Thermodynamics
= describes exchange of energy between system + environment
Thermo = heat ; dynamics = motion
→ biological systems
→ machine that uses energy
→ always about a system
→ explain everything that happens in cell
System = thing that your studying (body, cell, molecule, etc) → object of investigation
Environment = rest of the universe → everything outside the system
Internal energy (U) sometimes E
- has many contributions (bond energy, interaction energy, kinetic energy, etc)
- if a reaction is happening → what is the change in internal energy, where does
energy come from
- Internal energy decreases when for ex. a bond is broken in the cell. That energy is
released → used to do work or produce heat.
- Often not possible to determine total U for a system ; we only focus on change in U
First Law of thermodynamics
= energy is conserved
- energy cannot disappear → it cannot be generated
- energy can only be converted from 1 to another
- internal energy for: do work or produce heat
- if system does work → internal energy decreases
- positive flux of heat (q) means that energy is added to system → internal energy
increases
- negative q ⇒ means system produces heat → loses internal energy
- ΔU = q - w
- q = heat
- w = work
- positive q → heat goes into system → U increases
- negative q → heat goes out of system → U decreases
- positive w → system does work → U decreases
- +/- → in case of doubt → always reason from perspective of system
Work
- Steam engines → have steel barrels and fluctuating pressure (puffing steam train) ⇒
constant volume + fluctuating pressure
→ volume work w = V * Δp
ΔU = q - V * Δp
- Biology works at constant temperature , constant pressure, fluctuating Volume
→ volume work w = p * ΔV
ΔU = q - p * ΔV
,Enthalpy (H)
= heat added or produced by system at constant pressure
At constant pressure we write
- ΔU = qp - p * ΔV
qp = the heat added to (+) or produced by (-) the system at constant pressure
→ qp = ΔU + pΔV ≡ ΔH
→ ΔH = ΔU + pΔV → constant pressure + temperature
- in most processes → volume changes are negligible ⇒ ΔH = ΔU (except for volume
changes)
What drives transfer of energy?
- it is all about probability
Probability
Molecule diffuses → thermal energy
- how many ways to divide the particles over compartments
- how many ways to achieve that
Both states are equally likely → both unique distributions
4 blue left, 4 red right
2 blue left, 2 red right → 36 x more likely
3 blue left, 3 red right → 16 x more likely
W = multiplicity
= number of microscopic arrangements that have the same macroscopic
appearance
- count how many molecules are in one compartment
→ cannot tell one molecule from another
- microscopic states ⇒ 4:0 → means 4 molecules in left compartment and
0 on right
How many microscopic / macroscopic states?
- 1+1+4+4+6 = 16 microscopic states
- 4:0, 0:4, 1:3, 3:1, 2:2 = 5 macroscopic states
Change to find the state
- 4:0 → 1/16 → p(molec 1 is in compartment l) x p (molec 2 is in comp l) x p (molec
3 is in comp l) x p (molec 4 is in comp ll) = 0.5 x 0.5 x 0.5 x 0.5 = 1/16
- 3:1 → 4/16 → probability to find this state is 4 x (0.5)4 → because there are 4
ways to achieve this state (macroscopically)
- 2:2 → 6/16
,Probability drive
- molecules move randomly → it is a matter of probability p(2:2) is 6 times more likely
than p(4:0)
- It is not a force that drives them → it is probability
- increase molecules added → smaller change to find them all in …
- Gas expansion → distribute more over area (due to probability drive)
- System is in equilibrium ⇒ equally distributed → individual particles still move but
there is no net change
- Why does a cup of coffee cool down → heat will distribute over system (heat will
distribute over 2 systems → one new system?) ⇒ 2 systems are brought in thermal
contact ⇒ iso-terminal state
Entropy (S)
= thermodynamics calls probability → entropy
- S = kBIn(W)
- kB = Boltzmann constant, Ln = natural log
Second law of thermodynamics ; in a spontaneous reaction, the total entropy needs to
increase
- Coffee will cool down because it leads to increased S
- 2nd law tells you in which direction a process or reaction will run spontaneously, and
in which direction it requires an input of energy
- S leads to an even distribution of particles/energy over the system because of
maximal W in that state
Life appears to be in conflict with second law of thermodynamics
⇒ Cells are highly structured → putting different molecules in specific places →
against spontaneous distribution
- Also need to calculate environment into aquasion
- Cells are not isolated → they are in thermal contact with their environment (G=H-T*S)
< 0 ⇒ cells must produce heat in order to be a cell
Isolated system
- System that is thermally isolated will always develop towards maximal entropy
- process which increases entropy of the system will occur spontaneously
- process that decreases entropy of the system will not occur
- maximal entropy = equilibrium → no net changes (only small fluctuations)
- Reactions will occur if ΔSsys > 0
Open system
- can exchange energy
- System that can exchange heat, changes the entropy of the environment
- How do you calculate entropy of universe (environment) Senv
- process that increases total entropy will occur spontaneously
- process that decreases total entropy will not occur
- Reactions will occur if ΔStot = ΔSsys + ΔSenv > 0 (spontaneous)
Entropy (S) of the environment = measure of probability
- increase of entropy due to heat of system
- System increases entropy of environment via heat exchange
- Link between heat and entropy ⇒ ΔS = q/T
, - ΔStot = ΔSsys - qsys / T > 0
- qsys = ΔHsys
- ΔStot = ΔSsys - ΔHsys / T > 0 for spontaneous processes
S = kb ln W
- ln (=elog) = natural log (not 10log)
- highly structured systems (molec in 1 place) have low multiplicity and low entropy
Gibbs free energy
= used to predict if a certain process is going to happen spontaneously (ΔG <0) or not
(ΔG > 0)
- Calculated from the system, but accounts for the entropy increase of the environment
- It is not an energy ⇒ but an entropy balance ⇒ G can decrease, U cannot!
- It expresses how much work a system can be made to do
- The more negative ΔG → the larger the total entropy increase, the larger the
probability drive, the more potential to do work
- G = H - TS at constant pressure ⇒ gibbs free energy
- ΔG at equilibrium = 0 (no potential to do work)
- G = -TΔStot
ΔG = ΔHsys - TΔSsys < 0 (spontaneous) ⇒ cells
- organization decreases S of cell ⇒ must be compensated by ΔH <0 (cells must
produce heat)
Process that decreases total entropy (ΔG >0) will not occur unless…
- it can be driven by a second reaction that has a larger negative ΔG
Notes from Canvas
Variable = parameters that influence the behavior of the system
- State variables = they define the state in which the system is at a given moment
- for ex. temperature, place, position
- not a state variable: how much work you did today
State variables divided
1) intensive state variable
- average out
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