Exam 1 Topics

Degrees of Freedom

• How to count - translational , rotational , vibration
• Distribution of thermal energy (equal)
• $\frac{k_b *T}{2}$ per molecule per degree of freedom

Enthalpy

• Conditions (constant pressure)

• Meaning if positive or negative

• $\Delta H = \Delta U + P *\Delta V$

  • $\Delta U = Bond$
  • $\Delta V$ = volume/work

2nd Law

• Macrostates and Microstates
• $S = k_b *ln(W)$ , entropy for a macrostate
• Combining 2 systems, $S$ and $W$
• $^NC^R$ ( or $N$ choose $M$ )
• Equilibrium, choosing macrostate, direction of change
• Benefit of not being at equilibrium
• Connections between probability ( 1 coin ) and distribution ( many coins )
• $\Delta S = \frac{Q}{T}$

Gibbs Free Energy

• $\Delta G = \Delta H - \left(T *\Delta S\right)$
• Meaning if positive, negative and effect on Temperature

Boltzmann Distriubution

• Fluctuations of energy in 1 degree of freedom
• Distribution of energy per molecule
• $P(E_i) = A*e^{\frac{-E_i}{k_B *T}}$
• Effect of $T$ on $<E>$

Electric Field

• $\overset{\rightharpoonup}{F_{q_0}}^{net} = q_0 * \overset{\rightharpoonup}{E}^{net}$
• Doesn't depend on $q_0$ , but $\overset{\rightharpoonup}{E}^{net}$ is from other , usually fixed , charges
• Direction for positive and negative charges

Electric Potential

• $V = \frac{k_c *q}{r}$

  • Point Charge

• $U = q_0 * V$

  • Potential Energy

• Again, from other charges

• When large, when positive or negative

• Slope of $V$ vs Position = $E$

Electric Potential Energy

• $U = \frac{k_C * q_1 * q_2}{r}$
• Slope of $U$ vs Position = Force

Charge Arrangements

• Line of Charge

  • $\lambda , \frac{C}{m}$
  • $E$ direction
  • $E$ magnitude = $\frac{2*k_C*\lambda}{d}$

• Plane of Charge

  • $\sigma$ , $\frac{C}{m^2}$
  • $E$ direction
  • $E$ magnitude = $2 *\pi *k_C * \sigma$
  • If $E$ constant , $V$ linear