Air is compressed from an initial state of $1$ bar and $298\mathrm{.}15K$ to a final state of $3$ bar and $298\mathrm{.}15K$ by three different mechanically reversible processes in a closed system:

$($a$)$ Heating at constant volume followed by cooling at constant pressure.

$($b$)$ Isothermal compression.

$($c$)$ Adiabatic compression followed by cooling at constant volume.

These processes are shown in the figure. We assume air to be in its ideal$-$gas state, and assume constant heat capacities, $C_V^{ig}=20\mathrm{.}785$ and $C_P^{ig}=29\mathrm{.}100J*mo{l}^{-1}*K^{-1}.$ Calculate the work required, heat transferred, and the changes in internal energy and enthalpy of the air for each process.

Air is compressed from an initial state of $1$ bar and $298\mathrm{.}15K$ to a final state of $3$ bar and $298\mathrm{.}15K$ by three different mechanically reversible processes in a closed system: $($a$)$ Heating at constant volume followed by cooling at constant pressure. $($b$)$ Isothermal compression. $($c$)$ Adiabatic compression followed by cooling at constant volume. These processes are shown in the figure. We assume air to be in its ideal$-$gas state, and assume constant heat capacities, cig$=20\mathrm{.}785$ and cio $=29\mathrm{.}100J.$mol$-1-K-1.$ Calculate the work required, heat transferred, and the changes in internal energy and enthalpy of the air for each process. $6$ P bar $220525101520$ Vi$8$ x $103$ m$3$