Q2 Identify the following quantities by stating their definitions and their positions in the P-T (Pressure-Temperature) diagram provided: a. Critical Point b. Triple Point And calculate the degrees of freedom for the critical point and the triple point
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(III) $(a)$ From the van der Waals equation of state, show that the critical temperature and pressure are given by $$T_{\mathrm{cr}}=\frac{8 a}{27 b R}, \quad P_{\mathrm{cr}}=\frac{a}{27 b^{2}}.$$ [Hint: Use the fact that the $P$ versus $V$ curve has an inflection point at the critical point so that the first and second derivatives are zero.] (b) Determine $a$ and $b$ for $\mathrm{CO}_{2}$ from the measured values of $T_{\mathrm{cr}}=304 \mathrm{K}$ and $P_{\mathrm{cr}}=72.8 \mathrm{atm} .$
Define critical temperature and critical pressure.
(a) What is the significance of the triple point in a phase diagram? (b) Could you measure the triple point of water by measuring the temperature in a vessel in which water vapor, liquid water, and ice are in equilibrium under $101.32 \mathrm{kPa}$ of air? Explain.
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