Brownian Motion & Temperature | Interactive Physics model

Interactive experiment

Temperature (°C)

Absolute temperature293.15 K

Temperature control

Temperature20 °C

Relative diffusion1.00 ×

Elapsed time0.0 s

Adjust the temperature and observe the random particle motion.

Observation: Increase the temperature and compare how rapidly the particles spread. In this simplified model, the diffusion coefficient is taken as proportional to absolute temperature while viscosity and particle size remain fixed.

Brownian Motion Python Simulation

This simple Python model simulates Brownian motion as random particle movement. Change the temperature and compare how the particle motion changes with the interactive simulation above.

import numpy as np
import matplotlib.pyplot as plt

# Temperature
temp_c = 20.0
temp_k = temp_c + 273.15

# Reference conditions
reference_k = 293.15
D0 = 1.0

# Simplified model:
# D is proportional to absolute temperature
D = D0 * temp_k / reference_k

dt = 0.01
steps = 2000

x = np.zeros(steps)
y = np.zeros(steps)

# Brownian displacement:
# sigma = sqrt(2 D dt)
sigma = np.sqrt(2 * D * dt)

for i in range(1, steps):
    x[i] = x[i-1] + np.random.normal(0, sigma)
    y[i] = y[i-1] + np.random.normal(0, sigma)

plt.plot(x, y)
plt.xlabel("x")
plt.ylabel("y")
plt.title(
    f"Brownian motion at {temp_c} °C"
)
plt.axis("equal")
plt.show()

# In 2 dimensions:
# <r^2> = 4 D t

How Does Temperature Affect Brownian Motion?

Brownian motion is the irregular movement of small particles caused by collisions with surrounding molecules. As temperature increases, the molecules have greater average kinetic energy, producing more rapid random motion.

Challenge: Compare the motion at 0 °C, 20 °C and 100 °C. Why should the physics use absolute temperature (Kelvin), rather than simply multiplying the motion by the Celsius value?