solid expansion

Δl = {\alpha} \cdot l_{o} \cdot ΔT

ΔA = 2 \cdot {\alpha} \cdot \textit{A}_{\textit{0}} \cdot ΔT

ΔV = 3 \cdot {\alpha} \cdot V_{o} \cdot ΔT

liquid expansion

ΔV = {\beta} \cdot \textit{V}_{\textit{0}} \cdot ΔT

sensible heat

Q = m \cdot c \cdot ΔT

latent heat

Q = m \cdot L

ideal gas law

P \cdot V = n \cdot R \cdot T

molecular constants

n \cdot R = N \cdot k


\operatorname{f} \left( E \right) = A \cdot \mathrm e^{ \operatorname{-} \frac{E}{k \cdot T}}

\operatorname{f} \left( v_{z} \right) = \sqrt{\frac{m}{2 \cdot {\pi} \cdot k \cdot T}} \cdot \mathrm e^{ \operatorname{-} \frac{m \cdot v_{z}^{2}}{2 \cdot k \cdot T}}

\operatorname{f} \left( v \right) = 4 \cdot {\pi} \cdot \left( \frac{m}{2 \cdot {\pi} \cdot k \cdot T} \right)^{\frac{3}{2}} \cdot v^{2} \cdot \mathrm e^{ \operatorname{-} \frac{m \cdot v_{z}^{2}}{2 \cdot k \cdot T}}

molecular kinetic energy

K = \frac{3}{2} \cdot k \cdot T

molecular speeds

v_{p} = \sqrt{\frac{2 \cdot k \cdot T}{m}}

v = \sqrt{\frac{8 \cdot k \cdot T}{{\pi} \cdot m}}

v_{rms} = \sqrt{\frac{3 \cdot k \cdot T}{m}}

heat flow

P_{avg} = \frac{ΔQ}{Δt}

P = \frac{dQ}{dt}

thermal conduction

P = \frac{k \cdot A \cdot ΔT}{l}

stefan-boltzmann wien displacement law

P = {\varepsilon} \cdot {\sigma} \cdot \operatorname{A} \left( T^{4}-T_{o}^{4} \right)

λ_{max} = \frac{b}{T}

internal energy

ΔU = \frac{3}{2} \cdot n \cdot R \cdot ΔT

ΔU = \frac{3}{2} \cdot N \cdot k \cdot ΔT

thermodynamic work

W = \operatorname{-} \int\! {P} \: \mathrm d {x}

1st law of thermodynamics

ΔU = Q+W


ΔS = \frac{ΔQ}{T}

S = k \cdot \operatorname{log}_{10} \left( w \right)


η_{real} = 1-\frac{Q_{c}}{Q_{H}}

η_{ideal} = 1-\frac{T_{C}}{T_{H}}


COP_{real} = \frac{Q_{C}}{Q_{H}-Q_{C}}

COP_{ideal} = \frac{T_{C}}{T_{H}-T_{C}}


[downloads ids=”2479,2482″ columns=”2″ full_content=”no” excerpt=”no”]

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