AHMAD ABDOULAZIZ

Q$1.(8$ points$)$ A gas mixture of $45$ mass $\%$ nitrogen, $10$ mass $\%$ oxygen, and the balance is Propane, is kept in a vessel at $-113C$ and a pressure of $140$ bar. Using the Lee$/$Kesler correlation estimate $V$ and $S^R$ for the gas mixture.

Q$2.(4$ Points$)$ For ideal liquids, show that $C_p=C_v$

Q$3.(6$ Points$)$ For a given compound at $25C$ and $1$atm,

$C_p=138k\frac{J}{\text{k}\text{m}\text{o}\text{l}\text{.}K},V=0\mathrm{.}090\frac{m^3}{k}$mol,$(\frac{\text{d}\text{e}\text{l}\text{V}}{\text{d}\text{e}\text{l}\text{T}}{)}_p=9\mathrm{.}0{10}^{-8}\frac{m^3}{K},(\frac{\text{d}\text{e}\text{l}\text{V}}{\text{d}\text{e}\text{l}\text{P}}{)}_r=9\mathrm{.}0{10}^{-9}\frac{m^3}{a}tm,$

Calculate $(\frac{\text{d}\text{e}\text{l}\text{H}}{\text{d}\text{e}\text{l}\text{P}}{)}_{TT}$

Q$4.(12$ points$)$ Show that

$(C_P-C_V)\frac{dT}{T}=VdP+\frac{}{}dV$

$(\frac{\text{d}\text{e}\text{l}\text{C}\text{V}}{\text{d}\text{e}\text{l}\text{P}})T=T(\frac{\text{d}\text{e}\text{l}\text{V}}{\text{d}\text{e}\text{l}\text{P}})T(\frac{de{l}^{2}P}{del{T}^2})V$