Problem $3$: Consider a rigid container $($fixed volume$)$ filled with $7$ kg air. Assume that you can

treat the air as an ideal gas. The two specific heat values $($constant pressure and constant volume

specific heat$)$ for air are: $c_p=1\mathrm{.}00k\frac{J}{k}g-K,$ and $c_v=0\mathrm{.}71k\frac{J}{k}g-K.$ Assume that the specific heat

is constant as a function of temperature. The initial pressure is $100$ kPa $,$ and the initial

temperature is $25C.$ The final pressure is $200$ kPa $.$ For your analyses, use $R=8\mathrm{.}3145\frac{J}{m}ol-K,$

and use a molar mass of $28\mathrm{.}97\frac{g}{m}ol$ for air. Find:

$($i$)$ The initial volume, in $m^3,$ rounded to the nearest $2$ decimal places

$($ii$)$ The final temperature, in $C,$ rounded to the nearest $2$ decimal places

$($iii$)$ The final volume, in $m^3,$ rounded to the nearest $2$ decimal places

$($iv$)$ The change in internal energy across the process, in J$,$ rounded to the nearest whole

number

$($v$)$ The work done by the gas during this process, in J$,$ rounded to the nearest whole

number

$($vi$)$ The heat transferred to the gas during this process, in J$,$ rounded to the nearest whole

number

$($vii$)$ Draw the process on a P$-$V diagram $($use this for your schematic$)$

Known:

Find:

Schematic and Given Data:

Assumptions:

Analysis: