Fluid Mechanics: |
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| Bernoulli's equation: | P + ρgh + ½ρv2= constant. |
| Poiseuille's law | Q = π∆Pr4/(8ηL) |
| Volume flow rate = π*(pressure difference)*(pipe radius)4/[8*(pipe length)*viscosity) | |
Kinetic Theory: |
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| Ideal gas law: | PV = nRT = NkBT |
| Kinetic theory: | PV = (2/3)N(m<v2>/2) |
| Avg. kinetic energy per particle: | <KE> = (3/2)kBT |
Temperature and Heat: |
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| Linear expansion: | Δl = αlΔT. |
| Volume expansion: | ΔV = βVΔT |
| Thermal conductivity: | ΔQ/Δt = -kA ΔT/Δx. |
| Specific heat capacity: | c = ΔQ/(m ΔT). |
| Wien's law: | λmax ∝ 1/T. |
| Stefan-Boltzmann Law | Radiated power = emissivity * σ * T4 * Area |
Thermodynamics |
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| First law of thermodynamics: | ΔU = ΔQ - ΔW |
| Carnot cycle: | Q1/T1 = Q2/T2 |
| Efficiency of a heat engine: | e = W/Qhigh = (Qhigh - Qlow)/Qhigh |
| COP of refrigerator: | COP = Qlow/(-W) = Qlow/(Qhigh - Qlow) |
| COP of heat pump: | COP = Qhigh/(-W) = Qhigh/(Qhigh - Qlow) |
| Change in entropy: | ΔS = ∫if dQr/T, dS = dQ/T |
1 Cal = 1 kcal = 4186 J
kB = 1.381*10-23 J/K, R = 8.31 J/(mol K)
Electric field and potential |
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| Coulomb's law: | F12 = (keq1q2/r122) (r12/r12). |
| Electrostatic field of a point charge: | E = (keq/r2) (r/r). |
| Gauss' law: | Φe(through closed surface) = Qinside/ε0. |
| Electrostatic potential energy: | ∆U = UB - UA = -q ∫ABE·dr. |
| Electrostatic potential difference: | ∆V = ∆U/q |
| The potential of a point charge: | V(r) = kq/r (convention: V = 0 at infinity.) |
| Field and potential: | Ex = -dV/dx, Ey = -dV/dy, Ez = -dV/dz |
Capacitors |
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| Capacitance: | C = Q/V |
| Parallel plate capacitor: | C = εA/d |
| Energy stored in a capacitor: | U = ½(Q2/C) = ½CV2 |
| Capacitors in series | 1/C = (1/C1) + (1/C2) + (1/C3) |
| Parallel capacitors: | C = C1 + C2 + C3 |