114年 - 114 國立宜蘭大學_碩士班考試入學招生試題_化學工程與材料工程學系：物理化學 (含熱力學與動力學)#147940

(a) Boyle's law (4%)

(b) The van der Waals equation of state (4%)

(c) Boyle temperature (4%)

(d) Efficiency of a reversible Carnot engine (4%)

(e) The colligative properties (4%)

2. An ideal gas at 298.15 K and 1 bar is expanded in a reversible adiabatic process to a final pressure of 1/2 bar. Calculate $q$ per mol, $w$ per mole, and $\Delta U$. (assume: $Cv=\frac{3}{2}R$, $Cp=\frac{5}{2}R$) (10%)

3. One mole of an ideal gas is compressed isothermally and reversibly at 100 °C from a pressure of 2 bar to 10 bar. Calculate (a) $q$, (b) $w$, (c) $\Delta H$, (d) $\Delta S$, and (e) $\Delta G$ of this process. (10%)

(a) Derive the Gibbs-Helmholtz equation $[\frac{\partial}{\partial T}(\frac{\Delta G}{T})]P = -\frac{\Delta H}{T^2}$ from $(\frac{\partial \Delta G}{\partial T})P = -\Delta S$. (5%)

(b) Derive the van't Hoff equation $\frac{d\ln K_P^0}{d(\frac{1}{T})} = -\frac{\Delta H^0}{R}$ from Gibbs-Helmholtz equation. (5%)

5. The boiling point of hexane at 101.325 kPa is 341.9 K. What is the boiling point at 100 kPa? (Given: The vapor pressure of hexane at 322.8 K is 53.32 kPa.) (5%)

(a) Determine the amount and composition (in percentage) of each phase in a Cu-40% Ni alloy at 1300 °C and 1250 °C. (5%)

(b) Determine the degree of freedom of a Cu-40% Ni alloy at 1300 °C and 1250°C. (5%)

(a) Derive the second-order equation of \( \mathrm{A} + \mathrm{B} \rightarrow \mathrm{Z} \). The initial concentrations of A and B are both a0. (5%)

(b) Derive the second-order equation of \( \mathrm{A} + \mathrm{B} \rightarrow \mathrm{Z} \). The initial concentrations of A and B are a0 and b0, respectively. (10%)

(a) What order is the reaction? (Explain why) (5%)

(b) What is the value of the rate constant at \( 100^{\circ}\mathrm{C} \) (5%)

(a) Derive the half-life of a first-order reaction is $t_{1/2} = \frac{\ln 2}{k}$. (5%)

(b) The half-life of $^{60}\mathrm{Co}$ is $1.9 \times 10^3$ days. What is the rate constant for the decay process? (5%)