Problem $2$: Consider a piston$-$cylinder assembly filled with $34\mathrm{.}5$ mol of a gas $($which has a

critical pressure of $3770$ kPa and critical temperature of $133$ K $)$ with an initial temperature of

$26\mathrm{.}85C,$ and an initial pressure of $101\mathrm{.}3$ kPa $($state $1).$ The gas is then compressed to a final

volume of $0\mathrm{.}4m^3($state $2).$ For parts $($i$)$ and $($ii$),$ use the ideal gas model. Use $R=8\mathrm{.}3145\frac{J}{m}ol$

K$.$ Find:

$($i$)$ The final temperature, in $C,$ rounded to the nearest two decimal places, if

compression occurs at constant pressure $($call this state $2$ A $)$

$($ii$)$ The final pressure, in kPa $,$ rounded to the nearest one decimal place, if compression

occurs at constant temperature $($call this State $2$B$)$

$($iii$)$ The reduced pressure for state $1,$ rounded to the nearest two decimal places

$($iv$)$ The reduced temperature for state $1,$ rounded to the nearest two decimal places

$($v$)$ Based on the reduced pressure and temperature you found in parts $($iii$)$ and $($iv$),$ label

state $1$ on the compressibility factor chart $($provided in the Schematic and Given Data

section$)$; an approximate point is fine

$($vi$)$ Based on the compressibility factor from the chart, is the ideal gas model valid?

$($vii$)$ Draw the process from part $($i$)$ and the process from part $($ii$)$ on a P$-$V diagram $($add

this to the Schematic and Given Data section$).$

Known:

Find:

Schematic and Given Data:

Assumptions:

Analysis: