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Heat (>, <, or = 0?)
 If q>0, then heat is added to the system
 If q<0, then heat is removed from the system
 If q=0, then dU=w

Work (> or < 0?)
 If w>0, work is being done on the system.
 If w<0, work is being done by the system.

Internal Energy (dU) > Any Conditions
 dU = q + w
 dU = nc_{v}(dT)

Heat > General (Any Conditions)
q = c(dT)

Enthalpy Change > Any Conditions
 dH = dU + d(PV)
 dH = nc_{p}(dT)

Work Against a Constant External Pressure
w = P_{ext}(dV)

Reversible, Isothermal Work
w = nRTln(V_{2}/V_{1})

Work at Constant Volume
w = 0

Relate c_{p} and c_{v}
c_{p} = c_{v} + R

Heat at Constant Volume
 q = nc_{v}(dT)
 Note: This also equals dU, because at constant volume, w=0.

Heat at Constant Pressure
 q = nc_{p}(dT)
 Note: This also equals dH

Enthalpy
 A state function that represents the heat transferred for a system under constant pressure (q_{p})
 dH = dU + d(PV)
 For an ideal monatomic gas, this can be rewritten as: dH = dU + d(nRT)
 dH = q_{p} = nc_{p}(dT)

Molar Heat Capacities for Ideal, Monatomic Gases at Constant V and Constant P
 c_{v} = (3/2)R
 c_{p} = (5/2)R

Boltzman's Equation
 S = K_{B}ln(omega)
 K_{B} = 1.38 x 10^{23} J/K

Entropy Change for Reversible, Isothermal Expansion
 dS = nRln(V_{2}/V_{1})
 dS = q_{rev}/T

Entropy Change at Constant Pressure
dS = nc_{p}ln(T_{2}/T_{1})

Entropy Change at Constant Volume
dS = nc_{v}ln(T_{2}/T_{1})

Entropy Change for Phase Changes
dS = (dH_{PT})/T

dS_{universe} and Spontaneity
 If dS_{univ} > 0, the process is spontaneous as written
 If dS_{univ} < 0, the process is spontaneous in the reverse direction
 If dS_{univ} = 0, the process is at equilibrium

Gibbs Free Energy
dG = dH  TdS

