Exercise $2\mathrm{.}5($additional exercise$)$

A piston cylinder system is filled with nitrogen $($state $1$:$V_1=1m^3,p_1=\frac{1}{b}ar,t_1=20C).$ Nitrogen

can be considered an ideal gas.

a$)$ Determine the mass $m$ and the amount of substance $n$ of nitrogen in the system.

b$)$ Determine the density ${}_1$ and the specific volume $v_1$ of nitrogen.

c$)$ Determine the pressure $p_2$ of nitrogen at constant volume when the temperature after heating is

$t_2=100C.$

d$)$ Determine the pressure $p_3$ of nitrogen that results from a compression at constant temperature from

state $1$ to half of the volume.

e$)$ Determine the density ${}_4$ of nitrogen that results from heating up from state $1$ to $t_4=100C$ at

constant pressure.

f$)$ Schematically illustrate the four state points in a $p,v-$diagram including all relevant isotherms.

$R_m=8\mathrm{.}31446\frac{J}{\text{m}\text{o}\text{l}*K},M_{N2}=28\mathrm{.}013\frac{g}{m}ol$