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Formula sheet for physic 213, Cheat Sheet of Physics

Formula sheet with entropy, temperature, pressure and chemical potential, thermodynamic potential, Boltzmann factors, thermal radiations, heat capacity and ideal gas laws.

Typology: Cheat Sheet

2021/2022

Uploaded on 02/07/2022

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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
TdVμ
TdN
Ideal Gas Law:
pV = NkT
Thermodynamic potentials:
F U TS
G U TS+pV
Work:
dWon = −dWby = −pdV
First Law:
dU =dQpdV
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−1eEi
kBT,
Z = e−Ei/kBT
i
Thermal Radiation
J = σBT4
Counting particles
Distinguishable: Ω = MN
Indistinguishable: Ω = MN
N!
q quanta in N oscillators:
(𝑁1+𝑞
𝑞) = (𝑁 1 + 𝑞)!
𝑞!(𝑁 1)!
pf3

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Physics 213 Formula Sheet

First law: 𝒅𝑼 = 𝒅𝑸 + 𝒅𝑾𝒐𝒏

Second law: 𝒅𝑺 ≥ 𝟎

Entropy :

  • S ≡ k ln Ω
  • Stotal = S 1 + S 2

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 =

T

dU +

p

T

dV −

T

dN

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

+ p

dV

dT

Thermodynamic Processes:

  • Isothermal: T = const.
  • Isobaric: p = const.
  • Isochoric: V = const.
  • Adiabatic: Q = 0

Boltzmann Factor:

  • P(Ei) = Z−^1 e − Ei

kBT,

  • Z = ∑^ ie−Ei/kBT

Thermal Radiation

  • J = σBT^4

Counting particles

  • Distinguishable: Ω = M N
  • Indistinguishable: Ω = MN N!
  • q quanta in N oscillators:

Constants, Data, Definitions

  • Temperature: 0 K = − 273 .15°C = − 459 .67°F
  • Avogadro’s number: NA = 6. 022 × 1023 / mole
  • Boltzmann constant: k = 1. 38 × 10 −^23 J K

= 8. 617 × 10 −^5

eV K [note: also written as kB]

  • Universal gas constant: R = k NA = 8. 314 J mol∙K

= 8. 206 × 10 −^2

l∙atm mol∙K (Universal gas const.)

  • Planck’s constant: h = 6. 626 × 10 −^34 J ∙ s = 4. 136 × 10 −^15 eV ∙ s, ℏ = h 2π = 1. 055 × 10 −^34 J ∙ s ,
  • Magnetic moments: electron: μe = 9. 2848 × 10 −^24 J T , proton: μp = 1. 4106 × 10 −^26 J T
  • Mass: electron: me = 9. 109 × 10 −^31 kg , proton: mp = 1836 me = 1. 673 × 10 −^27 kg
  • STP: T = 0°C , p = 100 kPa
  • Stefan-Boltzmann constant: σB = 5. 670 × 10 −^8 W m^2 K^4
  • c = 2. 998 × 108 m s , 1 eV = 1. 602 × 10 −^19 J , g = 9. 8 m s^2 , 1 atm = 1. 013 × 105 Pa , 1 liter = 10 −^3 m^3 particle g/mol N 2 28 O 2 32 He 4 Ar 40 CO 2 44 H 2 2 Si 28 Ge 73 Cu 64 Al 27