Problems#$3$

A $25-$kg piston is being held in rest above a gas in a long vertical cylinder. Now the piston

is released from rest and accelerates up in the cylinder, reaching the end $5\mathrm{.}0$ m higher at a

velocity of $25\frac{m}{s}.$ The gas pressure drops during the process, so the average pressure is $600$

kPa with an outside atmosphere at $100$ kPa $.$ Neglect the change in gas kinetic and potential

energy. Assume, the temperature of the piston remains constant all the time. Find the needed

change in the gas volume, in $m^3.$

Problems#$4$

A gas undergoes a thermodynamic cycle in three processes in a series in a piston$-$

cylinder assembly.

Process $1($state $1$ to state $2)$: Constant pressure, $p=\frac{1\mathrm{.}4}{b}ar,V_1=0\mathrm{.}028m3,W_{1,2}=$

$10\mathrm{.}5$ kJ $.$

Process $2($state $2$ to state $3)$: Compression with $pV=$ constant, $U_2=U_3.$

Process $3($state $3$ to state $1)$: Constant volume, $(U_1-U_3)=-26\mathrm{.}4kJ.$

Assume, changes in kinetic and potential energies are negligible.

$($a$)$ Sketch the cycle on a $p-V$ diagram.

$($b$)$ Determine the net work for the cycle $(W_{1,2}+W_{2,3}+W_{3,1}),$ in kJ $.$

$($c$)$ Determine the heat transfer for process $1,$ process $2,$ and process $3,$ in kJ$.$