Learning Outcomes
A living cell’s primary tasks of obtaining, transforming, and using energy to do work may seem simple. However, the second law of thermodynamics explains why these tasks are harder than they appear. None of the energy transfers we’ve discussed, along with all energy transfers and transformations in the universe, is completely efficient. In every energy transfer, some amount of energy is lost in a form that is unusable. In most cases, this form is heat energy. Thermodynamically, heat energy is defined as the energy transferred from one system to another that is not doing work. For example, when an airplane flies through the air, some of the energy of the flying plane is lost as heat energy due to friction with the surrounding air. This friction actually heats the air by temporarily increasing the speed of air molecules. Likewise, some energy is lost as heat energy during cellular metabolic reactions. This is good for warm-blooded creatures like us, because heat energy helps to maintain our body temperature. Strictly speaking, no energy transfer is completely efficient, because some energy is lost in an unusable form.  Figure 1. Entropy is a measure of randomness or disorder in a system. Gases have higher entropy than liquids, and liquids have higher entropy than solids. An important concept in physical systems is that of order and disorder (also known as randomness). The more energy that is lost by a system to its surroundings, the less ordered and more random the system is. Scientists refer to the measure of randomness or disorder within a system as entropy. High entropy means high disorder and low energy (Figure 1). To better understand entropy, think of a student’s bedroom. If no energy or work were put into it, the room would quickly become messy. It would exist in a very disordered state, one of high entropy. Energy must be put into the system, in the form of the student doing work and putting everything away, in order to bring the room back to a state of cleanliness and order. This state is one of low entropy. Similarly, a car or house must be constantly maintained with work in order to keep it in an ordered state. Left alone, the entropy of the house or car gradually increases through rust and degradation. Molecules and chemical reactions have varying amounts of entropy as well. For example, as chemical reactions reach a state of equilibrium, entropy increases, and as molecules at a high concentration in one place diffuse and spread out, entropy also increases.
Set up a simple experiment to understand how energy is transferred and how a change in entropy results.
All physical systems can be thought of in this way: Living things are highly ordered, requiring constant energy input to be maintained in a state of low entropy. As living systems take in energy-storing molecules and transform them through chemical reactions, they lose some amount of usable energy in the process, because no reaction is completely efficient. They also produce waste and by-products that aren’t useful energy sources. This process increases the entropy of the system’s surroundings. Since all energy transfers result in the loss of some usable energy, the second law of thermodynamics states that every energy transfer or transformation increases the entropy of the universe. Even though living things are highly ordered and maintain a state of low entropy, the entropy of the universe in total is constantly increasing due to the loss of usable energy with each energy transfer that occurs. Essentially, living things are in a continuous uphill battle against this constant increase in universal entropy. Contribute!Did you have an idea for improving this content? We’d love your input. Improve this pageLearn More The second law of thermodynamics means hot things always cool unless you do something to stop them. It expresses a fundamental and simple truth about the universe: that disorder, characterised as a quantity known as entropy, always increases. The British astrophysicist Arthur Eddington have a stern warning to would-be theoretical physicists in 1915. “If your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation,” he wrote. The second law of thermodynamics is perhaps the most profound of the three laws of thermodynamics. Its importance is best expressed by sketching out a situation which violates it. Imagine placing 20 coins, heads up, on a tray, filming it as you give it a shake and then playing the film backwards. The coins start out as a jumbled mess, but all jump and eventually come to rest with the same side up – an unreal, slightly creepy sequence. Similarly imagine an egg yolk and white reassembling themselves after you’ve cracked it open, or even a world where it’s just as easy to pair up your socks in the right pairs as it is to jumble them up. The roots of thermodynamics lie in efforts to understand the steam engines that powered the industrial revolution of 18th and 19th-century Europe. The French engineer Sadi Carnot discovered that their heat always tends to dissipate, moving to cooler regions. Anything that goes against this grain requires additional energy to power it. That too is because the jostling molecules of something hot are more disordered than those of something cool. Entropy increase is so universal that many physicists propose it is why we see time flowing. It is certainly why our hearts must constantly pump blood, supplying our cells with energy as a temporary stay against the inevitable onset of decay and disorder. Is there any way out? Perhaps. The laws of thermodynamics only hold true as statistical averages, and some think the second law won’t be so cast-iron on the very small scales of quantum physics where few particles are involved. Some physicists even think quantum machines might bend the rules or cause them to be cast in a new form. That might not have much practical use on large scales, but one instance where quantum thermodynamics comes into play is at the event horizon of a black hole – so it could help solve the enduring riddle of how to unite general relativity with quantum theory. The second law in its classical form also determines the ultimate fate of the universe. As entropy increases, eventually there’s no more order to make chaos from, and ultimately interesting things will stop happening – a long, slow “heat death”. Or perhaps not. Other scenarios predict a more dramatic end. And the founder of classical statistical thermodynamics came up with a bizarre theory in 1896. Ludwig Boltzmann argued that, given enough time in a large enough universe, fluctuations might randomly create a sub-universe that looks like ours. More plausibly, it might create a brain that thinks it exists in just such a universe – and that thinks entropy is always on the up. In that case, all of thermodynamics’ cast-iron certainty might just been an illusion. Richard Webb The Second Law of Thermodynamics states that the state of entropy of the entire universe, as an isolated system, will always increase over time. The second law also states that the changes in the entropy in the universe can never be negative.
Why is it that when you leave an ice cube at room temperature, it begins to melt? Why do we get older and never younger? And, why is it whenever rooms are cleaned, they become messy again in the future? Certain things happen in one direction and not the other, this is called the "arrow of time" and it encompasses every area of science. The thermodynamic arrow of time (entropy) is the measurement of disorder within a system. Denoted as \(\Delta S\), the change of entropy suggests that time itself is asymmetric with respect to order of an isolated system, meaning: a system will become more disordered, as time increases.
If a given state can be accomplished in more ways, then it is more probable than the state that can only be accomplished in a fewer/one way. Assume a box filled with jigsaw pieces were jumbled in its box, the probability that a jigsaw piece will land randomly, away from where it fits perfectly, is very high. Almost every jigsaw piece will land somewhere away from its ideal position. The probability of a jigsaw piece landing correctly in its position, is very low, as it can only happened one way. Thus, the misplaced jigsaw pieces have a much higher multiplicity than the correctly placed jigsaw piece, and we can correctly assume the misplaced jigsaw pieces represent a higher entropy.
To understand why entropy increases and decreases, it is important to recognize that two changes in entropy have to considered at all times. The entropy change of the surroundings and the entropy change of the system itself. Given the entropy change of the universe is equivalent to the sums of the changes in entropy of the system and surroundings: \[\Delta S_{univ}=\Delta S_{sys}+\Delta S_{surr}=\dfrac{q_{sys}}{T}+\dfrac{q_{surr}}{T} \label{1}\] In an isothermal reversible expansion, the heat q absorbed by the system from the surroundings is \[q_{rev}=nRT\ln\frac{V_{2}}{V_{1}}\label{2}\] Since the heat absorbed by the system is the amount lost by the surroundings, \(q_{sys}=-q_{surr}\).Therefore, for a truly reversible process, the entropy change is \[\Delta S_{univ}=\dfrac{nRT\ln\frac{V_{2}}{V_{1}}}{T}+\dfrac{-nRT\ln\frac{V_{2}}{V_{1}}}{T}=0 \label{3}\] If the process is irreversible however, the entropy change is \[\Delta S_{univ}=\frac{nRT\ln \frac{V_{2}}{V_{1}}}{T}>0 \label{4}\] If we put the two equations for \(\Delta S_{univ}\)together for both types of processes, we are left with the second law of thermodynamics, \[\Delta S_{univ}=\Delta S_{sys}+\Delta S_{surr}\geq0 \label{5}\] where \(\Delta S_{univ}\) equals zero for a truly reversible process and is greater than zero for an irreversible process. In reality, however, truly reversible processes never happen (or will take an infinitely long time to happen), so it is safe to say all thermodynamic processes we encounter everyday are irreversible in the direction they occur.
The second law of thermodynamics can also be stated that "all spontaneous processes produce an increase in the entropy of the universe".
Given another equation: \[\Delta S_{total}=\Delta S_{univ}=\Delta S_{surr}+\Delta S{sys} \label{6}\] The formula for the entropy change in the surroundings is \(\Delta S_{surr}=\Delta H_{sys}/T\). If this equation is replaced in the previous formula, and the equation is then multiplied by T and by -1 it results in the following formula. \[-T \, \Delta S_{univ}=\Delta H_{sys}-T\, \Delta S_{sys} \label{7}\] If the left side of the equation is replaced by \(G\), which is know as Gibbs energy or free energy, the equation becomes \[\Delta G_{}=\Delta H-T\Delta S \label{8}\] Now it is much simpler to conclude whether a system is spontaneous, non-spontaneous, or at equilibrium.
According to the equation, when the entropy decreases and enthalpy increases the free energy change, \(\Delta G_{}\), is positive and not spontaneous, and it does not matter what the temperature of the system is. Temperature comes into play when the entropy and enthalpy both increase or both decrease. The reaction is not spontaneous when both entropy and enthalpy are positive and at low temperatures, and the reaction is spontaneous when both entropy and enthalpy are positive and at high temperatures. The reactions are spontaneous when the entropy and enthalpy are negative at low temperatures, and the reaction is not spontaneous when the entropy and enthalpy are negative at high temperatures. Because all spontaneous reactions increase entropy, one can determine if the entropy changes according to the spontaneous nature of the reaction (Equation \(\ref{8}).
Example \(\PageIndex{1}\) Lets start with an easy reaction: \[2 H_{2(g)}+O_{2(g)} \rightarrow 2 H_2O_{(g)}\] The enthalpy, \(\Delta H_{}\), for this reaction is -241.82 kJ, and the entropy, \(\Delta S_{}\), of this reaction is -233.7 J/K. If the temperature is at 25º C, then there is enough information to calculate the standard free energy change, \(\Delta G_{}\). The first step is to convert the temperature to Kelvin, so add 273.15 to 25 and the temperature is at 298.15 K. Next plug \(\Delta H_{}\), \(\Delta S_{}\), and the temperature into the \(\Delta G=\Delta H-T \Delta S_{}\). \(\Delta G\)= -241.8 kJ + (298.15 K)(-233.7 J/K) = -241.8 kJ + -69.68 kJ (Don't forget to convert Joules to Kilojoules) = -311.5 kJ
Example \(\PageIndex{2}\) Here is a little more complex reaction: \[2 ZnO_{(s)}+2 C_{(g)} \rightarrow 2 Zn_{(s)}+2 CO_{(g)}\] If this reaction occurs at room temperature (25º C) and the enthalpy, \(\Delta H_{}\), and standard free energy, \(\Delta G_{}\), is given at -957.8 kJ and -935.3 kJ, respectively. One must work backwards somewhat using the same equation from Example 1 for the free energy is given. -935.3 kJ = -957.8 kJ + (298.15 K) (\(\Delta S_{}\)) 22.47 kJ = (298.15 K) (\(\Delta S_{}\)) (Add -957.8 kJ to both sides) 0.07538 kJ/K = \(\Delta S_{}\) (Divide by 298.15 K to both sides) Multiply the entropy by 1000 to convert the answer to Joules, and the new answer is 75.38 J/K.
Example \(\PageIndex{3}\) For the following dissociation reaction \[O_{2(g)} \rightarrow 2 O_{(g)}\] under what temperature conditions will it occurs spontaneously? Solution By simply viewing the reaction one can determine that the reaction increases in the number of moles, so the entropy increases. Now all one has to do is to figure out the enthalpy of the reaction. The enthalpy is positive, because covalent bonds are broken. When covalent bonds are broken energy is absorbed, which means that the enthalpy of the reaction is positive. Another way to determine if enthalpy is positive is to to use the formation data and subtract the enthalpy of the reactants from the enthalpy of the products to calculate the total enthalpy. So, if the temperature is low it is probable that \(\Delta H_{}\) is more than \(T*\Delta S_{}\), which means the reaction is not spontaneous. If the temperature is large then \(T*\Delta S_{}\) will be larger than the enthalpy, which means the reaction is spontaneous.
Example \(\PageIndex{4}\) The following reaction \[CO_{(g)} + H_2O_{(g)} \rightleftharpoons CO_{2(g)} + H_{2(g)}\] occurs spontaneously under what temperature conditions? The enthalpy of the reaction is -40 kJ. Solution One may have to calculate the enthalpy of the reaction, but in this case it is given. If the enthalpy is negative then the reaction is exothermic. Now one must find if the entropy is greater than zero to answer the question. Using the entropy of formation data and the enthalpy of formation data, one can determine that the entropy of the reaction is -42.1 J/K and the enthalpy is -41.2 kJ. Because both enthalpy and entropy are negative, the spontaneous nature varies with the temperature of the reaction. The temperature would also determine the spontaneous nature of a reaction if both enthalpy and entropy were positive. When the reaction occurs at a low temperature the free energy change is also negative, which means the reaction is spontaneous. However, if the reaction occurs at high temperature the reaction becomes nonspontaneous, for the free energy change becomes positive when the high temperature is multiplied with a negative entropy as the enthalpy is not as large as the product.
Example \(\PageIndex{5}\) Under what temperature conditions does the following reaction occurs spontaneously ? \[H_{2(g)} + I_{(g)} \rightleftharpoons 2 HI_{(g)}\] Solution Only after calculating the enthalpy and entropy of the reaction is it possible for one can answer the question. The enthalpy of the reaction is calculated to be -53.84 kJ, and the entropy of the reaction is 101.7 J/K. Unlike the previous two examples, the temperature has no affect on the spontaneous nature of the reaction. If the reaction occurs at a high temperature, the free energy change is still negative, and \(\Delta G_{}\) is still negative if the temperature is low. Looking at the formula for spontaneous change one can easily come to the same conclusion, for there is no possible way for the free energy change to be positive. Hence, the reaction is spontaneous at all temperatures.
The second law occurs all around us all of the time, existing as the biggest, most powerful, general idea in all of science.
When scientists were trying to determine the age of the Earth during 1800s they failed to even come close to the value accepted today. They also were incapable of understanding how the earth transformed. Lord Kelvin, who was mentioned earlier, first hypothesized that the earth's surface was extremely hot, similar to the surface of the sun. He believed that the earth was cooling at a slow pace. Using this information, Kelvin used thermodynamics to come to the conclusion that the earth was at least twenty million years, for it would take about that long for the earth to cool to its current state. Twenty million years was not even close to the actual age of the Earth, but this is because scientists during Kelvin's time were not aware of radioactivity. Even though Kelvin was incorrect about the age of the planet, his use of the second law allowed him to predict a more accurate value than the other scientists at the time.
Some critics claim that evolution violates the Second Law of Thermodynamics, because organization and complexity increases in evolution. However, this law is referring to isolated systems only, and the earth is not an isolated system or closed system. This is evident for constant energy increases on earth due to the heat coming from the sun. So, order may be becoming more organized, the universe as a whole becomes more disorganized for the sun releases energy and becomes disordered. This connects to how the second law and cosmology are related, which is explained well in the video below.
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What does the 2nd law of thermodynamics state?
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