QUESTION $2$

$($PO$2,$ CO$2,$ C$4)$

a$)$ Calculate the work $($ kJ $)$ involved during the process described in Question $1($b$).$ State whether the work is done by or on the system.

b$)$ A $500-$L rigid tank consists of $1\mathrm{.}5$ kg of air. Initially, the air is at $220$ kPa $.$ A $110-$V electrical resistor that draws $8$ A of current is attached to the system, hence supplies some amount of energy to the air every time it is switched ON$.$ If the tank is well insulated and assuming air is an ideal gas with a constant specific heat, and both changes in kinetic and potential energies are negligible,

i$.$ Write the first law equation of thermodynamics for the closed system described above.

ii$.$ Determine how long $($in minutes$)$ the resistor should be switched ON for the system to reach a final pressure of $750$ kPa $.$

Given:

$R_{\text{a}\text{i}\text{r}}=0\mathrm{.}287k\frac{J}{k}g.K$

$c_{p,\text{a}\text{i}\text{r}}=1\mathrm{.}005k\frac{J}{k}g.K$

$c_{v,\text{a}\text{i}\text{r}}=0\mathrm{.}718k\frac{J}{k}g.K$

$(12$ marks$)$