Category: Part 2: Thermodynamics

Problem Statement State Trouton’s rule for the entropy of vaporisation and verify it for water and benzene. 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…

Problem Statement Derive the critical radius $R^*$ for a droplet nucleus in a supersaturated vapour. 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…

Problem Statement Estimate the molar volume of saturated water vapour at $100°\text{C}$ using the ideal gas approximation and compare to the actual value. 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 Explain the phenomenon of critical opalescence near the critical point of a fluid. 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…

Problem Statement Solve the fluid mechanics problem: Find how the melting point of ice changes with pressure. ($L_{fus}=6.0\ \text{kJ/mol}$, $\Delta V_{fus} = -1.63\ \text{cm}^3/\text{mol}$) Clausius-Clapeyron for the solid-liquid boundary: $$\frac{dT}{dp} = \frac{T\Delta V_{fus}}{L_{fus}} = \frac{273\times(-1.63\times10^{-6})}{6000}$$ $$= \frac{-4.45 Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics…

Problem Statement Air at $T=25°\text{C}$ has a dew point of $T_d=15°\text{C}$. The saturation vapour pressures are $p_s(25°)=3167\ \text{Pa}$ and $p_s(15°)=1705\ \text{Pa}$. Find the relative humidity. 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…

Problem Statement Solve the thermodynamics problem: Find the entropy change when $1.0\ \text{mol}$ of ice melts at $0°\text{C}$ ($L_{fus}=6.0\ \text{kJ/mol}$). Melting is a reversible phase transition at constant $T=273\ \text{K}$: $$\Delta S = \frac{L_{fus}}{T} = \frac{6000}{273} \approx 22.0\ \text{J/mol·K}$$ This positive entropy change reflects t Given Information See problem statement for all given quantities. Physical…

Problem Statement State and derive the law of corresponding states from the van der Waals equation. 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…

Problem Statement Solve the thermodynamics problem: Find the internal energy change when water vaporises at $100°\text{C}$ and $1\ \text{atm}$. The latent heat is $L = 2260\ \text{J/g}$. The latent heat equals the enthalpy change: $L = \Delta H = \Delta U + p\Delta V$. Per mole ($M_{water}=18\ \text{g/mol}$): $L_m = 2260\times18 = 40680\ \text{J/mol} Given…

Problem Statement Solve the thermodynamics problem: The vapour pressure of ice is $p_1=4.58\ \text{mmHg}$ at $T_1=273\ \text{K}$ and $p_2=1.0\ \text{mmHg}$ at $T_2=253\ \text{K}$. Find the latent heat of sublimation. From the integrated Clausius-Clapeyron equation (assuming $L$ constant and ideal vapour): $$\ln\frac{p_2}{p_1} = -\frac{L}{R}\left(\fra Given Information See problem statement for all given quantities. Physical Concepts &…