# Where has all the entropy gone?

## Big Bang HTL 1, textbook

8s45gh Selected phenomena 59 work and energy 7 yes to put them back in order. But you know from experience that something like this does not happen. So there must be another law besides the energy conservation law. We still have to include what is known as entropy. Entropy is a measure of the disorder of a system (see Volume III). The greater the disorder, the greater the entropy. Info: Absurdly tiny Absurdly tiny In Fig. 7.29 you can see a box that is half filled with gas. So there is a very high order or a low entropy. Then the partition is removed. After a short time, the gas spreads evenly and becomes disordered. The entropy increases, but the energy remains. The law of conservation of energy does not therefore prohibit this process from proceeding from right to left again. Still, it won't happen! Why? What is the probability that a certain particle is in the left half? ½! And two specific particles? ½ · ½ = ¼! In general one can say: The probability that N certain particles are in one half is ½ N. The probability that there are a mere 23 certain particles in one half is as low as a 6 in the lottery, namely about 1 in 8 million. The probability that a whole mole of a gas (about 10 24 particles) happens to be in one half is only 1 in 10 10 10 24 18 128 452 296 328 812 1091626 ≈. Let this number melt on your tongue! The greatest probability occurs when there are equal numbers of particles on the left and right. That is why the state with the greatest disorder is automatically set in all natural processes and thus also the maximum entropy. That is the condition with the greatest probability. Fluctuations are possible, but the larger they are, the less likely they are (see Fig. 7.30). i Fig. 7.29 Fig. 7.30: Number of particles in the left half. At the beginning, of course, all the particles are on the left. Then the equilibrium levels off at around 50:50. The greater the fluctuations, the less likely it is. If you leave something to its own devices, i.e. if you don't expend any energy, then everything gets more and more messy. To check, all you need to do is not tidy your room for a while (tell your parents it's a physics experiment). The entropy is a measure of the disorder and therefore increases up to a certain (greatest) value. Then only small fluctuations are likely (Fig. 7.30). The greater the deviation from maximum disorder, the less likely it is. The law of conservation of energy does not forbid the lump of clay from jumping off the wall again by itself or for building a house by blasting it (Fig. 7.26). Nevertheless, neither of these will happen, because the probability is practically zero! But it could happen. Gradually, the entire energy is converted into heat (Section 7.4). Heat is the energy graveyard because that's where the greatest disorder occurs. So one can also say: The entropy of the entire universe tends towards a maximum value. Summary Energy can never be created or destroyed, it can only be transformed. The amount of joules in our universe must have stayed the same since the Big Bang. At the same time, however, the entropy of the universe grows, it becomes more and more disordered. All energy is gradually converted into heat. 7.7 Braking distance and salami tactics Examples of the law of conservation of energy In this section we apply the law of conservation of energy to four examples. All of them can also be solved with Newton's laws, but with the law of conservation of energy it is more convenient in these cases. Z A roller coaster is 20 m high and the carriage reaches 20 m / s below. This is too slow for you! How high does the runway have to be for the speed to double? Does the mass of the car matter? Can you estimate the possible jump height when pole vaulting with the help of the law of conservation of energy? Assume a run-up speed of 10 m / s! At what angle do two billiard balls fly apart if they are not hit centrally? Use the law of conservation of energy! The braking distance increases with the square of the speed (Section 4.4.2). Can you justify this with the help of the law of conservation of energy? F16 A1 F17 A1 Fig. 7.31 F18 A1 F19 A1 For testing purposes only - property of the publisher Öbv