You want to describe the real behavior of acetylene, which is to be loaded into a tank truck with $65$ m$^3.$ The virial equation in Berlin form is available to you:

z$=$p$*$v$/($Ra$*$T$)=1+$B$\text{'}($T$)*$p $////$ B$\text{'}($T$)=$B$($T$)/($Ra$*$T$)$ and B$($T$)=$lim $\backslash$rho goes $0($Z$/\backslash$rho $)$T

In addition, the vapor pressure of acetylene in the temperature range under consideration can be described using the Antoine equation:

log$10($x$)=$ A $-$ B $/($T $+$ C$)$ ; A$=4,66141$ B$=909,079$ C$=7\mathrm{.}947$

Consider the loading process approximately as a reversible isothermal compression with an initial pressure p$=1$ bar. The specific gas constant of acetylene is R $=320$ J$/($kg K$)$

a$)$ Calculate the vapor pressure of acetylene at T$1=30\backslash$deg C$.$

b$)$ Calculate B$($T$1).$ To do this, use the following van der Waals $($vdW$)$ parameters of acetylene avdW$=668$Pa m$^6$kg$^2$ and bvdW$=2\mathrm{.}0110^3$m$^3$kg$^1.$

Hint: Make an expression for zvdW$.$ Then use the given definition of B$($T$).$ p $=($ Ra$*$T $/($v$-$ bvdW$))-$ avdw $/$ v$^2$

C $)$ Calculate the maximum mass of gaseous acetylene that can be loaded into the tanker$.$

D$)$ Calculate the specific entropy change of acetylene after loading using the virial equation. Assume the total differential of the entropy and use the function B$($T$)$ calculated in b$).$

s$2$s$1=...$ J$/($kgK$)$

E$)$ Calculate the specific enthalpy change of acetylene after loading using the virial equation. Start from the total differential of the enthalpy and use the function B$($T$)$ calculated in b$).$

h$2$h$1=...$ kJ$/$kg

F$)$ f$)$ Calculate the specific amount of heat transferred after loading using the virial equation.

q$12=...$ kJ$/$kg