Category: Part 2: Thermodynamics

Problem Statement Solve the thermodynamics problem: Surface tension typically decreases with temperature. For water: $\sigma(T) \approx \sigma_0(1-T/T_c)^\mu$ with $\mu\approx1.26$ and $T_c=647\ \text{K}$. At $T=20°\text{C}$, estimate $\sigma$. (Given $\sigma_0\approx0.235\ \text{N/m}$) All quantities, constants, and constraints stated in the problem Given Information See problem statement for all given quantities. Physical Concepts & Formulas Thermodynamics governs energy transformations…

Problem Statement Explain the Marangoni effect and give an example. 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 units and sign…

Problem Statement Solve the thermodynamics problem: Solve the thermodynamics problem: Find the chemical potential $\mu$ of an ideal gas as a function of $T$ and $p$. For a single-component system, $G = \nu\mu$. From $dG = -SdT + Vdp$: $$\mu = \left(\frac{\partial G}{\partial\nu}\right)_{T,p}$$ For an ideal gas, integrating $(\partial\mu/\partial p)_T Given Information See problem statement…

Problem Statement Solve the thermodynamics problem: Solve the thermodynamics problem: Explain the Gibbs paradox: why is the entropy of mixing zero when two identical gases mix, but positive when different gases mix? Different gases: $\Delta S_{mix} = -R\sum_i x_i\ln x_i > 0$. For equal amounts: $\Delta S = R\ln2$ per mole. Physically: the gases are…

Problem Statement Solve the nuclear physics problem: Find the separation factor for $^{235}$UF$_6$ and $^{238}$UF$_6$ in one stage of gaseous diffusion. ($M_1=349$, $M_2=352$) All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) This problem draws on fundamental physical princi Given Information See problem statement for all…

Problem Statement Solve the work-energy problem: Solve the work-energy problem: Write the Helmholtz free energy of a van der Waals gas and use it to derive the equation of state. For a van der Waals gas, integrating from $U = \nu C_v T – a\nu^2/V$: $$F = U – TS = \nu C_v T –…

Problem Statement Show that for an ideal gas, $\kappa = \eta C_v/M$ (per unit mass), and that $D\rho = \eta$ to first approximation. 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…

Problem Statement At $T=373\ \text{K}$, water vaporises with $L=40.7\ \text{kJ/mol}$ and $\Delta V = 30.0\ \text{L/mol}$. Find $dp/dT$ for the liquid-vapour coexistence curve. 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…

Problem Statement Solve the fluid mechanics problem: Solve the fluid mechanics problem: Find the reduction in vapour pressure when $n_s = 0.1\ \text{mol}$ of NaCl (fully dissociated) is dissolved in $n_w = 1.0\ \text{mol}$ of water at $T=100°\text{C}$. Raoult’s law: vapour pressure of solvent is reduced by the mole fraction of solute. NaCl fully disso…

Problem Statement State Gibbs’ phase rule $F = C – P + 2$ and apply it to: (a) water at the triple point, (b) water–ice equilibrium, (c) a single-phase pure gas. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The…