5.1: A very little thermodynamics
- Page ID
- 4140
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)While the diversity of organisms and the unique properties of each individual organism are the products of evolutionary processes, initiated billions of years ago, it is equally important to recognize that all biological systems and processes, from growth and cell division to thoughts and feelings, obey the rules of chemistry and physics, and in particular the laws of thermodynamics. What makes biological systems unique is that, unlike simpler physicochemical systems that move toward thermodynamic equilibrium, organisms must maintain a non-equilibrium state in order to remain alive. While a chemical reaction system is easy to assemble de novo, every biological system has been running continuously for billions of years. So, before we continue we have be clear about what it means and implies when we say that a system is at equilibrium versus being in a obligate non-equilibrium state.
To understand the meaning of thermodynamic equilibrium we have to learn the see the world differently, and learn new meanings for a number of words. First we have to make clear the distinction between the macroscopic world that we directly perceive and the sub-microscopic, molecular world that we can understand based on scientific observations and conclusions - it is this molecular world that is particularly important in the context of biological systems. The macroscopic and the molecular worlds behave very differently. To illustrate this point we will use a simpler model that displays the basic behaviors that we want to consider but is not as complex as a biological system. In our case let us consider a small, well-insulated air-filled room in which there is a table with a bar of gold – we use gold since it is chemically rather inert, that is, un-reactive. Iron bars, for example, could rust, which would complicate things. In our model the room is initially at a cosy 70 ºF (~21 ºC) and the bar of gold is at 200ºC. What will happen? Can you generate a graph that describes how the system will behave over time? Our first task is the define the system – that is, that the part of the universe in which we are we interested. We could define the system as the gold bar or the room with the gold bar in it. Notice, we are not really concerned about how the system came to be the way it is, its history. We could, if we wanted to, demonstrate quite convincingly that the system’s history will have no influence on its future behavior – this is a critical difference between biological and simple physicochemical systems. For now we will use the insulated room as the system, but it doesn't really matter as long as we clearly define what we consider the system to be.
Common sense tells us that energy will be transferred from the gold bar and the rest of the room and that the temperature of the gold bar will decrease over time; the behavior of system has a temporal direction. Why do you think that is? Why doesn't the hot bar get hotter and the room get cooler? We will come back to this question shortly. What may not be quite as obvious is that the temperature of the room will increase slightly as well. Eventually the block of gold and the room will reach the same temperature and the system will be said to be at equilibrium.
Remember we defined the system as isolated from the rest of the universe, but what does that mean? Basically, no matter or energy passes into or out of the room – such a system is said to be a closed system. Because it is a closed system, once the system reaches its final temperature, NºC, no further macroscopic change will occur. This does not mean, however, that nothing is going on. If we could look at the molecular level we would see that molecules of air are moving, constantly colliding with one another, and with molecules within the of bar and the table. The molecules within the bar and the table are also vibrating. These collisions can change the velocities of the colliding molecules. (What happens if there was no air in the room? How would this change your graph of the behavior of the system?) The speed of these molecular movements is a function of temperature, the higher (or lower) the temperature, the faster (or slower) these motions would be. As we will consider further on, all of the molecules in the system have kinetic energy, which is the energy of motion. Through their interactions, the kinetic energy of any one particular molecule will be constantly changing. At the molecular level the system is dynamic, even though at the macroscopic level it is static. We will come back to this insight repeatedly in our considerations of biological systems.
And this is what is important about a system at equilibrium: it is static. Even at the molecular level, while there is still movement, there is no net change. The energy of two colliding molecules is the same after a collision as before, even though the energy may be distributed differently between the colliding molecules. The system as a whole cannot really do anything. In physical terms, it cannot do work - no macroscopic changes are possible. This is a weird idea, since (at the molecular level) things are still moving. So, if we return to living systems, which are clearly able to do lots of things, including moving macroscopically, growing, thinking, and such, it is clear that they cannot be at equilibrium.
We can ask, what is necessary to keep a system from reaching equilibrium? The most obvious answer (we believe) is that unlike our imaginary closed room system, a non-equilibrium system must be open, that is, energy and matter must be able to enter and leave it. An open system is no longer isolated from the rest of the universe, it is part of it. For example, we could imagine a system in which energy, in the form of radiation, can enter and leave our room. We could maintain a difference in the temperature between the bar and the room by illuminating the bar and removing heat from the room as a whole. A temperature difference between the bar and the room could then (in theory) produce what is known as a heat engine, which can do work (that is, produce macroscopic change.) As long as we continue to heat one block and remove heat from the rest of the system, we can continue to do work, that is, macroscopically observable changes can happen.
Cryptobiosis: At this point, we have characterized organisms as dynamic, open, non-equilibrium systems. An apparent exception to the dynamic aspect of life are organisms that display a rather special phenotypic adaptation, known generically as cryptobiosis. Organisms, such as the tardigrad (or water bear), can be freeze-dried and persist in a state of suspended animation for decades. What is critical to note, however, is that when in this cryptobiotic state the organism is not at equilibrium, in much the same way that a piece of wood in air is not at equilibrium, but capable of reacting. The organism can be reanimated when returned to normal conditions147. Cryptobiosis is an genetically-based adaptation that takes energy to produce and energy is used to emerge from stasis. While the behavior of tardigrads is extreme, many organisms display a range of adaptive behaviors that enable them to survive hostile environmental conditions.
Contributors and Attributions
Michael W. Klymkowsky (University of Colorado Boulder) and Melanie M. Cooper (Michigan State University) with significant contributions by Emina Begovic & some editorial assistance of Rebecca Klymkowsky.