Question $1$

Consider isentropic$-$ and real compression processes in a single$-$stage reciprocating compressor

with a clearance volume.

Q$\mathrm{.}1\mathrm{.}1$ Show the isentropic$-$ and real compression processes on a $T-$s diagram.

Q$\mathrm{.}1\mathrm{.}2$ Starting with the first law of Thermodynamics, fully derive an equation for the

outlet$-$to$-$inlet temperature ratio for compression in a reciprocating compressor

if the pressure ratio, isentropic compression efficiency and $-$value of the

working fluid are known.

Q$\mathrm{.}1\mathrm{.}3$ A single stage reciprocating air compressor with a clearance volume has a

pressure ratio of $5$:$1$ and an isentropic compression efficiency of $79\%.$ Calculate

the outlet air temperature if the inlet air temperature is $60C.$ The $-$value of air

is $1,4.$

Q$\mathrm{.}1\mathrm{.}4$ For the compressor specifications given in Q$\mathrm{.}1\mathrm{.}3$ above, calculate the equivalent

polytropic compression efficiency.