Física
Explora los principios de la física a través de simulaciones interactivas
103 visualizations
Capillary Action - 毛细现象
Interactive visualization of capillary action and Jurin's Law - Comprehensive tool for understanding liquid behavior in narrow tubes. Features four visualization modes: (1) Single Tube Mode - Detailed capillary rise/fall simulation with real-time Jurin's law calculation h = 2γcosθ/(ρgr), accurate physical properties for 6 liquids (Water, Ethanol, Mercury, Olive Oil, Glycerol, Blood Plasma), 4 tube materials (Glass hydrophilic, Teflon hydrophobic, Paraffin hydrophobic, Plastic mixed) with different contact angles, animated liquid rise from 0 to equilibrium height, meniscus shape rendering (concave for θ < 90° wetting liquids, convex for θ > 90° non-wetting), surface tension vector visualization at meniscus interface, height measurement indicator with real-time mm display, and external liquid level reference line. (2) Tube Comparison Mode - Multi-tube side-by-side comparison showing inverse relationship between tube radius and capillary height (h ∝ 1/r), 4 preset tube radii (0.2mm, 0.5mm, 1.0mm, 1.5mm) with individual show/hide toggles, simultaneous height calculation and display for each tube, visual demonstration that halving radius doubles height, quantitative comparison with height labels for each tube, and practical understanding of why capillary action is significant in microscopic vessels (plant xylem: 10-100 μm). (3) Force Balance Mode - Detailed physics analysis showing equilibrium condition F↑ = F↓, upward surface tension force F↑ = 2πrγcosθ acting along circumference with green vector, downward gravitational force F↓ = ρπr²hg acting on liquid column with red vector, force magnitude calculation and display, center of mass indication for weight force, meniscus force application point visualization, and real-time force balance equation display with substituted values. (4) Jurin's Law Derivation - Step-by-step mathematical derivation with 5 interactive stages: Step 1 Force Balance (F↑ = F↓), Step 2 Surface Tension Force (F↑ = γ·L = γ·2πr·cosθ), Step 3 Gravitational Force (F↓ = m·g = ρ·V·g = ρ·πr²h·g), Step 4 Equate Forces (γ·2πr·cosθ = ρ·πr²h·g), Step 5 Solve for Height (h = 2γcosθ/(ρgr)). Each step includes visual diagram annotations on canvas showing parameters (h, r, θ), color-coded parameter highlights, and formula progression. Adjustable parameters: tube radius (0.1-2.0 mm), contact angle (0-180°), temperature (0-100°C) affecting surface tension, gravity (1.6-25.0 m/s²) showing planetary effects (Moon 1.6, Earth 9.8, Jupiter 24.8), liquid type selection, and tube material selection. Real-time statistics panel displays: capillary height h (mm), surface tension γ (mN/m), contact angle θ (°), tube radius r (mm), liquid density ρ (kg/m³), gravity g (m/s²), and live formula calculation with substituted values. Liquid properties panel shows: liquid name, wetting behavior (Hydrophilic θ<90°, Hydrophobic θ>90°, Neutral θ=90°), meniscus type (Concave, Convex, Flat), and tube material. Applications showcase 6 real-world uses: Plants (xylem water transport from roots to leaves), Paper & Fabric (ink absorption, sweat wicking), Inkjet Printing (microscopic nozzle ink delivery), Medical Testing (capillary tube blood samples, pregnancy tests), Sponges (porous water absorption), and Oil Recovery (migration through porous rock). Comprehensive educational content covering: What is capillary action? (liquid flow in narrow spaces without external forces, balance between surface tension and gravity), Jurin's Law historical context (James Jurin 1718, complete formula explanation, inverse radius relationship h ∝ 1/r), Role of contact angle (θ<90° wetting liquids rise with cosθ>0, θ>90° non-wetting liquids fall with cosθ<0, θ=90° no capillary effect), Effect of tube radius (microscopic significance, plant xylem applications, demonstrated in comparison mode), Wetting vs Non-wetting (water in glass θ≈30° strong rise, mercury in glass θ≈140° depression, material dependence), Gravity effects (Moon 6× higher rise, Jupiter 40% lower rise, space applications), and Limitations of Jurin's Law (5 assumptions: cylindrical tube, constant contact angle, complete wetting, no evaporation, static equilibrium). Formula display uses mathematical notation with fraction rendering for h = (2γcosθ)/(ρgr). Responsive design with mode selection panel, main canvas (600px height), statistics panel (380px width), controls grid, comparison options, derivation steps panel, and applications grid. Multi-language support (zh, en, es, fr, de, ru, pt) with complete translations. Canvas-based rendering with smooth rise animation, gradient liquid colors per liquid type, realistic meniscus curves, force vector arrows, parameter annotations, and grid overlay option.
Surface Tension - 表面张力
Interactive visualization of surface tension phenomena - Explore droplet formation, molecular forces, capillary action, and contact angle effects. Features four comprehensive visualization modes: (1) Droplet Formation - Animated spherical droplet formation showing surface tension minimization effect, real-time surface tension coefficient (γ) calculation based on temperature, liquid type selection (Water, Ethanol, Mercury, Olive Oil, Glycerol) with accurate physical properties, pressure difference visualization using Laplace equation ΔP = γ(1/R₁ + 1/R₂), adjustable droplet size with surface tension force vectors pointing inward, and molecular animation showing surface molecule behavior. (2) Molecular Forces - Microscopic view of liquid molecules demonstrating cohesive forces, bulk molecules (pulled equally in all directions) vs surface molecules (no upward neighbors, net inward force), interactive force vector visualization showing F↓, F↙, F↘ directions, hydrogen bonding animation for water molecules, surface tension as net force causing surface area minimization, and temperature effect on molecular motion with particle animation. (3) Capillary Action - Dynamic capillary rise/fall simulation in glass tube, accurate height calculation using h = 2γcosθ/(ρgr) formula where γ = surface tension, θ = contact angle, ρ = density, g = gravity, r = tube radius, real-time meniscus shape rendering (concave for wetting liquids like water, convex for non-wetting like mercury), adjustable tube radius (0.1-2.0 mm), liquid property database with density and viscosity data, surface tension vector visualization at meniscus, height indicator with measurement display, and practical examples showing different contact angles on various surfaces (glass: 30° for water, 140° for mercury; Teflon: 110° for water; paraffin: 105° for water). (4) Contact Angle & Wetting - Interactive contact angle visualization with adjustable θ (0-180°), solid surface with realistic texture rendering, droplet shape deformation based on contact angle (spreading for θ < 90° hydrophilic, beading for θ > 90° hydrophobic), Young's equation force balance visualization: γ_sg = γ_sl + γ_lg·cosθ showing solid-gas, solid-liquid, and liquid-gas interface tensions, real-time wetting behavior classification (hydrophilic vs hydrophobic), superhydrophobic demonstration (lotus leaf effect with θ > 150°), and comparison of different liquid-solid pairings. Adjustable parameters: temperature (0-100°C) affecting surface tension via γ(T) = γ₀ + (dγ/dT)×T, liquid selection with accurate physical constants (Water: γ₀=75.6 mN/m at 0°C, ρ=998 kg/m³; Ethanol: γ₀=24.0 mN/m, ρ=789 kg/m³; Mercury: γ₀=490 mN/m, ρ=13534 kg/m³; Olive Oil: γ₀=35 mN/m, ρ=920 kg/m³; Glycerol: γ₀=66 mN/m, ρ=1260 kg/m³), animation speed control (0.1-3.0x), droplet size adjustment, tube radius for capillary mode, and contact angle parameter. Display options: show molecules animation, show force vectors, show grid overlay, real-time information panel displaying current surface tension value, temperature, contact angle, capillary height, and pressure difference. Comprehensive educational content covering: What is surface tension? (elastic sheet behavior, inward net force, surface area minimization), Molecular level explanation (cohesive forces, interior vs surface molecules, spherical droplets), Factors affecting surface tension (temperature dependence, critical point, intermolecular force strength, water vs mercury comparison), Capillary action applications (plants water transport, paper towels, inkjet printing, biological systems, Jurin's law), Contact angle and wetting (Young's equation, hydrophilic vs hydrophobic surfaces, superhydrophobic lotus effect, θ < 90° good wetting, θ > 90° poor wetting), and Practical applications (soap bubbles, water strider insects, raindrops, emulsions and foams, painting/coating, detergents and cosmetics, oil recovery). Physical equations rendered with clear notation: Surface force F = γL, Laplace equation ΔP = γ(1/R₁ + 1/R₂), Capillary height h = 2γcosθ/(ρgr), and Young's equation γ_sg = γ_sl + γ_lg·cosθ. Responsive layout with phenomenon selection panel, main visualization canvas, real-time statistics display, liquid properties detail panel, comprehensive controls section with sliders and buttons, and extensive explanation section. Multi-language support (zh, en, es, fr, de, ru, pt) with complete translations of all interface elements, educational content, and scientific terminology. Canvas-based rendering with smooth animations, force vector arrows, gradient shading for realistic liquid appearance, and interactive parameter adjustment.
Quantum Harmonic Oscillator - 量子谐振子可视化
Interactive visualization of quantum harmonic oscillator demonstrating equally spaced energy levels, parabolic potential well, and Hermite polynomial wave functions. Features the fundamental quantum system V(x) = ½mω²x² with characteristic properties: zero-point energy E₀ = ½ħω (ground state energy due to uncertainty principle), equally spaced energy levels Eₙ = (n + ½)ħω where adjacent levels are separated by exactly ħω, wave functions ψₙ(ξ) = Nₙ·Hₙ(ξ)·e^(-ξ²/2) using Hermite polynomials Hₙ(ξ) with dimensionless coordinate ξ = √(mω/ħ)·x. Each energy level has exactly n nodes (where ψ = 0) showing increasing complexity with quantum number. Parabolic potential visualization with classical turning points x_tp = ±√(2Eₙ/mω²) shown as dashed lines. Real-time wave function display with real part Re[ψ] (blue) and probability density |ψ|² (purple). Energy level ladder diagram showing first 15 levels with equal spacing characteristic, current level highlighting with energy value, and wave function thumbnails. Node visualization with labeled node positions (n₁, n₂, ...). Probability density display with classical region highlighting between turning points and quantum tunneling effect outside. Transition visualization showing absorption (n→n+1, upward green arrow) and emission (n→n-1, downward red arrow) processes with photon emission/absorption diagrams. Classical turning points visualization showing forbidden region penetration depth decreasing with energy. Expected position calculation ⟨x⟩ = 0 for all eigenstates (due to symmetry). Adjustable parameters: oscillator frequency ω (0.5-3.0 rad/fs), particle mass m (0.1-5.0 electron masses), quantum number n (0-10), maximum display levels (3-15). Quick presets: ground state (n=0), first excited (n=1), high energy (n=5), classical comparison (n=10). Display options: toggle real part, probability density, nodes, classical turning points. Transition options: initial level n_i, final level n_f, absorption/emission buttons. Educational content covers harmonic oscillator concept, parabolic potential and Hooke's law, Hermite polynomials (H₀=1, H₁=2ξ, H₂=4ξ²-2, H₃=8ξ³-12ξ, etc.), equally spaced levels (unique property leading to coherent states), zero-point energy and quantum fluctuations, classical correspondence (probability concentrates at turning points for large n), applications (molecular vibrations with vibrational spectra, phonons in solid state physics, quantum field theory foundation, coherent states in quantum optics, laser physics). Multi-language support (zh, en, es, fr, de, ru, pt).
Infinite Square Well - 无限深方势阱可视化
Interactive visualization of particle in infinite square well potential (particle in a box). Features the fundamental quantum mechanical problem demonstrating energy quantization, wave-particle duality, zero-point energy, and the uncertainty principle. Boundary conditions: ψ(0) = ψ(a) = 0 leading to quantized energy levels Eₙ = n²π²ħ²/(2ma²) where n = 1, 2, 3, ... is the quantum number. Wave functions: ψₙ(x) = √(2/a)·sin(nπx/a) representing standing waves with n-1 nodes inside the well. Time-dependent wave function: ψₙ(x,t) = ψₙ(x)·e^(-iEₙt/ħ) showing phase evolution. Probability density: |ψₙ(x)|² = (2/a)·sin²(nπx/a) showing particle position distribution. Potential well visualization V(x) = 0 for 0 < x < a, V(x) = ∞ otherwise with infinite walls at boundaries. Real-time wave function display with real part Re[ψ] (blue) and probability density |ψ|² (purple). Energy level diagram showing first 10 quantized levels with E ∝ n² spacing. Current state highlighting with energy value display. Superposition states: single state, double state (n₁ + n₂), triple state (n₁ + n₂ + n₃) with time-dependent probability density oscillations. Wave function animation showing time evolution and phase dynamics. Node visualization showing ψ = 0 points (n-1 nodes for state n). Probability density display with gradient fill and maximum probability tracking. Expected position calculation ⟨x⟩ = ∫x|ψ|²dx. Adjustable parameters: well width a (0.5-3.0 nm), quantum number n (1-10), particle mass m (0.1-10.0 electron masses), animation speed. Quick presets: ground state (n=1), first excited (n=2), superposition state, wide well. Display options: toggle real part, probability density, nodes, grid. Educational content covers infinite square well concept, boundary conditions and quantization, wave function properties (standing waves, nodes, probability distributions), energy quantization (ground state zero-point energy, excited state spacing Eₙ ∝ n², photon transitions), superposition states and time evolution, applications (quantum dots, conjugated molecules, nuclear shell model), classical limit (n → ∞ correspondence principle with uniform probability), and fundamental quantum concepts (Heisenberg uncertainty principle, wave-particle duality). Multi-language support (zh, en, es, fr, de, ru, pt).
Quantum Tunneling - 量子隧穿可视化
Interactive visualization of quantum tunneling effect through potential barriers. Features the fundamental quantum mechanical phenomenon where particles can pass through barriers even when energy E < barrier height V₀. Three-region analysis: Region I (x < 0): ψ = Ae^(ikx) + Be^(-ikx) with incident and reflected waves, Region II (0 ≤ x ≤ a): ψ = Ce^(κx) + De^(-κx) showing exponential decay, Region III (x > a): ψ = Fe^(ikx) representing transmitted wave. Key equations: wave number k = √(2mE)/ħ, decay constant κ = √[2m(V₀-E)]/ħ, transmission coefficient T ≈ e^(-2κa), reflection coefficient R = 1 - T. Potential barrier visualization showing rectangular barrier with adjustable parameters. Real-time wave function display with real part Re[ψ] (blue), imaginary part Im[ψ] (green), and probability density |ψ|² (purple). Wave packet animation using Gaussian envelope showing incident packet approaching barrier, partial transmission and reflection. Probability bars displaying transmission probability T (%) and reflection probability R (%). Classical vs quantum comparison: classical particles reflect when E < V₀, quantum particles have non-zero tunneling probability. Adjustable parameters: particle energy E (0.1-2.0 eV), barrier height V₀ (0.2-3.0 eV), barrier width a (0.2-3.0 nm), particle mass m (0.1-5.0 electron masses), wave packet width σ (0.2-1.5 nm). Quick presets: electron (m=1me), proton (m=1836me), high tunneling (thin barrier), low tunneling (thick barrier). Display options: toggle real/imaginary parts, probability density, region labels (I, II, III). Educational content covers quantum tunneling concept, wave-particle duality explanation, exponential barrier penetration, key factors affecting tunneling (energy, barrier height/width, particle mass), applications: scanning tunneling microscope (STM, 1986 Nobel Prize), flash memory, nuclear fusion in stars (proton tunneling through Coulomb barrier), alpha decay, tunnel diodes, and classical limit for macroscopic objects. Multi-language support (zh, en, es, fr, de, ru, pt).
Hydrogen Atom Wave Function - 氢原子波函数可视化
Interactive 3D visualization of hydrogen atom electron clouds using quantum mechanical wave functions. Features the complete solution to Schrödinger equation: ψ_nlm(r,θ,φ) = R_nl(r) · Y_lm(θ,φ), where R_nl(r) are associated Laguerre polynomials for radial part and Y_lm(θ,φ) are spherical harmonics for angular part. Three-dimensional volumetric rendering using Three.js particle system with rejection sampling for probability density |ψ|². Quantum number controls: principal quantum number n (1-4), azimuthal quantum number l (0 to n-1), magnetic quantum number m (-l to +l). Real-time electron cloud visualization with color mapping from blue (low probability) to red (high probability). Multiple view modes: electron cloud (probability density), isosurface display, and nodal surfaces showing ψ=0 regions. 2D slice planes (XY, XZ, YZ) for examining wave function cross-sections. Orbital presets for quick access to common orbitals: 1s, 2s, 2p_z, 2p_x, 3s, 3p_z, 3d_z², 3d_xz, 4s, 4f_z³. Interactive 3D controls: mouse drag to rotate, scroll to zoom, auto-rotation with adjustable speed. Educational content covers quantum number meanings, wave function equations (radial part with Laguerre polynomials, angular part with spherical harmonics), nodal surfaces (radial nodes: n-l-1, angular nodes: l), orbital shapes (s: spherical, p: dumbbell, d: cloverleaf, f: complex), and applications in chemical bonding theory (LCAO), periodic table, spectroscopy, quantum computing, and materials science. Historical context from Bohr's 1913 model through Schrödinger's 1926 wave equation and Pauli's exclusion principle. Multi-language support (zh, en, es, fr, de, ru, pt).
Coriolis Force - 科里奥利力
Interactive visualization of Coriolis force demonstrating Earth's rotation effects on moving objects, projectile deflection, Foucault pendulum precession, and atmospheric circulation patterns. Features the fundamental equations: Coriolis force F_cor = -2mΩ × v showing cross product of angular velocity and velocity vectors, horizontal acceleration a_cor = 2Ωv sin(λ) with latitude dependence, Foucault pendulum period T = 24h/sin(λ) for precession rate, Earth's angular velocity Ω = 7.292 × 10⁻⁵ rad/s. Real-time visualization includes: (1) Earth view canvas showing rotating sphere with latitude/longitude grid lines, current latitude marker with animated position, rotation axis indicator, hemisphere labels (N/S), real-time rotation angle display showing Earth's spin; (2) Projectile trajectory view with dual reference frame comparison: inertial path (straight blue dashed line) vs rotating frame path (red curved line showing Coriolis deflection), velocity vector arrows (orange) showing initial direction, Coriolis force vectors (purple dashed) perpendicular to velocity, dynamic projectile position with trail visualization, deflection magnitude display updated in real-time; (3) Foucault pendulum demonstration showing pendulum bob oscillation, precessing swing plane tracing rosette pattern on floor (demonstrating Earth's rotation beneath), support point and string visualization, reference circle showing original swing direction, directional markers (N/E/S/W), accumulated precession angle display, theoretical vs actual precession comparison; (4) Atmospheric circulation panel showing cyclone (low pressure L) with inward spiraling flow (counterclockwise in Northern Hemisphere) and anticyclone (high pressure H) with outward spiraling flow (clockwise in Northern Hemisphere), particle animations demonstrating flow directions, hemisphere-dependent rotation direction (reversed in Southern Hemisphere), realistic spiral arm patterns with speed variations. Interactive parameters: latitude λ (-90° to +90°) with hemisphere auto-detection, Earth rotation speed multiplier (0.1-10x for visualization), projectile velocity v (10-500 m/s), launch direction (0-360°), flight time (1-100 s), animation speed control (0.1-5x). Quick presets: Mid-Latitude (45°, moderate deflection), Polar Region (80°, maximum Coriolis effect), Equatorial (0°, zero deflection), Long-Range Artillery (high velocity, extended flight time). Display options: toggle Earth grid overlay, velocity vectors, Coriolis force vectors, inertial reference frame path visualization. Educational content covers Coriolis force physics (rotating reference frame origin, angular momentum conservation, latitude dependence: sin(λ)=0 at equator, sin(λ)=±1 at poles, velocity dependence: faster objects deflect more), Foucault pendulum mechanics (plane precession demonstrating Earth's rotation, period formula T = 24h/sin(λ), 24h at poles, 33.9h at 45°, infinite at equator), atmospheric and oceanographic effects (cyclones/anticyclones rotation directions, trade winds deflection, ocean current gyres, jet stream patterns), practical applications (long-range artillery correction, aviation navigation calculations, meteorological weather prediction models, space launch site selection - equatorial launches get velocity boost), common misconceptions (toilet flush direction dominated by basin shape not Coriolis, sniper shots only affected at extreme ranges >1km, deflection varies with conditions not constant), and historical context (Gaspard-Gustave de Coriolis 1835 mathematical derivation, Léon Foucault 1851 pendulum demonstration, first practical use in artillery ballistics, fundamental to modern meteorology and oceanography). Multi-language support (zh, en, de, fr, es, pt, ru).
Stellar Aberration Visualization - 光行差效应可视化
Interactive visualization of relativistic stellar aberration and the headlight effect. Features the relativistic aberration formula: tan(θ') = sin(θ)/(γ(cos(θ) - v/c)), classical aberration: sin(θ - θ') = v/c, and headlight effect demonstrating forward concentration of light. Real-time 3D starfield visualization showing apparent shift in stellar positions due to observer motion, with adjustable velocity (v/c from 0 to 0.99) and field of view (60° to 180°). Side-by-side comparison views: rest frame vs moving frame observation. Star density control (100-2000 stars) with randomized brightness and spectral colors. Rotation animation with speed control (0-3x) to demonstrate aberration from all directions. Preset velocity buttons for quick comparison: stationary, 0.5c, 0.9c, 0.99c. Real-time statistics display: Lorentz factor γ, aberration angle for perpendicular stars. Visual demonstrations include: fisheye stereographic projection showing spherical sky, dramatic forward concentration at high velocities (at 0.99c, 180° field compressed to ~8°), relativistic 'searchlight effect' where universe appears concentrated ahead for near-light travelers, and comparison with classical rain analogy. Educational content covers aberration formula derivation using Lorentz transformations, Bradley's 1725 discovery proving Earth's motion, difference between classical and relativistic aberration, practical applications in astrometry (stellar position corrections), GPS satellite navigation, cosmic ray observations, and relativistic space travel visualization. Multi-language support (zh, en, fr, de, es, pt, ru).
Time Dilation Visualization - 时间膨胀可视化
Interactive visualization of time dilation in special relativity. Features the fundamental formulas: Δt = γ·Δt₀ = Δt₀/√(1 - v²/c²), length contraction: L = L₀/γ, and Lorentz factor: γ = 1/√(1 - v²/c²). Real-time dual-clock comparison showing stationary clock (proper time Δt₀) vs moving clock (observed time Δt) with animated analog clock faces. Light clock thought experiment visualization demonstrates photon bouncing between mirrors with diagonal path in moving frame illustrating why time dilates. Adjustable velocity control (v/c from 0 to 0.99) with real-time Lorentz factor calculation and time ratio display. Interactive γ vs v/c curve graph with logarithmic growth showing dramatic increase as v approaches c. Current velocity point highlighted on curve. Visual demonstrations include: proper time accumulation on stationary clock, dilated time accumulation on moving clock (slower by factor γ), photon clock with velocity arrow showing relativistic effect, and theoretical limit as v→c (γ→∞). Educational content covers time dilation concept, light clock thought experiment derivation, Lorentz factor behavior at different speeds (γ≈1 at everyday speeds, γ>7 at 0.99c), experimental verification (muon lifetime extension, Hafele-Keating atomic clock experiment, GPS satellite corrections), and practical applications: GPS navigation systems, particle accelerators, cosmic ray research, and theoretical possibilities for relativistic space travel and the twin paradox. Multi-language support (zh, en, fr, de, es, pt, ru).
Carnot Cycle Visualization - 卡诺循环可视化
Interactive visualization of the Carnot cycle, the ideal thermodynamic heat engine cycle. Features the four processes: isothermal expansion (Q₁ = nRT₁ln(V₂/V₁)), adiabatic expansion (TV^(γ-1) = constant), isothermal compression (Q₂ = nRT₂ln(V₄/V₃)), and adiabatic compression (TV^(γ-1) = constant). Real-time P-V diagram animation with color-coded processes: red for isothermal (heat transfer) and blue for adiabatic (no heat transfer). Adjustable parameters: high temperature T₁ (300-800 K), low temperature T₂ (200-500 K), initial volume V₁ (0.5-2.0 L), expansion ratio V₂/V₁ (1.5-3.0), working substance type with γ values: monatomic gas (γ=1.67), diatomic gas (γ=1.40), polyatomic gas (γ=1.33). Animation controls include play/pause, reset, and speed adjustment (0.1-3.0x). Energy flow vectors show heat input Q₁ (red arrow), heat output Q₂ (blue arrow), and work done W (green arrow). Real-time statistics display Carnot efficiency η = 1 - T₂/T₁, heat input Q₁, heat output Q₂, net work W = Q₁ - Q₂, and current cycle phase. Display options: show/hide energy flow vectors, value annotations, and complete cycle path. Temperature zones visualization highlights high-temperature (red gradient) and low-temperature (blue gradient) regions on the P-V diagram. Educational content covers the four Carnot cycle stages, efficiency derivation, Carnot's theorem (maximum possible efficiency for a heat engine operating between two temperatures), and practical applications: understanding heat engine limitations, refrigeration cycles, and the foundation of the second law of thermodynamics. Multi-language support (zh, en, fr, de, es, pt, ru).
Heat Conduction Simulation - 热传导模拟
Interactive simulation of heat conduction demonstrating the heat equation and temperature evolution in materials. Features the fundamental heat equation: ∂T/∂t = α·∇²T in 1D and 2D, thermal diffusivity: α = k/(ρc), Dirichlet boundary conditions (fixed temperature), and Neumann boundary conditions (insulated/zero flux). Two visualization modes: (1) 1D Rod mode showing temperature distribution curve T(x) evolving over time with color-coded temperature bar (blue=cold 100K to red=hot 1000K), temperature vs position graph, and real-time statistics (time, max/min temperatures); (2) 2D Plate mode showing temperature heatmap with isothermal colors evolving over time, color gradient visualization, and real-time statistics (time, max/min/average temperatures). Adjustable parameters: thermal diffusivity α (1-200), grid size (20-100), animation speed (0.1-3.0x), initial temperature (100-1000 K), left boundary condition (fixed/insulated), right boundary condition (fixed/insulated), and boundary temperatures (100-1000 K). Initial condition options: uniform temperature, Gaussian heat source (central hot spot), step function (hot/cold regions), and random distribution. Finite difference numerical method with automatic stability adjustment: dt ≤ dx²/(4α). Educational content covers heat conduction mechanism (atomic/molecular collisions), heat equation derivation from energy conservation, boundary condition types and effects, steady-state solutions, thermal diffusivity of common materials (copper, aluminum, steel), and practical applications: building insulation design, electronics cooling, heat exchanger optimization, cooking and food processing, geothermal systems, and thermal protection in spacecraft. Multi-language support (zh, en, fr, de, es, ru, pt).
Ideal Gas Simulation - 理想气体模拟
Interactive simulation of ideal gas demonstrating Maxwell-Boltzmann distribution, pressure, and temperature. Features the fundamental equations: Ideal Gas Law pV = Nk_BT, RMS Speed v_rms = √(3k_BT/m), and Maxwell-Boltzmann Distribution f(v) = 4π(m/2πk_BT)^(3/2)·v²·e^(-mv²/2k_BT). Real-time visualization includes: (1) Main canvas showing 2D container with N particles undergoing elastic collisions, color-coded by speed (blue=slow, red=fast), optional velocity vectors, and wall collision detection for pressure calculation; (2) Speed distribution panel displaying real-time histogram comparing actual particle speeds with theoretical Maxwell-Boltzmann curve; (3) Real-time statistics: temperature T, pressure P (calculated from wall collisions), volume V, and average particle speed. Adjustable parameters: particle count N (10-500), temperature T (100-1000 K), volume V (0.5-3.0 L), particle mass m (2-200 amu), and animation speed. Gas presets: Helium (4 amu), Neon (20 amu), Nitrogen (28 amu), Oxygen (32 amu), CO₂ (44 amu), Xenon (131 amu). Display options: show/hide velocity vectors, color by speed, highlight collisions, and grid. Educational content covers ideal gas assumptions (point particles, no intermolecular forces, elastic collisions), Maxwell-Boltzmann distribution derivation, pressure from molecular collisions, RMS speed dependence on mass and temperature, and applications in atmospheric physics, engineering, chemistry, and astrophysics. The simulation demonstrates how temperature increase shifts speed distribution rightward and increases pressure, how lighter particles move faster at same temperature, and validates the theoretical Maxwell-Boltzmann distribution against experimental particle data. Multi-language support (zh, en, fr, de, es, ru, pt).