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• Notes

* Vander waals :
$\left(P+\frac{9}{V^{2}}\right)(V-b)=R T$

where $a = \frac{27 R^{2} T_{cr}^{2}}{64 \ P_{c r}}, \quad b=\frac{R T_{cr}}{8 \ P_{c r}}$

*  Beattie - Bridgeman :
$P=\frac{R_{v} T}{\overline{J}^{2}}\left(1-\frac{c}{\overline{v} T^{3}}\right)(\overline{v}+B)-\frac{A}{\overline{v}^{2}}$

where $A=A_{0}\left(1-\frac{9}{\overline{v}}\right) \quad, \quad B=B_{0}\left(1-\frac{b}{\overline{v}}\right)$

$* A_{0}, a, B_{0}, b \text { and } C \longrightarrow Table \ 3-4$

$P=1.6 \mathrm{MPa} \longrightarrow 1600 \mathrm{KPa}$

$V=0.01343 \quad m^{3} / k g$

(a) ideal gas      $p v=R T \longrightarrow T=\frac{P{v}}{R}$

$∴ T=\frac{1600 * 0.01343}{0.08149}=263.688 k$

(b) Vander Waals :
$\left(P+\frac{9}{V^{2}}\right)(v-b)=RT$

$a=\frac{27 R^{2} T_{c r}^{2}}{64 \ P_{c r}}=\frac{27*(0.08149)^{2} (374.2)^{2}}{64*4059}=0.0966$

$b=\frac{R T_{c r}}{8 P_{c r}}=\frac{0.08149 * 374.2}{8 * 4059}=9.39*10^{-4}$

$∴ T=327347 \mathrm{k}$

(c) Tables :
$[A-12] @ P=1600 \mathrm{kPa}$

$v>v g \rightarrow \text { superheated }$

$∴ A-13 \quad @ P=1.6 \mathrm{MPa}$

$\longrightarrow T=70 \mathrm{c}^{\circ}$

$273+70=343k$