A mass of $50kg$ is placed on a $10c{m}^2$ area weightless piston $($cf$.$ Figure $7).$ The ambient is a vacuum, i$.$e$.,$ the pressure is zero in it $($The initial gas pressure is $100$ bar, and the initial volume is $10c{m}^2.$ The cylinder height is $10cm.$ A pin, constraining the piston in place is suddenly released. Consider the gases in the piston$-$cylinder assembly to constitute a system A$.$ If the process in system $A$ is internally reversible and isothermal, determine the work output of the gas. Let system B be such that it includes the piston, weight, and ambient, but excludes the gases. What is the velocity of the piston when its position is at the cylinder rim? Assume. system $B$ to be adiabatic.

Air at $1$ bar and $298\mathrm{.}15K(25C)$ is compressed to $5$ bar and $298\mathrm{.}15K$ by two different mechanically reversible processes:

$($a$)$ Cooling at constant pressure followed by heating at constant volume.

$($b$)$ Heating at constant volume followed by cooling at constant pressure:

Calculate the heat and work requirements and $U$ and $H$ of the air for each path. The foliowing heat capacities for air may be assumed independent of temperature: $C_V=20\mathrm{.}78$ and $C_p=29\mathrm{.}10Jmo{l}^{-1}{K}^{-1}$

ssume aiso for air that PVIT is a constant, regardless of the changes it undergoes. At $298,15$ and $1$ bar, the molar volume of air is $0\mathrm{.}02479m^{3}mo{l}^{-1}.$