Thermodynamics

Heat, entropy, engines · 8 formulas

Thermodynamics★★★★★

Ideal Gas Law

PV=nRTPV = nRT

Pressure times volume is proportional to temperature for a fixed amount of gas.

Thermodynamics★★★★★

First Law of Thermodynamics

ΔU=Q−W\Delta U = Q - W

Energy in (heat) minus energy out (work) equals the change stored inside.

Thermodynamics★★★★★

Fourier's Law of Heat Conduction

q=−kdTdxq = -k \frac{dT}{dx}

Heat flows from hot to cold, faster through better conductors and steeper gradients.

Thermodynamics★★★★★

Linear Thermal Expansion

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

Materials grow longer when heated — by an amount proportional to their length and temperature rise.

Thermodynamics★★★★★

Carnot Efficiency

η=1−TCTH\eta = 1 - \frac{T_C}{T_H}

No engine can beat the efficiency set by the ratio of its cold and hot reservoir temperatures.

Thermodynamics★★★★★

Stefan-Boltzmann Law

P=σAT4P = \sigma A T^4

Hot objects radiate energy as light — and the power skyrockets with temperature (fourth power!).

Thermodynamics★★★★★

Entropy Change

ΔS=∫δQrevT\Delta S = \int \frac{\delta Q_{\text{rev}}}{T}

Entropy measures how much energy has spread out — it always increases in the universe overall.

Thermodynamics★★★★★

Maxwell-Boltzmann Speed Distribution

f(v)=4πn(m2πkBT)3/2v2e−mv22kBTf(v) = 4\pi n \left(\frac{m}{2\pi k_B T}\right)^{3/2} v^2 e^{-\frac{mv^2}{2k_BT}}

Gas molecules have a spread of speeds — most cluster near a peak, with a long tail of fast outliers.