Physical equations to remember

Work Done (in terms of applied force) and 2 equations to calculate force

work done = force * distance

force = mass * acceleration

force = external pressure * area

Irreversible work (hint: what remains constant?)

pressure remains constant

= - external p * (∆V)

Reversible work equation which can be linked to which entropy equation and why?

w = -nRT * ln(∆V)

linked to: ∆S = nR * ln(∆V)

why:

∆S = ∆q / T

isothermal system ∆U = 0

∆U = q + w

0 = q + w

-w = q

means ∆S = q / T = (nRT * ln (∆V)) / T

T cancels out

Real gas equation

(p + (a n²)/V² ) * (V - nb) = RT

Eq for U in terms of k_B for one degree of freedom.

multiplier for U of monatomic gases:

multiplier for U of diatomic gases:

multiplier for U of polyatomic gases:

U = (k_BT) / 2

monatomic gases: 3

diatomic gases: 5

polyatomic gases: 6

Enthalpy in terms of internal energy

H = U + pV

Entropy at constant P using Specific heat capacity

Entropy at constant T using Specific heat capacity

∆S = Cp*ln (T₂/T₁)

∆S = nR*ln (V_f/V_i)

Kirchoff’s law eq and what condition is required?

Integrated form of eq

∆H = Cp*∆T condition = constant pressure

∆H₂ = Cp*(T₂ - T₁) + ∆H₁

What Gibbs Free Energy eq lets us see the effects of changing T and P?

Constant T eq

dG = Vdp - SdT

nRT*ln( p_f / p_i )

Van’t Hoff eq

which integrated version of the eq do you want to use to plot a graph?

which integrated version of the eq is derived by using limits?

d lnK / d T = ∆rH / RT²

indefinite

definite

∆G of a reaction at equilibrium

∆rG = -RT * lnK

frequency

in terms of symbol

what units?

speed of light / wavelength

v = c / wavelength

units = s-1 = Hz

Wavenumber and what units do we want?

Wavenumber = frequency / speed of light

units : cm-1

energy of light

units?

= planck’s constant * frequency

units: J

angular frequency

2* pi * frequency

moment of inertia of diatomic molecule

I = reduced mass (in kg) * bond length ²