Albert Einstein's dissertation "A New Determination of Molecular Dimensions" (1905) presents a method to determine the size of molecules in a dilute solution by analyzing the internal friction and diffusion of the solution. The work builds on the kinetic theory of gases and addresses the challenge of determining molecular dimensions in liquids, which had previously been difficult due to the complexity of molecular motion in liquids. Einstein shows that the size of dissolved molecules can be determined by considering their behavior as rigid spheres suspended in a solution, allowing the application of hydrodynamic equations to model their motion and interaction with the solvent. The dissertation begins by discussing the influence of a small suspended sphere on the motion of a fluid, deriving equations that describe how the presence of a sphere modifies the fluid's motion. It then extends this analysis to a large number of small suspended spheres, showing how the presence of these spheres affects the fluid's viscosity and energy dissipation. In the second section, Einstein calculates the friction coefficient of a fluid containing many small suspended spheres, demonstrating that the presence of these spheres reduces the energy dissipation in the fluid. This leads to the conclusion that the friction coefficient of a mixture of fluid and suspended spheres is larger than that of the pure fluid. In the third section, Einstein applies these findings to determine the volume of a dissolved substance, assuming that the volume of a dissolved molecule is much larger than that of a solvent molecule. He uses the known friction coefficient of a sugar solution to estimate the volume of a sugar molecule, comparing it to the volume of a rigid sphere that would have the same effect on the fluid's viscosity. In the fourth section, Einstein examines the diffusion of a non-dissociated substance in a liquid solution. He derives the diffusion coefficient based on the osmotic pressure and the friction coefficient of the solvent, showing that the diffusion coefficient can be used to determine the number of molecules and their effective radius. In the fifth section, Einstein uses the derived relationships to calculate the molecular dimensions of a dissolved substance. By combining the results from the previous sections, he determines the effective radius and the number of molecules in a gram-mole of a substance, using experimental data on the friction coefficient and diffusion coefficient of a sugar solution. The results are consistent with the known size of molecules, confirming the validity of the theoretical approach.Albert Einstein's dissertation "A New Determination of Molecular Dimensions" (1905) presents a method to determine the size of molecules in a dilute solution by analyzing the internal friction and diffusion of the solution. The work builds on the kinetic theory of gases and addresses the challenge of determining molecular dimensions in liquids, which had previously been difficult due to the complexity of molecular motion in liquids. Einstein shows that the size of dissolved molecules can be determined by considering their behavior as rigid spheres suspended in a solution, allowing the application of hydrodynamic equations to model their motion and interaction with the solvent. The dissertation begins by discussing the influence of a small suspended sphere on the motion of a fluid, deriving equations that describe how the presence of a sphere modifies the fluid's motion. It then extends this analysis to a large number of small suspended spheres, showing how the presence of these spheres affects the fluid's viscosity and energy dissipation. In the second section, Einstein calculates the friction coefficient of a fluid containing many small suspended spheres, demonstrating that the presence of these spheres reduces the energy dissipation in the fluid. This leads to the conclusion that the friction coefficient of a mixture of fluid and suspended spheres is larger than that of the pure fluid. In the third section, Einstein applies these findings to determine the volume of a dissolved substance, assuming that the volume of a dissolved molecule is much larger than that of a solvent molecule. He uses the known friction coefficient of a sugar solution to estimate the volume of a sugar molecule, comparing it to the volume of a rigid sphere that would have the same effect on the fluid's viscosity. In the fourth section, Einstein examines the diffusion of a non-dissociated substance in a liquid solution. He derives the diffusion coefficient based on the osmotic pressure and the friction coefficient of the solvent, showing that the diffusion coefficient can be used to determine the number of molecules and their effective radius. In the fifth section, Einstein uses the derived relationships to calculate the molecular dimensions of a dissolved substance. By combining the results from the previous sections, he determines the effective radius and the number of molecules in a gram-mole of a substance, using experimental data on the friction coefficient and diffusion coefficient of a sugar solution. The results are consistent with the known size of molecules, confirming the validity of the theoretical approach.