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Thermodynamics & Heat

Heat, temperature, gas laws and the laws of thermodynamics

Heat Energy

Basic
Q=mcΔTQ = mc\Delta T

Heat needed to change a substance’s temperature.

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Latent Heat

Intermediate
Q=mLQ = mL

Heat for a phase change at constant temperature.

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Ideal Gas Law

Intermediate
PV=nRTPV = nRT

Relates pressure, volume, moles and temperature.

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Boyle's Law

Basic
P1V1=P2V2P_1 V_1 = P_2 V_2

Pressure and volume are inversely related at constant T.

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Charles's Law

Basic
V1T1=V2T2\frac{V_1}{T_1} = \frac{V_2}{T_2}

Volume is proportional to temperature at constant P.

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Gay-Lussac's Law

Intermediate
P1T1=P2T2\frac{P_1}{T_1} = \frac{P_2}{T_2}

Pressure is proportional to temperature at constant V.

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Combined Gas Law

Intermediate
P1V1T1=P2V2T2\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}

Combines Boyle, Charles and Gay-Lussac.

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First Law of Thermodynamics

Intermediate
ΔU=QW\Delta U = Q - W

Energy conservation for a thermodynamic system.

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Carnot Efficiency

Advanced
η=1TCTH\eta = 1 - \frac{T_C}{T_H}

Maximum efficiency of a heat engine.

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Entropy Change

Advanced
ΔS=QT\Delta S = \frac{Q}{T}

Reversible entropy change at temperature T.

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Linear Thermal Expansion

Intermediate
ΔL=αL0ΔT\Delta L = \alpha L_0 \Delta T

Length change of a solid when heated.

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Heat Conduction (Fourier)

Advanced
Q=kAΔTtdQ = \frac{kA\Delta T\,t}{d}

Heat conducted through a slab over time.

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Celsius to Fahrenheit

Basic
F=95C+32F = \tfrac{9}{5}C + 32

Convert Celsius to Fahrenheit.

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Celsius to Kelvin

Basic
K=C+273.15K = C + 273.15

Convert Celsius to Kelvin.

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RMS Molecular Speed

Advanced
vrms=3RTMv_{rms} = \sqrt{\frac{3RT}{M}}

Root-mean-square speed of gas molecules.

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Average KE of a Gas Molecule

Advanced
Eˉ=32kBT\bar{E} = \tfrac{3}{2}k_B T

Mean translational kinetic energy per molecule.

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Coefficient of Performance

Advanced
COP=QCWCOP = \frac{Q_C}{W}

Efficiency measure of a refrigerator or heat pump.

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