Question Three

$[20$ Marks$]$

A Double acting piston$-$cylinder device has a volume of $0\mathrm{.}05m^3$ on each side of the pist

There are two identical valves on each side of the cylinder that open to deliver a unit mast

compressed gas at $($your Fourth, Fifth and Sixth Digits of your SIN$)$ Degrees Celcius and

pressure of $250$ bar each time they open. A linear spring that has a spring constant of

$k\frac{N}{m}$ touches the piston rowards the end of the stroke to cushion the piston against impac

the cylinder end walls on both sides of the double acting cylinder. When the fixed unit mas

compressed gas is released inti the cylinder, it casuses the the piston to move from left to

or viceversa and the piston compresses the spring by $30$ mm until the volume on the expan

side of the the cylinder tripples. If the cross$-$sectional areas of the piston on the left face is

$0\mathrm{.}3m^2$ and $A2=0\mathrm{.}25m^2,$ determine $($a$)$ the final pressure inside the cylinder at the end o

expansion from left to right and from right to left.

$($b$)$ the total work done by the gas, from left to right and from right to left

$($c$)$ the fraction of this work done against the spring to compress it in one direction.

$($d$)$ If one full cycle involves movement from left to right and then from right to left and

connecting rod attached to the piston is connected to a crank shaft that revolves at $3100$

determine the power of the engine under these conditions

Note: state clearly all valld assumptions.

MOVEMENT