Lecture 9

Readings

http://umdberg.pbworks.com/w/page/63473552/Boltzmann%20distribution%20%282013%29

http://umdberg.pbworks.com/w/page/63473565/Boltzmann%20distribution%20and%20Gibbs%20free%20energy%20%282013%29

• Clarification:

  • This is the probability for a small part of a large system.
  • Small is typically 1 molecule.
  • Large is around ${10}^{20}$$10^{20}$ molecules.
  • So this probability distribution doesn't work for say 2 large objects in contact with each other

• Change with temperature:

• Average energy goes up as temperature goes up

• Still, $E_i=0$$E_i = 0$ remains the most common state, even at high $T$$T$

• Spread of possible energies increases greatly at high $T$$T$

• Thus, finding a molecule at $E_i=0$$E_i = 0$ is uncommon at hight $T$$T$

• The $E_i$$E_i$ term ( the horizontal axis ) is roughly enthalpy for biology systems because most systems are at a constant Pressure and Temperature

• But there is also a correction term for entropy

  • If some $E_i$$E_i$ for a molecule has more microstates ( = greater entropy ), it gets a bump up in probability

• Gibb's Free Energy exactly accounts for this

• So the best form for biology is:

• Where $G=H-(T\ast S)$$G = H - \left(T*S\right)$

  • Note, not $\mathrm{\Delta }G$$\Delta G$ this time.

    • This is absolute $G$$G$, which is always positive

• But mostly, just think of $G_i$$G_i$ as the "energy" in a molecule or the "energy" in a degree of freedom