Question $2-$ Thermodynamics

$[$Total $25$ Marks$]$

a$)$ Steam at temperature of $190C$ and vapour mixture fraction of $0\mathrm{.}87$ enters a compressor with a mass flow rate of $400k\frac{g}{s}.$ Steam is compressed to a pressure of $1\mathrm{.}8$ MPa and temperature of $600C.$ Assume that the compressor is adiabatic. $($Hint: Use steam tables, not ideal gas law$)$

i$.$ Find the pressure at the compressor inlet.

$[2$ mark$]$

ii$.$ Calculate the specific volume and specific enthalpy at the compressor inlet and exit.

$[3$ marks$]$

iii. Sketch the process $1-2$ on a T$-$v diagram showing the constant pressure lines and the saturated mixture dome.

$[5$ marks$]$

iv$.$ Use the Steady Flow Energy Equation to calculate the work done on the compressor stating assumptions used to simplify the equation.

$[5$ marks$]$

$($b$)$ A Carnot heat pump is operating between temperatures of $5C$ and $25C.$ Calculate the coefficient of performance $($COP$)$ of the refrigerator.

$[10$ marks$]$