Physics 213 Formula Sheet
First law: 𝒅𝑼 =𝒅𝑸+𝒅𝑾𝒐𝒏
Second law: 𝒅𝑺 ≥ 𝟎
Entropy:
• S ≡ klnΩ
• Stotal = S1+S2
Temperature, pressure, and
chemical potential:
• T−1 ≡ (dS
dU)V,N
• p ≡ T(dS
dV)U,N
• −μ ≡ T(dS
dN)U,V
= − (dF
dN)T,V
Fundamental relation:
dS =1
TdU+p
TdV−μ
TdN
Ideal Gas Law:
pV = NkT
Thermodynamic potentials:
• F ≡ U −TS
• G ≡ U −TS+pV
Work:
dWon = −dWby = −pdV
First Law:
dU =dQ−pdV
Equipartition:
U = (1
2)kBT per quadratic degree
of freedom
Heat Capacity:
• C ≡ dQ
dT
• Constant volume: CV=dU
dT
• Constant pressure:
Cp=dU
dT +pdV
dT
Thermodynamic Processes:
• Isothermal: T = const.
• Isobaric: p = const.
• Isochoric: V = const.
• Adiabatic: Q = 0
Boltzmann Factor:
• P(Ei)= Z−1e−Ei
kBT,
• Z = ∑e−Ei/kBT
i
Thermal Radiation
• J = σBT4
Counting particles
• Distinguishable: Ω = MN
• Indistinguishable: Ω = MN
N!
• q quanta in N oscillators:
(𝑁−1+𝑞
𝑞) = (𝑁 − 1 + 𝑞)!
𝑞!(𝑁 − 1)!
