QUESTION $1[$TOTAL $30$ MARKS$]$

$\backslash (0\mathrm{.}03\backslash$mathrm$\{$~m$\}^\{3\}\backslash )$ Nitrogen gas $($molar mass $\backslash (\backslash$mathbf$\{28$ ~ k g $/$ k m o l $)\}\backslash )$ is contained in a cylinder piston arrangement, it is initially at $1\mathrm{.}05$ bar and $\backslash (15^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ The gas is compressed to $4\mathrm{.}2$ bar

Take for the Nitrogen gas: $\backslash ($ C$\_\{\backslash$mathbb$\{$R$\}\}=1\mathrm{.}039\backslash$mathrm$\{$~kJ$\}/\backslash$mathrm$\{$kg$\}.\backslash$mathrm$\{$K$\},\backslash$mathrm$\{$y$\}=1\mathrm{.}4\backslash )$

Assuming Nitrogen gas is a perfect gas

a$)$ Calculate

L$.$ the specific gas constant for Nitrogen gas, R

ii$.$ the specific heat capacity at constant volume, Cy

$[1\mathrm{.}5$ marks$]$

iii. the mass of the Nitrogen gas

$[1\mathrm{.}0$ marks$]$

$[2\mathrm{.}0$ marks$]$

b$)$ If the compression is reversible isothermal process

Calculate

i$.$ the final volume

ii$.$ the final temperature

iii. the work transter, in kJ

$[1\mathrm{.}5$ marks$]$

iv$.$ the heat transfor, in k$.$J

$[1\mathrm{.}5$ marks$]$

$[1\mathrm{.}5$ marks$]$

$[1\mathrm{.}5$ marks$]$

v$.$ the change in internal energy, in k$.$J

$[1\mathrm{.}5$ marks$]$

c$)$ If the compression is reversible adiabatic process

Galculate

i$.$ the final volume

ii$.$ the final temperature

iii. the work transfer, in k$.$J

iv$.$ the heat transfer, in kJ

v$.$ the change in internal energy, in kJ

$[1\mathrm{.}5$ marks$]$

$[1\mathrm{.}5$ marks$]$

$[1\mathrm{.}5$ marks$]$

$[15$ marks$]$

$[1\mathrm{.}5$ marks$]$

d$)$ If the compression is reversible polytropic process, according to $\backslash (\backslash$mathrm$\{$PV$\}^\{1\mathrm{.}32\}=\backslash )$ constant

Calculate

i$.$ the tinal volume

ii$.$ the final temperature

iii. the work transfer, in kJ

iv$.$ the heat transfer, in k$.$J

$[1\mathrm{.}5$ marks$]$

$[1\mathrm{.}5$ marks$]$

$[15$ marks$]$

$[1\mathrm{.}5$ marks$]$

v$.$ the change in internal energy, in k$.$J

$[15$ marks$]$

e$)$ Plot Pressure $-$ volume $(\backslash (\backslash$mathbf$\{$P$\}\backslash )-$ v$)$ diagram

$[3\mathrm{.}0$ marks$]$