QUESTION $1$

$($PO$1,$ CO$1,$ C$2)$

Consider a system consisting of $1$ kg of $\backslash (\backslash$mathrm$\{$H$\}\_\{2\}\backslash$mathrm$\{$O$\}\backslash )$ undergoes the processes as given below:

Process $\backslash (1\backslash$rightarrow $2\backslash )$ : isobaric expansion of saturated liquid to saturated vapour

Process $\backslash (2\backslash$rightarrow $3\backslash )$ : isochoric cooling to $\backslash (80^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$

Process $\backslash (3\backslash$rightarrow $4\backslash )$ : isothermal compression

Process $\backslash (4\backslash$rightarrow $1\backslash )$ : isochoric heating back to $400$ kPa

a$)$ Sketch the cycle, showing all four processes on a P$-$v diagram with respect to saturation lines. Include the isotherms and label the states, $\backslash (\backslash$mathrm$\{$P$\},\backslash$mathrm$\{$v$\}\backslash )$ and T values on the diagram.

b$)$ Calculate the heat transfer $($in kJ $)$ for each process above

$(20$ marks$)$