Sci 190E Lecture 09 Thermodynamics Thermodynamics is the only physical theory of universal content which, within the framework of the applicability of its basic concepts, I am convinced will never be overthrown. Albert Einstein Recommended books: L. Stryer. Biochemistry. W.H. Freeman and Company, NY Chapter 8. Enzymes D. Voet, J. G. Voet. Biochemistry. Chapter 3. Thermodynamic Principles Energy is driving life Energy of sun ultimately drives most of life on Earth In the process, energy is converted between its different forms therme - heat (Greek) dynamis - power Thermodynamics - an elegant description of the relationships between various forms of energy and how energy affects matter. 1 Energy is driving life With a knowledge of thermodynamics we can determine if a physical process is possible and explain: • how a macromolecule folds • why molecules cross the membrane • how muscles generate mechanical force • how energy of light is converted in plants • …. Thermodynamics tells us what can happen System and surroundings Important definitions: System - part of the universe that is of interest Surroundings - the rest of the universe Open system - system can exchange energy with surroundings Closed system - system cannot exchange energy with surroundings Tea in a cup: open system Tea in a thermos: closed system (approximation) 2 Work and energy d Fpull Work: effect of force d F d Double the force – double the work 2F Work is proportional to force 3 Work: effect of time and distance d Work is proportional to the distance, but not time! work ~ d Energy the capacity of a physical system to do work Work W is proportional to the applied force F and the distance d over which an object is moved Joule . W = F||d (J ≡ N m) A living system spends energy to perform work M. Bryan, "Man Pushing Boulder" The force can take many forms - gravitational, expansion of gas, electric force etc. When any of these forces performs work an energy is spent - potential energy of gravitational field, energy stored in gas pressure, electric potential energy etc. 4 The first law of thermodynamics Conservation of energy: the energy can be neither created nor destroyed The first law of thermodynamics: The total energy of a system and its surrounding is a constant There's no such thing as a free lunch! w or k ∆Esystem ≡ E final − Einitial = Q −W system work done by the system heat change in the energy of the system heat absorbed by the system from surroundings Sign convention: Q > 0 - system receives heat from surroundings (endothermic process) Q < 0 - system releases heat into surroundings (exothermic process) W > 0 - work is done by system against external force The first law of thermodynamics ∆E ≡ E final − Einitial = Q −W Force Units: Newton - N Energy Units: Joule, 1 J = 1 N.m Calorie 1 cal = 4.184 J (1 cal heats 1 g of water from 14.5o to 15.5o) Large calorie: 1 Cal = 1 kcal = 4184 J favored by nutritionists Adult human (system) needs to receive 2000-3000 Cal daily from surroundings to perform work necessary to stay alive. (2000 Cal is enough energy to carry 30-40 cars onto top of Physics building) 5 State of a system ∆E ≡ E final − Einitial = Q −W Energy of a system depends only on its current properties (or state), not on how it reached that state. Example: The state of gas is completely described by its pressure P and temperature T The energy of gas is only function of its state-functions (P and T) State-functions -quantities that depend only on the state of the system (Energy itself is also a state-function) (Work and heat are not) • ∆E depends only on initial and final states, not on the path of transformation • There is no change in the energy E if the system returns into its initial state (cyclic process) Enthalpy (H) Any combination of state-functions must also be a state-function Enthalpy: H=E+PV ∆E ≡ E final − Einitial = Q −W Why use enthalpy? - most biological processes occur at constant pressure - V changes in biological processes are small - ∆H is equal to heat transferred to the system (if W=0) Example problem: Want to measure enthalpy change due to complete oxidation of 1 g of glucose into CO2 and H2O in my muscle tissue. This process is extremely complex Solution: H is a state function → it does not matter what way we perform the change We can burn glucose and measure ∆H of combustion - heat - at constant P ∆H for any reaction pathway can be determined from ∆H for any other reaction pathway between the same reactants and products 6 Spontaneous process Is he coming out from water? If he jumps in the kinetic energy is converted into motion of the molecules of water. Newton laws and the first law of thermodynamics do not prohibit the backward process: the molecules of water kicking the swimmer out in a coherent (concerted) motion Second law of thermodynamics: Spontaneous processes occur in the directions that increase the overall disorder in the universe (toward chaos) Note: this law does not say anything about the rate of the process The measure of order gas vacuum - ordered system Did total energy - valve opened, disorder change? There are many ways N molecules can be divided between two volumes Measure of disorder - the number n of equivalent ways of arranging the components of the system Molecules Left Right n N 0 1 - only one way N-1 1 N ways N-2 2 N(N-1)/2 ways ….. 7 The measure of order In general, number of ways: N! nL = (N-L) L L!(N − L)! molecules molecule Total number of possibilities = 2N The probability to find system in particular state with L out of N N molecules in the right bulb: pL = nL / 2 The system will spontaneously evolve into its most probable (and least ordered) configuration - i.e. L=N/2 Real system (N~1023): the probability that L differs from N/2 by 1 part in 10 billion is 10-434 Equal distribution of molecules between the two bulbs is not due to laws of motion, the energy is the same. It is because the aggregate probability of all other states is insignificant! Entropy n is too large in real systems. 1877: Ludwig Boltzmann introduced entropy S S = kB ln n entropy: en - in (Greek) Boltzmann constant trope – turning -23 . kB = 1.3807×10 J K turning pure states to mixed ones Entropy is a state function Ludwig Boltzmann 1844-1906 For the previous example, total number of N ways to arrange N atoms was 2 , and S = kB N ln 2 The laws of random chance cause any system of reasonable size to adopt its most probable arrangement - one with maximum entropy S = kB ln1 = 0 S = kB ln N S = kB ln(N[N −1]/ 2) 8 The second law of thermodynamics For any constant energy process (∆E = 0), a process can occur spontaneously only if the entropy (disorder) increases: ∆Ssystem + ∆Ssurroundings = ∆Suniverse > 0 The entropy of the universe tends towards maximum There's no lunch that's worth what you paid for it. Example: Transport of O2 from the lungs to the tissues Transport of CO2 from the tissues to the lungs Concentration Lungs Tissue O2 high low CO2 low high Note: thermodynamics does not predict rates The second law of thermodynamics "The law that entropy always increases - the Second Law of Thermodynamics - holds, I think, the supreme position among the laws of physics. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations - then so much the worse for Maxwell's equations. If it is found to be contradicted by observation - well, these experimentalists do bungle things from time to time. But 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." Sir Arthur Eddington 9 Can we decrease entropy? How can we increase order? Need to pump: energy! ∆Ssystem + ∆Ssurroundings = ∆Suniverse > 0 A system can only be ordered (∆Ssystem>0) at the expense of increasing the disorder of surroundings by the application of energy to the system Living organisms are ordered systems - at the expense of disordering the nutrients they consume Conformation of proteins: to large extent are driven by water structure that tends to maximize disorder The third law of thermodynamics As temperature goes to zero, the entropy of a system approaches a constant You must have lunch. Alternative form: It is impossible by any procedure, no matter how idealized, to reduce any system to the absolute zero of temperature in a finite number of operations' We will be not concerned about this law in this course 10 Measuring entropy Living systems are too complex to calculate S directly. 1864, Rudolf Clausius For spontaneous processes: final dQ This definition of S is ∆S ≥ — equivalent to Boltzmann’s initial T Change in heat over the temperature at which it occurs Rudolf Clausius Equivalence only occurs for reversible processes, 1822-1888 in which the system remains in equilibrium at all times (ideal, not achievable). In real processes, even if you change the state of the system and then return back to the same state, the Suniverse increases. Q In biology: temperature is often constant: ∆S ≥ T Gibbs free energy Spontaneous process is one that increases disorder of the universe hard to monitor H O2 H 2 2 2H2O Example: + + + Process is spontaneous - but order increases? Protein folding - order increases? Need a state function that predicts if process is spontaneous 1878, Gibbs free energy G ≡ H − TS ∆G ≡ ∆H − T∆S Indicator of spontaneity for processes that occur at constant pressure and temperature Willard Gibbs 1839-1903 11 Gibbs free energy and spontaneous process Q ∆G ≡ ∆H − T∆S ∆G = Q − T∆S , but ∆S ≥ T heat transferred to the system* For spontaneous process under constant T and P: ∆G ≤ 0 ∆G < 0 - exergonic process, can do work ∆G > 0 - endergonic process, must be driven by input of energy ∆G = 0 - equilibrium ∆G varies with temperature Consequence (example): Proteins unfold when temperature rises above melting temperature http://www.cs.stedwards.edu/chem/Chemistry/Biotext/Chapter6.HTML *This is true for most biological systems (no work), but not universal 12.