month later, on Nov. 21, Pilâtre de Rozier and theMarquis d'Arlandes, a French military officer, made the first free ascent in a hot air balloon. The pair flew from the center of Paris to the suburbs, about 5.5 miles (9 km), in 25 minutes. Benjamin Franklinwrote in his journal about witnessing the balloon take off:

How effective chimney draught excluders are depends on a couple of factors. The main thing you need to concentrate on is ensuring you buy the right sized product for your chimney. You will need to measure your flue carefully. In some cases, it will be necessary to have a draught excluder custom made to fit.

Jean-François Pilâtre de Rozier, a chemistry and physics teacher, and the Marquis d’Arlandes, a military officer, flew nearly six miles, from the center of Paris to the suburbs, in 25 minutes. This time, Benjamin Franklin was among the spectators, according to Space.com. He later marveled in his journal about the experience, writing, “We observed [the balloon] lift off in the most majestic manner. When it reached around 250 feet in altitude, the intrepid voyagers lowered their hats to salute the spectators. We could not help feeling a certain mixture of awe and admiration.” Joseph-Michel and Jacques-Étienne Montgolfier, also called the Montgolfier brothers, (respectively, born Aug. 26, 1740, Annonay, France—died June 26, 1810, Balaruc-les-Bains; born Jan. 6, 1745, Annonay, France—died Aug. 2, 1799, enroute from Lyon to Annonay), French brothers who were pioneer developers of the hot-air balloon and who conducted the first untethered flights. Modifications and improvements of the basic Montgolfier design were incorporated in the construction of larger balloons that, in later years, opened the way to exploration of the upper atmosphere. Say we’ve got three sheep. These sheep are shuffling about in a farm, pretty much at random. And this farm is split into three plots of lands. Now, let’s assume the sheep are equally likely to be in any of these 462 arrangements. (Since they move randomly, there's no reason to prefer one arrangement over another.) In that case, we're most likely to find the sheep evenly distributed between the two farms, because this state has the most arrangements (it's the biggest bar in the graph).And that’s just 50 atoms. When we get to an object as big as an ice cube in a glass of water, with something like 10 When you heat a solid, you're adding energy to it. We usually think of energy as something continuous, something that flows. But when you get down to the atomic level, quantum mechanics teaches us that energy comes in discrete chunks. Meanwhile, there are only 28 possible arrangements for the state we started off in, with all 6 sheep on the top farm (the bar to the right of the graph). So we're less likely to find the sheep in this lower entropy state.