Life, Order, Thermodynamics

Transcription

1 Life, Order, Thermodynamics 1

2 A key question about order How order is created and maintained in biological systems? Through energy fluxes Biological Physics, updated 1st ed. ( Philip C. Nelson) 2

3 Energy: conservation and conversion Mechanical energy (kinetic + potential): conserved in the absence of friction. Thermal energy (heat): due to friction forces. Total energy (mechanical + thermal): is always conserved! 3

4 Energy: conservation and conversion Mechanical energy (kinetic + potential): conserved in the absence of friction. Thermal energy (heat): due to friction forces. Total energy (mechanical + thermal): is always conserved! Indeed energy can be converted into different forms: potential into kinetic (e.g. dynamics in a force field). mechanical into thermal (e.g. viscous friction). 4

5 Energy: conservation and conversion Mechanical energy (kinetic + potential): conserved in the absence of friction. Thermal energy (heat): due to friction forces. Total energy (mechanical + thermal): is always conserved! Indeed energy can be converted into different forms: potential into kinetic (e.g. dynamics in a force field). mechanical into thermal (e.g. viscous friction). Principles of Thermo-dynamics (valid also for chemical energy) 5

6 Principles of thermodynamics 1. The variation of total energy (internal+kinetic+potential) in an open system (allows flux of matter and energy) is equal to the heat absorbed minus the work done on the surrounding environment: ΔE = Q W 6

7 Principles of thermodynamics 1. The variation of total energy (internal+kinetic+potential) in an open system (allows flux of matter and energy) is equal to the heat absorbed minus the work done on the surrounding environment: ΔE = Q W 2. Different way of expressing the 2 nd theorem: 1. Heat never flows spontaneously from one body to another with higher temperature (Clausius formulation). 2. In a isolated system the entropy is a not decreasing function of time, and its variation is maximal during a reversible process: ds dt 0 ds = dq rev T dq T Definition of irreversible process, linked to the time arrow 7

8 Principles of thermodynamics 1. The variation of total energy (internal+kinetic+potential) in an open system (allows flux of matter and energy) is equal to the heat absorbed minus the work done on the surrounding environment: ΔE = Q W 2. Different way of expressing the 2 nd theorem: 1. Heat never flows spontaneously from one body to another with higher temperature (Clausius formulation). 2. In a isolated system the entropy is a not decreasing function of time, and its variation is maximal during a reversible process: ds dt 0 ds = dq rev T dq T Definition of irreversible process, linked to the time arrow 3. In the minimum energy state the entropy has a well defined value which only depends on the degeneracy of this fundamental state. 8

9 So, energies of different quality? Heat is a particular form of mechanical energy, namely the kinetic energy due to random motions of atoms and molecules building up matter. 9

10 So, energies of different quality? Heat is a particular form of mechanical energy, namely the kinetic energy due to random motions of atoms and molecules building up matter. The mechanical energy producing work is ordered (fall of a stone, functioning of a turbine, etc ). 10

11 So, energies of different quality? Heat is a particular form of mechanical energy, namely the kinetic energy due to random motions of atoms and molecules building up matter. The mechanical energy producing work is ordered (fall of a stone, functioning of a turbine, etc ). Is organization the key parameter to distinguish between high-quality energy (which can be used to produce work) and low-quality energy (which comes out from a partial conversion of high-quality energy)? 11

12 So, energies of different quality? Heat is a particular form of mechanical energy, namely the kinetic energy due to random motions of atoms and molecules building up matter. The mechanical energy producing work is ordered (fall of a stone, functioning of a turbine, etc ). Is organization the key parameter to distinguish between high-quality energy (which can be used to produce work) and low-quality energy (which comes out from a partial conversion of high-quality energy)? How to mathematize this concept? 12

13 Free energy Defines high-quality energy as the difference between the total energy and that due to disorder, which is proportional to the temperature times the entropy: F = E TS 13

14 Free energy Defines high-quality energy as the difference between the total energy and that due to disorder, which is proportional to the temperature times the entropy: F = E TS A system at a given temperature T can change spontaneously its status (evolve) only if the free energy change is negative. This can happen either through a reduction in E (e.g. in the fall of a stone) or through an increase in S (e.g. during isothermal expansion of a gas, or the formation of a solution). High quality when TS << E F E 14

15 How to create order in living world? F = E TS In a process leading to a reduction in F, TS could also drop if a larger reduction in E occurs. This does not violate the second principle of thermodynamics if the system is not an isolated one (e.g. can exchange heat with the surroundings). 15

16 How to create order in living world? F = E TS In a process leading to a reduction in F, TS could also drop if a larger reduction in E occurs. This does not violate the second principle of thermodynamics if the system is not an isolated one (e.g. can exchange heat with the surroundings). Examples are: Vapour condensation (ΔS < 0, ΔE < 0). Interaction of matter with electromagnetic fields. Formation of a chemical bond. Appearance of organized life on Earth. 16

17 Free energy and order So, an energy flux crossing a given system could lead to an increase in the order of the system! Principle of free energy transductions (anabolism) in animals and plants. Biological Physics, updated 1st ed. ( Philip C. Nelson) 17

18 Osmosis and energy transduction A mechanism of energy transduction that is shared among living and non-living systems is that known as osmosis. Biological Physics, updated 1 st ed. ( Philip C. Nelson) 18

19 Osmotic flux A mechanism of energy transduction that is shared among living and non-living systems is that known as osmosis. Biological Physics, updated 1 st ed. ( Philip C. Nelson) Just after the solution is formed, flux of water through the semipermeable membrane towards the region with highest solute concentration. An osmotic flux can be exploited to perform mechanical work (ΔU load > 0). Associated to increase in entropy of system (spontaneous process), and heat adsorption if work is performed. Osmotic pressure does not depend on type of solute, only on its concentration (colligative property). 19

20 Osmotic flux Inverse osmosis Biological Physics, updated 1 st ed. ( Philip C. Nelson) If we pull the left end we increase the concentration of solute in the region on the right of the semipermeable membrane. This process is called inverse osmosis or ultrafiltration. The mechanical work performed leads to increase in order of the system (reduction of entropy), although part of it is dissipated as heat to the surrounding environment. 20

21 Osmosis in living organisms 21

22 Osmosis in living organisms Hypertonic Isotonic Hypotonic 22

23 References Books Nelson, chap. 1 Online resources /02/app13.pdf Movies UUX0iY&list=PL933F4D318515DDD0&index=11 23

24 Exercise Demonstrate that the Van t Hoff equation for a mixture of ideal gases particles, which relates the osmotic pressure Π to the molarity M and to the temperature T of the solution, reads: Π = R T M Hint you need to evaluate the entropy of mixing of an ideal gas, and to recall the form of the first law of thermodynamics for an ideal gas 24