Thermodynamics Formula Sheet (Ch. 15 & 16)
Chapter 15 - Heat and the First Law of Thermodynamics
1st Law of Thermodynamics:
DeltaE = Q - W
DeltaE: Change in internal energy
Q: Heat added to the system
W: Work done by the system
Heat Capacity:
At constant volume: Q = C_V DeltaT
At constant pressure: Q = C_P DeltaT
Ideal gases: C_P = C_V + Nk_B
Equipartition Theorem:
Average energy per degree of freedom = (1/2) k_B T
Ideal Gas Law:
PV = Nk_B T or PV = nRT
Work Done by Ideal Gas:
W = integralP dV
Isothermal: W = Nk_B T ln(V_f / V_i)
Isobaric: W = P DeltaV
Isochoric: W = 0
Internal Energy (monatomic ideal gas):
E = (3/2) Nk_B T
Chapter 16 - Entropy and the Second Law
Entropy Definition:
S = k_B ln(Omega)
Omega: Number of accessible microstates
Entropy Change (Reversible Process):
dS = dQ_rev / T
Entropy of Ideal Gas:
dS = (C_V / T) dT + (Nk_B / V) dV
Second Law of Thermodynamics:
DeltaS >= 0
Carnot Efficiency:
eta = 1 - (T_C / T_H)
Combined First and Second Law:
dE = T dS - P dV
Boltzmann Factor:
P proportional to e^(-E / k_B T)
Chemical Potential:
dE = T dS - P dV + dN