Solution:
A process consists of two steps: (\uppercase\expandafter{\romannumeral 1}) one mole of gas ($CO_2$ : stem $= 4 : 1$ by mole) at $T = 560\ K$ and $P = 4\ bar$ is heated at constant volume to $T = 840\ K$, and \uppercase\expandafter{\romannumeral 2} this gas is then cooled at constant pressure until its temperature reaches $560\ K$. If this two–step process is replaced by a singe isothermal expansion of the gas from $560\ K$ and $4\ bar$ to the final pressure $P$. Please answer the following questions:
\begin{parts}
\part [5] What is the value of $P$ which the work of the two process (two–step process and single–process) is the same?
\part [8] Heat, work, $\Delta U$, and $\Delta H$ for each process.
\end{parts}
Assume (a) gas is an ideal gas; (b) heat capacity of linear gaseous $C_{pm} = 7 R / 2$ and heat capacity of nonlinear gaseous $C_{pm} = 4R$; and (c) all the process are reversible.
