Modern Thermodynamics with Julia in CoCalc

import Pkg; Pkg.add("PlotThemes")

using Plots, Printf, Statistics, LinearAlgebra
using PlotThemes
theme(:bright)

# Fundamental constants (2018 CODATA values)
const k_B = 1.380649e-23      # Boltzmann constant (J/K)
const N_A = 6.02214076e23     # Avogadro's number (1/mol)
const R = k_B * N_A           # Universal gas constant (J/mol·K)

println("🧬 MODERN THERMODYNAMICS: BIOLOGICAL SYSTEMS")
println(repeat("=", 55))
println("Exploring thermodynamics in living organisms")
println()
println("Biological Constants:")
println("• Boltzmann constant: k_B = $(k_B) J/K")
println("• Avogadro's number: N_A = $(N_A) molecules/mol")
println("• Gas constant: R = $(R) J/(mol·K)")

using Printf

const N_A = 6.02214076e23  # 1/mol, Avogadro's number

# Biological thermodynamics functions
function atp_energy_release()
    """Standard ATP hydrolysis energy in J/mol"""
    return 30.5e3  # J/mol (standard conditions)
end

function cellular_atp_energy()
    """ATP hydrolysis energy under cellular conditions in J/mol"""
    return 55e3  # J/mol (typical cellular conditions)
end

function basal_metabolic_rate(mass_kg)
    """Kleiber's law: BMR = 70 * M^0.75 kcal/day for mammals"""
    bmr_kcal_day = 70 * mass_kg^0.75
    bmr_watts = bmr_kcal_day * 4184 / (24 * 3600)  # Convert to watts
    return bmr_watts
end

function photosynthesis_efficiency()
    """Typical photosynthesis efficiency"""
    return 0.02  # 2% average efficiency
end

println("=== BIOLOGICAL THERMODYNAMICS ===")
println("Energy and Entropy in Living Systems")
println()

# ATP energetics
ΔG_ATP_standard = atp_energy_release()
ΔG_ATP_cellular = cellular_atp_energy()
T_body = 37 + 273.15  # K (body temperature)

println("=== CELLULAR ENERGY CURRENCY (ATP) ===")
@printf "• Standard ATP hydrolysis: ΔG° = %.1f kJ/mol\n" (ΔG_ATP_standard / 1000)
@printf "• Cellular conditions: ΔG ≈ %.1f kJ/mol\n" (ΔG_ATP_cellular / 1000)
@printf "• Body temperature: T = %.1f K = %.1f°C\n" T_body (T_body - 273.15)
println()

# Human ATP turnover
human_mass = 70.0  # kg (average adult)
bmr_human = basal_metabolic_rate(human_mass)
daily_energy = bmr_human * 24 * 3600  # J/day
atp_molecules_per_day = daily_energy / ΔG_ATP_cellular * N_A

println("Human Energy Metabolism:")
@printf "• Adult human mass: %.0f kg\n" human_mass
@printf "• Basal metabolic rate: %.0f W\n" bmr_human
@printf "• Daily energy expenditure: %.1f MJ/day\n" (daily_energy / 1e6)
@printf "• ATP molecules hydrolyzed: %.2e molecules/day\n" atp_molecules_per_day
@printf "• ATP turnover rate: %.2e molecules/second\n" (atp_molecules_per_day / (24 * 3600))
@printf "• Equivalent ATP mass: %.0f kg/day (recycled ~1000 times!)\n" (atp_molecules_per_day * 507 / N_A / 1000)
println()

# Metabolic scaling
println("=== METABOLIC SCALING (KLEIBER'S LAW) ===")
animals = [
    ("Mouse", 0.025),
    ("Rat", 0.3),
    ("Cat", 4.0),
    ("Human", 70.0),
    ("Horse", 500.0),
    ("Elephant", 5000.0)
]

println("Metabolic Rate Scaling (BMR ∝ M^0.75):")
println(repeat("-", 60))
@printf "%-15s %10s %12s %15s\n" "Animal" "Mass (kg)" "BMR (W)" "BMR/Mass (W/kg)"
println(repeat("-", 60))

for (animal, mass) in animals
    bmr = basal_metabolic_rate(mass)
    bmr_per_kg = bmr / mass
    @printf "%-15s %10.3f %12.1f %15.2f\n" animal mass bmr bmr_per_kg
end

println()
println("Metabolic Insights:")
println("• Larger animals have lower metabolic rate per unit mass")
println("• Surface area to volume ratio affects heat loss")
println("• Metabolic efficiency improves with size")
println("• Evolutionary advantage of larger size in cold climates")
println()

using Printf

# Photosynthesis analysis
println("=== PHOTOSYNTHESIS: SOLAR ENERGY CONVERSION ===")

solar_irradiance = 1000  # W/m² (peak sunlight)
photosynthesis_eff = photosynthesis_efficiency()
leaf_areas = [0.001, 0.01, 0.1, 1.0]  # m² (different leaf sizes)
leaf_descriptions = ["Small leaf (1 cm²)", "Medium leaf (10 cm²)", "Large leaf (100 cm²)", "Plant canopy (1 m²)"]

println("Plant Solar Energy Conversion:")
println(repeat('-', 70))
@printf "%-20s %10s %12s %15s %15s\n" "System" "Area (cm²)" "Solar (W)" "Chemical (W)" "Daily Energy (kJ)"
println(repeat('-', 70))

for (i, area) in enumerate(leaf_areas)
    solar_power = solar_irradiance * area
    chemical_power = solar_power * photosynthesis_eff
    daily_energy = chemical_power * 8 * 3600 / 1000  # 8 hours daylight in kJ
    
    @printf "%-20s %10.1f %12.3f %15.4f %15.2f\n" leaf_descriptions[i] (area*10000) solar_power chemical_power daily_energy
end

println()
println("Photosynthesis Efficiency Analysis:")
@printf "• Average efficiency: %.1f%% (solar → chemical energy)\n" (photosynthesis_eff * 100)
println("• Theoretical maximum: ~11% (thermodynamic limit)")
println("• Loss mechanisms: reflection, non-photosynthetic absorption,")
println("  quantum yield losses, metabolic costs")
println("• Still remarkably efficient for a biological process!")
println()

# Compare to human energy needs
human_daily_energy = bmr_human * 24 * 3600 / 1000  # kJ/day
forest_area_needed = human_daily_energy / (photosynthesis_eff * solar_irradiance * 8 * 3600 / 1000)

println("Sustaining Human Life through Photosynthesis:")
@printf "• Human daily energy need: %.0f kJ/day\n" human_daily_energy
@printf "• Forest area required: %.1f m² per person\n" forest_area_needed
@printf "• That's a %.1f × %.1f meter square of forest!\n" sqrt(forest_area_needed) sqrt(forest_area_needed)
println("• Demonstrates the fundamental role of plants in ecosystems")
println()