Category: Part 2: Thermodynamics

Problem Statement Solve the fluid mechanics problem: Explain capillary condensation: why vapour condenses in narrow pores at pressures below the bulk saturation pressure. All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) This problem draws on fundamental physical principles. Given Information See problem statement for all…

Problem Statement Solve the thermodynamics problem: Solve the thermodynamics problem: State the Onsager reciprocal relations and give an example of their application (thermoelectric effects). In linear irreversible thermodynamics, thermodynamic fluxes $J_i$ are linearly related to forces $X_j$: $J_i = \sum_j L_{ij}X_j$. Onsager’s theorem: The kinetic Given Information See problem statement for all given quantities. Physical…

Problem Statement Solve the oscillation/wave problem: Solve the Newton’s Laws / mechanics problem: A soap film of thickness $d=500\ \text{nm}$ and refractive index $n=1.33$ is illuminated by white light. What colours are missing (destructive interference)? Light reflecting from the top surface undergoes a phase shift of $\pi$ (denser medium below). Lig Given Information See problem…

Problem Statement Describe the structure of the liquid-vapour interface and estimate its thickness. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation laws and equations of motion, then solving systematically with careful attention to…

Problem Statement Explain the concept of critical micelle concentration (CMC) and how it manifests in surface tension measurements. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation laws and equations of motion, then solving…

Problem Statement Derive the Langmuir adsorption isotherm for a gas adsorbing on a surface with $N_{sites}$ identical sites. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation laws and equations of motion, then solving…

Problem Statement Derive the Gibbs adsorption isotherm relating surface tension change to solute concentration. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation laws and equations of motion, then solving systematically with careful attention…

Problem Statement An oil-in-water emulsion has droplets of radius $R=1\ \mu\text{m}$ and $\sigma_{oil-water}=0.05\ \text{N/m}$. Find the excess pressure inside a droplet and the free energy per droplet relative to bulk separation. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The…

Problem Statement Solve the fluid mechanics problem: Solve the Newton’s Laws / mechanics problem: Explain the Rayleigh-Plateau instability: why a liquid jet breaks into droplets. A cylinder of liquid of radius $R$ and length $L$ has surface area $A = 2\pi RL$. If perturbed sinusoidally with wavelength $\lambda$, the jet breaks into spherical droplets Given…

Problem Statement Solve the fluid mechanics problem: Solve the fluid mechanics problem: Explain what determines the stability of a soap foam film. A soap film consists of two surfactant monolayers enclosing a thin water layer (thickness $h$). The stability is determined by the disjoining pressure $\Pi(h)$ — the net pressure between the two interfaces. Given…