An ideal gas is one for which PV$/$T is a constant regardless of thechanges it undergoes. Such a gas has a volume of $0\mathrm{.}02271$ m$^3/$molat $0\backslash$deg C and $1$ bar. In the following problem, air may be considered anideal gas with constant heat capacities, CP $=(7/2)$R and CV $=(5/2)$R$,$where R $=8\mathrm{.}314$ J$/$ mol K $.$ The initial conditions of the air are $1$ barand $25\backslash$deg C$.$ It is compressed to $5$ bar and $25\backslash$deg C by two differentmechanically reversible processes. Calculate the heat and workrequirements and U and H of the air for each path:$($a$)$ Cooling at constant pressure followed by heating at constantvolume.$($b$)$ Heating at constant volume followed by cooling at constantpressure.